Sp(4) 4 | VerlindeDB

\(\operatorname{Sp}(4)_{4}\): \( C_{2} \) at level \(4\)

Fusion Ring

\[ \begin{array}{lllllllllllllll} \htmlTitle{1\otimes 1}{1} & & & & & & & & & & & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1} & & & & & & & & & & & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{4} & \htmlTitle{3\otimes 3}{1 \oplus 5 \oplus 9} & & & & & & & & & & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{3} & \htmlTitle{4\otimes 3}{6 \oplus 10 \oplus 2} & \htmlTitle{4\otimes 4}{1 \oplus 5 \oplus 9} & & & & & & & & & & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{6} & \htmlTitle{5\otimes 3}{3 \oplus 13} & \htmlTitle{5\otimes 4}{14 \oplus 4} & \htmlTitle{5\otimes 5}{1 \oplus 9 \oplus 8} & & & & & & & & & & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{5} & \htmlTitle{6\otimes 3}{14 \oplus 4} & \htmlTitle{6\otimes 4}{3 \oplus 13} & \htmlTitle{6\otimes 5}{8 \oplus 10 \oplus 2} & \htmlTitle{6\otimes 6}{1 \oplus 9 \oplus 8} & & & & & & & & & \\ \htmlTitle{7\otimes 1}{7} & \htmlTitle{7\otimes 2}{7} & \htmlTitle{7\otimes 3}{11 \oplus 12} & \htmlTitle{7\otimes 4}{11 \oplus 12} & \htmlTitle{7\otimes 5}{15 \oplus 7} & \htmlTitle{7\otimes 6}{15 \oplus 7} & \htmlTitle{7\otimes 7}{1 \oplus 5 \oplus 8 \oplus 6 \oplus 2} & & & & & & & & \\ \htmlTitle{8\otimes 1}{8} & \htmlTitle{8\otimes 2}{8} & \htmlTitle{8\otimes 3}{13 \oplus 14} & \htmlTitle{8\otimes 4}{13 \oplus 14} & \htmlTitle{8\otimes 5}{5 \oplus 15 \oplus 6} & \htmlTitle{8\otimes 6}{5 \oplus 15 \oplus 6} & \htmlTitle{8\otimes 7}{8 \oplus 15 \oplus 7} & \htmlTitle{8\otimes 8}{1 \oplus 9 \oplus 8 \oplus 7 \oplus 10 \oplus 2} & & & & & & & \\ \htmlTitle{9\otimes 1}{9} & \htmlTitle{9\otimes 2}{10} & \htmlTitle{9\otimes 3}{3 \oplus 13 \oplus 11} & \htmlTitle{9\otimes 4}{14 \oplus 12 \oplus 4} & \htmlTitle{9\otimes 5}{5 \oplus 9 \oplus 15} & \htmlTitle{9\otimes 6}{15 \oplus 6 \oplus 10} & \htmlTitle{9\otimes 7}{9 \oplus 15 \oplus 10} & \htmlTitle{9\otimes 8}{9 \oplus 8 \oplus 15 \oplus 10} & \htmlTitle{9\otimes 9}{1 \oplus 5 \oplus 9 \oplus 8 \oplus 15 \oplus 7} & & & & & & \\ \htmlTitle{10\otimes 1}{10} & \htmlTitle{10\otimes 2}{9} & \htmlTitle{10\otimes 3}{14 \oplus 12 \oplus 4} & \htmlTitle{10\otimes 4}{3 \oplus 13 \oplus 11} & \htmlTitle{10\otimes 5}{15 \oplus 6 \oplus 10} & \htmlTitle{10\otimes 6}{5 \oplus 9 \oplus 15} & \htmlTitle{10\otimes 7}{9 \oplus 15 \oplus 10} & \htmlTitle{10\otimes 8}{9 \oplus 8 \oplus 15 \oplus 10} & \htmlTitle{10\otimes 9}{8 \oplus 15 \oplus 6 \oplus 7 \oplus 10 \oplus 2} & \htmlTitle{10\otimes 10}{1 \oplus 5 \oplus 9 \oplus 8 \oplus 15 \oplus 7} & & & & & \\ \htmlTitle{11\otimes 1}{11} & \htmlTitle{11\otimes 2}{12} & \htmlTitle{11\otimes 3}{9 \oplus 15 \oplus 7} & \htmlTitle{11\otimes 4}{15 \oplus 7 \oplus 10} & \htmlTitle{11\otimes 5}{13 \oplus 11 \oplus 12} & \htmlTitle{11\otimes 6}{11 \oplus 14 \oplus 12} & \htmlTitle{11\otimes 7}{3 \oplus 13 \oplus 14 \oplus 4} & \htmlTitle{11\otimes 8}{13 \oplus 11 \oplus 14 \oplus 12} & \htmlTitle{11\otimes 9}{3 \oplus 13 \oplus 11 \oplus 14 \oplus 12} & \htmlTitle{11\otimes 10}{13 \oplus 11 \oplus 14 \oplus 12 \oplus 4} & \htmlTitle{11\otimes 11}{1 \oplus 5 \oplus 9 \oplus 8 \oplus 15 \oplus 6 \oplus 10} & & & & \\ \htmlTitle{12\otimes 1}{12} & \htmlTitle{12\otimes 2}{11} & \htmlTitle{12\otimes 3}{15 \oplus 7 \oplus 10} & \htmlTitle{12\otimes 4}{9 \oplus 15 \oplus 7} & \htmlTitle{12\otimes 5}{11 \oplus 14 \oplus 12} & \htmlTitle{12\otimes 6}{13 \oplus 11 \oplus 12} & \htmlTitle{12\otimes 7}{3 \oplus 13 \oplus 14 \oplus 4} & \htmlTitle{12\otimes 8}{13 \oplus 11 \oplus 14 \oplus 12} & \htmlTitle{12\otimes 9}{13 \oplus 11 \oplus 14 \oplus 12 \oplus 4} & \htmlTitle{12\otimes 10}{3 \oplus 13 \oplus 11 \oplus 14 \oplus 12} & \htmlTitle{12\otimes 11}{5 \oplus 9 \oplus 8 \oplus 15 \oplus 6 \oplus 10 \oplus 2} & \htmlTitle{12\otimes 12}{1 \oplus 5 \oplus 9 \oplus 8 \oplus 15 \oplus 6 \oplus 10} & & & \\ \htmlTitle{13\otimes 1}{13} & \htmlTitle{13\otimes 2}{14} & \htmlTitle{13\otimes 3}{5 \oplus 9 \oplus 8 \oplus 15} & \htmlTitle{13\otimes 4}{8 \oplus 15 \oplus 6 \oplus 10} & \htmlTitle{13\otimes 5}{3 \oplus 13 \oplus 11 \oplus 14} & \htmlTitle{13\otimes 6}{13 \oplus 14 \oplus 12 \oplus 4} & \htmlTitle{13\otimes 7}{13 \oplus 11 \oplus 14 \oplus 12} & \htmlTitle{13\otimes 8}{3 \oplus 13 \oplus 11 \oplus 14 \oplus 12 \oplus 4} & \htmlTitle{13\otimes 9}{3 \oplus 2\cdot13 \oplus 11 \oplus 14 \oplus 12} & \htmlTitle{13\otimes 10}{13 \oplus 11 \oplus 2\cdot14 \oplus 12 \oplus 4} & \htmlTitle{13\otimes 11}{5 \oplus 9 \oplus 8 \oplus 2\cdot15 \oplus 7 \oplus 10} & \htmlTitle{13\otimes 12}{9 \oplus 8 \oplus 2\cdot15 \oplus 6 \oplus 7 \oplus 10} & \htmlTitle{13\otimes 13}{1 \oplus 5 \oplus 2\cdot9 \oplus 8 \oplus 2\cdot15 \oplus 6 \oplus 7 \oplus 10} & & \\ \htmlTitle{14\otimes 1}{14} & \htmlTitle{14\otimes 2}{13} & \htmlTitle{14\otimes 3}{8 \oplus 15 \oplus 6 \oplus 10} & \htmlTitle{14\otimes 4}{5 \oplus 9 \oplus 8 \oplus 15} & \htmlTitle{14\otimes 5}{13 \oplus 14 \oplus 12 \oplus 4} & \htmlTitle{14\otimes 6}{3 \oplus 13 \oplus 11 \oplus 14} & \htmlTitle{14\otimes 7}{13 \oplus 11 \oplus 14 \oplus 12} & \htmlTitle{14\otimes 8}{3 \oplus 13 \oplus 11 \oplus 14 \oplus 12 \oplus 4} & \htmlTitle{14\otimes 9}{13 \oplus 11 \oplus 2\cdot14 \oplus 12 \oplus 4} & \htmlTitle{14\otimes 10}{3 \oplus 2\cdot13 \oplus 11 \oplus 14 \oplus 12} & \htmlTitle{14\otimes 11}{9 \oplus 8 \oplus 2\cdot15 \oplus 6 \oplus 7 \oplus 10} & \htmlTitle{14\otimes 12}{5 \oplus 9 \oplus 8 \oplus 2\cdot15 \oplus 7 \oplus 10} & \htmlTitle{14\otimes 13}{5 \oplus 9 \oplus 8 \oplus 2\cdot15 \oplus 6 \oplus 7 \oplus 2\cdot10 \oplus 2} & \htmlTitle{14\otimes 14}{1 \oplus 5 \oplus 2\cdot9 \oplus 8 \oplus 2\cdot15 \oplus 6 \oplus 7 \oplus 10} & \\ \htmlTitle{15\otimes 1}{15} & \htmlTitle{15\otimes 2}{15} & \htmlTitle{15\otimes 3}{13 \oplus 11 \oplus 14 \oplus 12} & \htmlTitle{15\otimes 4}{13 \oplus 11 \oplus 14 \oplus 12} & \htmlTitle{15\otimes 5}{9 \oplus 8 \oplus 15 \oplus 7 \oplus 10} & \htmlTitle{15\otimes 6}{9 \oplus 8 \oplus 15 \oplus 7 \oplus 10} & \htmlTitle{15\otimes 7}{5 \oplus 9 \oplus 8 \oplus 15 \oplus 6 \oplus 10} & \htmlTitle{15\otimes 8}{5 \oplus 9 \oplus 2\cdot15 \oplus 6 \oplus 7 \oplus 10} & \htmlTitle{15\otimes 9}{5 \oplus 9 \oplus 8 \oplus 2\cdot15 \oplus 6 \oplus 7 \oplus 10} & \htmlTitle{15\otimes 10}{5 \oplus 9 \oplus 8 \oplus 2\cdot15 \oplus 6 \oplus 7 \oplus 10} & \htmlTitle{15\otimes 11}{3 \oplus 2\cdot13 \oplus 11 \oplus 2\cdot14 \oplus 12 \oplus 4} & \htmlTitle{15\otimes 12}{3 \oplus 2\cdot13 \oplus 11 \oplus 2\cdot14 \oplus 12 \oplus 4} & \htmlTitle{15\otimes 13}{3 \oplus 2\cdot13 \oplus 2\cdot11 \oplus 2\cdot14 \oplus 2\cdot12 \oplus 4} & \htmlTitle{15\otimes 14}{3 \oplus 2\cdot13 \oplus 2\cdot11 \oplus 2\cdot14 \oplus 2\cdot12 \oplus 4} & \htmlTitle{15\otimes 15}{1 \oplus 5 \oplus 2\cdot9 \oplus 2\cdot8 \oplus 3\cdot15 \oplus 6 \oplus 7 \oplus 2\cdot10 \oplus 2} \\ \end{array} \]

Frobenius-Perron Dimensions

SimpleNumericSymbolic
\( 1\)\(1.000\)\( 1 \)
\( 2\)\(1.000\)\( 1 \)
\( 3\)\(3.049\)\( - 2 \cos{\left(\frac{3 \pi}{7} \right)} + 1 + 4 \cos{\left(\frac{2 \pi}{7} \right)} \)
\( 4\)\(3.049\)\( - 2 \cos{\left(\frac{3 \pi}{7} \right)} + 1 + 4 \cos{\left(\frac{2 \pi}{7} \right)} \)
\( 5\)\(3.247\)\( 2 \cos{\left(\frac{2 \pi}{7} \right)} + 2 \)
\( 6\)\(3.247\)\( 2 \cos{\left(\frac{2 \pi}{7} \right)} + 2 \)
\( 7\)\(3.604\)\( - 4 \cos{\left(\frac{3 \pi}{7} \right)} + 2 + 4 \cos{\left(\frac{2 \pi}{7} \right)} \)
\( 8\)\(4.494\)\( 2 + 4 \cos{\left(\frac{2 \pi}{7} \right)} \)
\( 9\)\(5.049\)\( - 2 \cos{\left(\frac{3 \pi}{7} \right)} + 4 \cos{\left(\frac{2 \pi}{7} \right)} + 3 \)
\( 10\)\(5.049\)\( - 2 \cos{\left(\frac{3 \pi}{7} \right)} + 4 \cos{\left(\frac{2 \pi}{7} \right)} + 3 \)
\( 11\)\(5.494\)\( 4 \cos{\left(\frac{2 \pi}{7} \right)} + 3 \)
\( 12\)\(5.494\)\( 4 \cos{\left(\frac{2 \pi}{7} \right)} + 3 \)
\( 13\)\(6.851\)\( - 4 \cos{\left(\frac{3 \pi}{7} \right)} + 6 \cos{\left(\frac{2 \pi}{7} \right)} + 4 \)
\( 14\)\(6.851\)\( - 4 \cos{\left(\frac{3 \pi}{7} \right)} + 6 \cos{\left(\frac{2 \pi}{7} \right)} + 4 \)
\( 15\)\(8.098\)\( - 4 \cos{\left(\frac{3 \pi}{7} \right)} + 4 + 8 \cos{\left(\frac{2 \pi}{7} \right)} \)
\( D^2\)345.655\(- 112 \cos{\left(\frac{3 \pi}{7} \right)} + 280 \cos{\left(\frac{2 \pi}{7} \right)} + 196\)

Modular Data

Twist Factors

\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{0} & \htmlTitle{\theta_{3}}{\frac{5}{14}} & \htmlTitle{\theta_{4}}{\frac{19}{14}} & \htmlTitle{\theta_{5}}{\frac{4}{7}} & \htmlTitle{\theta_{6}}{\frac{4}{7}} & \htmlTitle{\theta_{7}}{\frac{2}{7}} & \htmlTitle{\theta_{8}}{\frac{10}{7}} & \htmlTitle{\theta_{9}}{\frac{6}{7}} & \htmlTitle{\theta_{10}}{\frac{6}{7}} & \htmlTitle{\theta_{11}}{\frac{3}{2}} & \htmlTitle{\theta_{12}}{\frac{1}{2}} & \htmlTitle{\theta_{13}}{\frac{15}{14}} & \htmlTitle{\theta_{14}}{\frac{1}{14}} & \htmlTitle{\theta_{15}}{\frac{12}{7}} \end{pmatrix} \]

S Matrix

\[ \left(\begin{array}{lllllllllllllll} \htmlTitle{S_{1; 1}}{1} & & & & & & & & & & & & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{1} & & & & & & & & & & & & & \\ \htmlTitle{S_{3; 1}}{-2 \zeta_{56}^{20} + \zeta_{56}^{16} - \zeta_{56}^{12} + 2 \zeta_{56}^{8} + 1} & \htmlTitle{S_{3; 2}}{2 \zeta_{56}^{20} - \zeta_{56}^{16} + \zeta_{56}^{12} - 2 \zeta_{56}^{8} - 1} & \htmlTitle{S_{3; 3}}{-3 \zeta_{56}^{20} + 2 \zeta_{56}^{16} - 2 \zeta_{56}^{12} + 3 \zeta_{56}^{8} + 4} & & & & & & & & & & & & \\ \htmlTitle{S_{4; 1}}{-2 \zeta_{56}^{20} + \zeta_{56}^{16} - \zeta_{56}^{12} + 2 \zeta_{56}^{8} + 1} & \htmlTitle{S_{4; 2}}{2 \zeta_{56}^{20} - \zeta_{56}^{16} + \zeta_{56}^{12} - 2 \zeta_{56}^{8} - 1} & \htmlTitle{S_{4; 3}}{3 \zeta_{56}^{20} - 2 \zeta_{56}^{16} + 2 \zeta_{56}^{12} - 3 \zeta_{56}^{8} - 4} & \htmlTitle{S_{4; 4}}{-3 \zeta_{56}^{20} + 2 \zeta_{56}^{16} - 2 \zeta_{56}^{12} + 3 \zeta_{56}^{8} + 4} & & & & & & & & & & & \\ \htmlTitle{S_{5; 1}}{-\zeta_{56}^{20} + \zeta_{56}^{8} + 2} & \htmlTitle{S_{5; 2}}{-\zeta_{56}^{20} + \zeta_{56}^{8} + 2} & \htmlTitle{S_{5; 3}}{-2 \zeta_{56}^{20} + 2 \zeta_{56}^{8} + 3} & \htmlTitle{S_{5; 4}}{-2 \zeta_{56}^{20} + 2 \zeta_{56}^{8} + 3} & \htmlTitle{S_{5; 5}}{-2 \zeta_{56}^{20} + \zeta_{56}^{16} - \zeta_{56}^{12} + 2 \zeta_{56}^{8} + 3} & & & & & & & & & & \\ \htmlTitle{S_{6; 1}}{-\zeta_{56}^{20} + \zeta_{56}^{8} + 2} & \htmlTitle{S_{6; 2}}{-\zeta_{56}^{20} + \zeta_{56}^{8} + 2} & \htmlTitle{S_{6; 3}}{2 \zeta_{56}^{20} - 2 \zeta_{56}^{8} - 3} & \htmlTitle{S_{6; 4}}{2 \zeta_{56}^{20} - 2 \zeta_{56}^{8} - 3} & \htmlTitle{S_{6; 5}}{-2 \zeta_{56}^{20} + \zeta_{56}^{16} - \zeta_{56}^{12} + 2 \zeta_{56}^{8} + 3} & \htmlTitle{S_{6; 6}}{-2 \zeta_{56}^{20} + \zeta_{56}^{16} - \zeta_{56}^{12} + 2 \zeta_{56}^{8} + 3} & & & & & & & & & \\ \htmlTitle{S_{7; 1}}{-2 \zeta_{56}^{20} + 2 \zeta_{56}^{16} - 2 \zeta_{56}^{12} + 2 \zeta_{56}^{8} + 2} & \htmlTitle{S_{7; 2}}{-2 \zeta_{56}^{20} + 2 \zeta_{56}^{16} - 2 \zeta_{56}^{12} + 2 \zeta_{56}^{8} + 2} & \htmlTitle{S_{7; 3}}{0} & \htmlTitle{S_{7; 4}}{0} & \htmlTitle{S_{7; 5}}{4 \zeta_{56}^{20} - 2 \zeta_{56}^{16} + 2 \zeta_{56}^{12} - 4 \zeta_{56}^{8} - 4} & \htmlTitle{S_{7; 6}}{4 \zeta_{56}^{20} - 2 \zeta_{56}^{16} + 2 \zeta_{56}^{12} - 4 \zeta_{56}^{8} - 4} & \htmlTitle{S_{7; 7}}{2} & & & & & & & & \\ \htmlTitle{S_{8; 1}}{-2 \zeta_{56}^{20} + 2 \zeta_{56}^{8} + 2} & \htmlTitle{S_{8; 2}}{-2 \zeta_{56}^{20} + 2 \zeta_{56}^{8} + 2} & \htmlTitle{S_{8; 3}}{0} & \htmlTitle{S_{8; 4}}{0} & \htmlTitle{S_{8; 5}}{-2 \zeta_{56}^{20} + 2 \zeta_{56}^{16} - 2 \zeta_{56}^{12} + 2 \zeta_{56}^{8} + 2} & \htmlTitle{S_{8; 6}}{-2 \zeta_{56}^{20} + 2 \zeta_{56}^{16} - 2 \zeta_{56}^{12} + 2 \zeta_{56}^{8} + 2} & \htmlTitle{S_{8; 7}}{-4 \zeta_{56}^{20} + 2 \zeta_{56}^{16} - 2 \zeta_{56}^{12} + 4 \zeta_{56}^{8} + 6} & \htmlTitle{S_{8; 8}}{-2 \zeta_{56}^{20} + 2 \zeta_{56}^{8} + 4} & & & & & & & \\ \htmlTitle{S_{9; 1}}{-2 \zeta_{56}^{20} + \zeta_{56}^{16} - \zeta_{56}^{12} + 2 \zeta_{56}^{8} + 3} & \htmlTitle{S_{9; 2}}{-2 \zeta_{56}^{20} + \zeta_{56}^{16} - \zeta_{56}^{12} + 2 \zeta_{56}^{8} + 3} & \htmlTitle{S_{9; 3}}{-3 \zeta_{56}^{20} + 2 \zeta_{56}^{16} - 2 \zeta_{56}^{12} + 3 \zeta_{56}^{8} + 4} & \htmlTitle{S_{9; 4}}{-3 \zeta_{56}^{20} + 2 \zeta_{56}^{16} - 2 \zeta_{56}^{12} + 3 \zeta_{56}^{8} + 4} & \htmlTitle{S_{9; 5}}{1} & \htmlTitle{S_{9; 6}}{1} & \htmlTitle{S_{9; 7}}{-2 \zeta_{56}^{20} + 2 \zeta_{56}^{8} + 2} & \htmlTitle{S_{9; 8}}{4 \zeta_{56}^{20} - 2 \zeta_{56}^{16} + 2 \zeta_{56}^{12} - 4 \zeta_{56}^{8} - 4} & \htmlTitle{S_{9; 9}}{-\zeta_{56}^{20} + \zeta_{56}^{8} + 2} & & & & & & \\ \htmlTitle{S_{10; 1}}{-2 \zeta_{56}^{20} + \zeta_{56}^{16} - \zeta_{56}^{12} + 2 \zeta_{56}^{8} + 3} & \htmlTitle{S_{10; 2}}{-2 \zeta_{56}^{20} + \zeta_{56}^{16} - \zeta_{56}^{12} + 2 \zeta_{56}^{8} + 3} & \htmlTitle{S_{10; 3}}{3 \zeta_{56}^{20} - 2 \zeta_{56}^{16} + 2 \zeta_{56}^{12} - 3 \zeta_{56}^{8} - 4} & \htmlTitle{S_{10; 4}}{3 \zeta_{56}^{20} - 2 \zeta_{56}^{16} + 2 \zeta_{56}^{12} - 3 \zeta_{56}^{8} - 4} & \htmlTitle{S_{10; 5}}{1} & \htmlTitle{S_{10; 6}}{1} & \htmlTitle{S_{10; 7}}{-2 \zeta_{56}^{20} + 2 \zeta_{56}^{8} + 2} & \htmlTitle{S_{10; 8}}{4 \zeta_{56}^{20} - 2 \zeta_{56}^{16} + 2 \zeta_{56}^{12} - 4 \zeta_{56}^{8} - 4} & \htmlTitle{S_{10; 9}}{-\zeta_{56}^{20} + \zeta_{56}^{8} + 2} & \htmlTitle{S_{10; 10}}{-\zeta_{56}^{20} + \zeta_{56}^{8} + 2} & & & & & \\ \htmlTitle{S_{11; 1}}{-2 \zeta_{56}^{20} + 2 \zeta_{56}^{8} + 3} & \htmlTitle{S_{11; 2}}{2 \zeta_{56}^{20} - 2 \zeta_{56}^{8} - 3} & \htmlTitle{S_{11; 3}}{-2 \zeta_{56}^{20} + \zeta_{56}^{16} - \zeta_{56}^{12} + 2 \zeta_{56}^{8} + 1} & \htmlTitle{S_{11; 4}}{2 \zeta_{56}^{20} - \zeta_{56}^{16} + \zeta_{56}^{12} - 2 \zeta_{56}^{8} - 1} & \htmlTitle{S_{11; 5}}{3 \zeta_{56}^{20} - 2 \zeta_{56}^{16} + 2 \zeta_{56}^{12} - 3 \zeta_{56}^{8} - 4} & \htmlTitle{S_{11; 6}}{-3 \zeta_{56}^{20} + 2 \zeta_{56}^{16} - 2 \zeta_{56}^{12} + 3 \zeta_{56}^{8} + 4} & \htmlTitle{S_{11; 7}}{0} & \htmlTitle{S_{11; 8}}{0} & \htmlTitle{S_{11; 9}}{-2 \zeta_{56}^{20} + \zeta_{56}^{16} - \zeta_{56}^{12} + 2 \zeta_{56}^{8} + 1} & \htmlTitle{S_{11; 10}}{2 \zeta_{56}^{20} - \zeta_{56}^{16} + \zeta_{56}^{12} - 2 \zeta_{56}^{8} - 1} & \htmlTitle{S_{11; 11}}{-2 \zeta_{56}^{20} + 2 \zeta_{56}^{8} + 3} & & & & \\ \htmlTitle{S_{12; 1}}{-2 \zeta_{56}^{20} + 2 \zeta_{56}^{8} + 3} & \htmlTitle{S_{12; 2}}{2 \zeta_{56}^{20} - 2 \zeta_{56}^{8} - 3} & \htmlTitle{S_{12; 3}}{2 \zeta_{56}^{20} - \zeta_{56}^{16} + \zeta_{56}^{12} - 2 \zeta_{56}^{8} - 1} & \htmlTitle{S_{12; 4}}{-2 \zeta_{56}^{20} + \zeta_{56}^{16} - \zeta_{56}^{12} + 2 \zeta_{56}^{8} + 1} & \htmlTitle{S_{12; 5}}{3 \zeta_{56}^{20} - 2 \zeta_{56}^{16} + 2 \zeta_{56}^{12} - 3 \zeta_{56}^{8} - 4} & \htmlTitle{S_{12; 6}}{-3 \zeta_{56}^{20} + 2 \zeta_{56}^{16} - 2 \zeta_{56}^{12} + 3 \zeta_{56}^{8} + 4} & \htmlTitle{S_{12; 7}}{0} & \htmlTitle{S_{12; 8}}{0} & \htmlTitle{S_{12; 9}}{-2 \zeta_{56}^{20} + \zeta_{56}^{16} - \zeta_{56}^{12} + 2 \zeta_{56}^{8} + 1} & \htmlTitle{S_{12; 10}}{2 \zeta_{56}^{20} - \zeta_{56}^{16} + \zeta_{56}^{12} - 2 \zeta_{56}^{8} - 1} & \htmlTitle{S_{12; 11}}{2 \zeta_{56}^{20} - 2 \zeta_{56}^{8} - 3} & \htmlTitle{S_{12; 12}}{-2 \zeta_{56}^{20} + 2 \zeta_{56}^{8} + 3} & & & \\ \htmlTitle{S_{13; 1}}{-3 \zeta_{56}^{20} + 2 \zeta_{56}^{16} - 2 \zeta_{56}^{12} + 3 \zeta_{56}^{8} + 4} & \htmlTitle{S_{13; 2}}{3 \zeta_{56}^{20} - 2 \zeta_{56}^{16} + 2 \zeta_{56}^{12} - 3 \zeta_{56}^{8} - 4} & \htmlTitle{S_{13; 3}}{-2 \zeta_{56}^{20} + 2 \zeta_{56}^{8} + 3} & \htmlTitle{S_{13; 4}}{2 \zeta_{56}^{20} - 2 \zeta_{56}^{8} - 3} & \htmlTitle{S_{13; 5}}{-2 \zeta_{56}^{20} + \zeta_{56}^{16} - \zeta_{56}^{12} + 2 \zeta_{56}^{8} + 1} & \htmlTitle{S_{13; 6}}{2 \zeta_{56}^{20} - \zeta_{56}^{16} + \zeta_{56}^{12} - 2 \zeta_{56}^{8} - 1} & \htmlTitle{S_{13; 7}}{0} & \htmlTitle{S_{13; 8}}{0} & \htmlTitle{S_{13; 9}}{2 \zeta_{56}^{20} - 2 \zeta_{56}^{8} - 3} & \htmlTitle{S_{13; 10}}{-2 \zeta_{56}^{20} + 2 \zeta_{56}^{8} + 3} & \htmlTitle{S_{13; 11}}{3 \zeta_{56}^{20} - 2 \zeta_{56}^{16} + 2 \zeta_{56}^{12} - 3 \zeta_{56}^{8} - 4} & \htmlTitle{S_{13; 12}}{-3 \zeta_{56}^{20} + 2 \zeta_{56}^{16} - 2 \zeta_{56}^{12} + 3 \zeta_{56}^{8} + 4} & \htmlTitle{S_{13; 13}}{2 \zeta_{56}^{20} - \zeta_{56}^{16} + \zeta_{56}^{12} - 2 \zeta_{56}^{8} - 1} & & \\ \htmlTitle{S_{14; 1}}{-3 \zeta_{56}^{20} + 2 \zeta_{56}^{16} - 2 \zeta_{56}^{12} + 3 \zeta_{56}^{8} + 4} & \htmlTitle{S_{14; 2}}{3 \zeta_{56}^{20} - 2 \zeta_{56}^{16} + 2 \zeta_{56}^{12} - 3 \zeta_{56}^{8} - 4} & \htmlTitle{S_{14; 3}}{2 \zeta_{56}^{20} - 2 \zeta_{56}^{8} - 3} & \htmlTitle{S_{14; 4}}{-2 \zeta_{56}^{20} + 2 \zeta_{56}^{8} + 3} & \htmlTitle{S_{14; 5}}{-2 \zeta_{56}^{20} + \zeta_{56}^{16} - \zeta_{56}^{12} + 2 \zeta_{56}^{8} + 1} & \htmlTitle{S_{14; 6}}{2 \zeta_{56}^{20} - \zeta_{56}^{16} + \zeta_{56}^{12} - 2 \zeta_{56}^{8} - 1} & \htmlTitle{S_{14; 7}}{0} & \htmlTitle{S_{14; 8}}{0} & \htmlTitle{S_{14; 9}}{2 \zeta_{56}^{20} - 2 \zeta_{56}^{8} - 3} & \htmlTitle{S_{14; 10}}{-2 \zeta_{56}^{20} + 2 \zeta_{56}^{8} + 3} & \htmlTitle{S_{14; 11}}{-3 \zeta_{56}^{20} + 2 \zeta_{56}^{16} - 2 \zeta_{56}^{12} + 3 \zeta_{56}^{8} + 4} & \htmlTitle{S_{14; 12}}{3 \zeta_{56}^{20} - 2 \zeta_{56}^{16} + 2 \zeta_{56}^{12} - 3 \zeta_{56}^{8} - 4} & \htmlTitle{S_{14; 13}}{-2 \zeta_{56}^{20} + \zeta_{56}^{16} - \zeta_{56}^{12} + 2 \zeta_{56}^{8} + 1} & \htmlTitle{S_{14; 14}}{2 \zeta_{56}^{20} - \zeta_{56}^{16} + \zeta_{56}^{12} - 2 \zeta_{56}^{8} - 1} & \\ \htmlTitle{S_{15; 1}}{-4 \zeta_{56}^{20} + 2 \zeta_{56}^{16} - 2 \zeta_{56}^{12} + 4 \zeta_{56}^{8} + 4} & \htmlTitle{S_{15; 2}}{-4 \zeta_{56}^{20} + 2 \zeta_{56}^{16} - 2 \zeta_{56}^{12} + 4 \zeta_{56}^{8} + 4} & \htmlTitle{S_{15; 3}}{0} & \htmlTitle{S_{15; 4}}{0} & \htmlTitle{S_{15; 5}}{2 \zeta_{56}^{20} - 2 \zeta_{56}^{8} - 2} & \htmlTitle{S_{15; 6}}{2 \zeta_{56}^{20} - 2 \zeta_{56}^{8} - 2} & \htmlTitle{S_{15; 7}}{2 \zeta_{56}^{20} - 2 \zeta_{56}^{8} - 4} & \htmlTitle{S_{15; 8}}{-2} & \htmlTitle{S_{15; 9}}{2 \zeta_{56}^{20} - 2 \zeta_{56}^{16} + 2 \zeta_{56}^{12} - 2 \zeta_{56}^{8} - 2} & \htmlTitle{S_{15; 10}}{2 \zeta_{56}^{20} - 2 \zeta_{56}^{16} + 2 \zeta_{56}^{12} - 2 \zeta_{56}^{8} - 2} & \htmlTitle{S_{15; 11}}{0} & \htmlTitle{S_{15; 12}}{0} & \htmlTitle{S_{15; 13}}{0} & \htmlTitle{S_{15; 14}}{0} & \htmlTitle{S_{15; 15}}{-4 \zeta_{56}^{20} + 2 \zeta_{56}^{16} - 2 \zeta_{56}^{12} + 4 \zeta_{56}^{8} + 6}\end{array}\right) \]

Central Charge

\[c = \frac{40}{7} \]