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Properties

Label 324.8.b
Level $324$
Weight $8$
Character orbit 324.b
Rep. character $\chi_{324}(323,\cdot)$
Character field $\Q$
Dimension $164$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 324.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(324, [\chi])\).

Total New Old
Modular forms 390 172 218
Cusp forms 366 164 202
Eisenstein series 24 8 16

Trace form

\( 164 q + 2 q^{4} + O(q^{10}) \) \( 164 q + 2 q^{4} - 260 q^{10} + 4 q^{13} - 31666 q^{16} + 105414 q^{22} - 2312496 q^{25} + 86592 q^{28} - 390698 q^{34} - 248324 q^{37} + 643252 q^{40} + 801876 q^{46} - 16470856 q^{49} + 2178040 q^{52} + 289744 q^{58} + 532576 q^{61} + 7669442 q^{64} + 9967836 q^{70} - 3202772 q^{73} - 130734 q^{76} + 21896038 q^{82} + 10664972 q^{85} + 17825598 q^{88} - 13620432 q^{94} - 10592720 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(324, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(324, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(324, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)