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Properties

Label 624.4.cz
Level $624$
Weight $4$
Character orbit 624.cz
Rep. character $\chi_{624}(115,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $672$
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.cz (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 208 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 1360 672 688
Cusp forms 1328 672 656
Eisenstein series 32 0 32

Trace form

\( 672 q + O(q^{10}) \) \( 672 q - 72 q^{10} + 416 q^{14} - 336 q^{16} + 220 q^{20} + 216 q^{22} + 180 q^{24} + 16800 q^{25} + 368 q^{26} + 796 q^{28} + 1440 q^{32} - 2184 q^{34} - 520 q^{38} + 1560 q^{40} - 432 q^{43} - 1432 q^{44} - 440 q^{46} - 344 q^{50} + 1608 q^{52} - 288 q^{55} + 1300 q^{56} - 2592 q^{58} + 1376 q^{59} + 2064 q^{60} + 768 q^{64} + 1032 q^{68} - 56 q^{70} - 448 q^{71} - 592 q^{73} + 7008 q^{74} + 1104 q^{75} - 7324 q^{76} - 72 q^{78} + 2044 q^{80} + 27216 q^{81} - 4648 q^{82} + 5360 q^{83} - 5312 q^{86} - 8220 q^{88} + 176 q^{89} + 5192 q^{91} - 1392 q^{92} + 7256 q^{94} - 2880 q^{96} + 18328 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(624, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)