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Properties

Label 462.8.c
Level $462$
Weight $8$
Character orbit 462.c
Rep. character $\chi_{462}(197,\cdot)$
Character field $\Q$
Dimension $168$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 462.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(462, [\chi])\).

Total New Old
Modular forms 680 168 512
Cusp forms 664 168 496
Eisenstein series 16 0 16

Trace form

\( 168 q + 104 q^{3} + 10752 q^{4} - 216 q^{9} + O(q^{10}) \) \( 168 q + 104 q^{3} + 10752 q^{4} - 216 q^{9} + 6656 q^{12} + 4088 q^{15} + 688128 q^{16} + 138112 q^{22} - 1975640 q^{25} + 519248 q^{27} + 1035192 q^{31} + 73080 q^{33} - 1225792 q^{34} - 13824 q^{36} - 103440 q^{37} - 2283936 q^{45} + 425984 q^{48} - 19765032 q^{49} - 91288 q^{55} + 1903232 q^{58} + 261632 q^{60} + 44040192 q^{64} - 4236032 q^{66} + 12557616 q^{67} + 4925744 q^{69} - 3973312 q^{70} + 12236080 q^{75} - 20666304 q^{78} + 2179232 q^{81} + 1451840 q^{82} + 8839168 q^{88} - 33899376 q^{91} - 20463384 q^{93} + 111947568 q^{97} + 59433752 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(462, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{8}^{\mathrm{old}}(462, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(462, [\chi]) \cong \)