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Properties

Label 624.4.bh
Level $624$
Weight $4$
Character orbit 624.bh
Rep. character $\chi_{624}(131,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $576$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 624.bh (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(624, [\chi])\).

Total New Old
Modular forms 680 576 104
Cusp forms 664 576 88
Eisenstein series 16 0 16

Trace form

\( 576 q + O(q^{10}) \) \( 576 q - 120 q^{10} + 216 q^{16} - 140 q^{18} - 48 q^{19} - 216 q^{22} - 500 q^{24} + 628 q^{30} - 984 q^{34} + 440 q^{36} + 288 q^{40} - 1920 q^{42} + 432 q^{43} + 168 q^{46} + 20 q^{48} + 28224 q^{49} + 1400 q^{51} + 936 q^{52} - 3188 q^{54} - 288 q^{55} - 1536 q^{58} - 1348 q^{60} + 1824 q^{61} + 3024 q^{64} + 3560 q^{66} + 3264 q^{67} + 6624 q^{70} + 1380 q^{72} - 3304 q^{75} - 312 q^{76} - 1668 q^{84} - 480 q^{85} - 2576 q^{87} - 11304 q^{88} - 1860 q^{90} - 6624 q^{94} - 6460 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(624, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(624, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(624, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)