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Properties

Label 624.4.x
Level $624$
Weight $4$
Character orbit 624.x
Rep. character $\chi_{624}(157,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $288$
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.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
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 680 288 392
Cusp forms 664 288 376
Eisenstein series 16 0 16

Trace form

\( 288 q + 40 q^{4} - 168 q^{8} + O(q^{10}) \) \( 288 q + 40 q^{4} - 168 q^{8} - 144 q^{10} + 80 q^{11} + 24 q^{12} + 280 q^{14} - 240 q^{15} + 384 q^{16} + 72 q^{18} - 48 q^{19} - 688 q^{22} - 456 q^{24} - 800 q^{29} + 408 q^{30} + 1488 q^{31} + 408 q^{34} + 912 q^{35} - 216 q^{36} - 32 q^{37} - 2072 q^{38} - 288 q^{40} - 2048 q^{43} - 2064 q^{44} + 24 q^{46} + 1056 q^{48} - 14112 q^{49} - 4256 q^{50} - 1488 q^{51} + 936 q^{52} - 1504 q^{53} - 216 q^{54} - 2688 q^{56} - 3872 q^{58} + 1824 q^{61} + 1464 q^{62} + 1008 q^{63} + 112 q^{64} + 2736 q^{66} + 4512 q^{67} - 1936 q^{68} + 1056 q^{69} - 1656 q^{70} + 1224 q^{72} + 1680 q^{74} - 1104 q^{75} - 1968 q^{76} - 3808 q^{77} - 5664 q^{79} - 1424 q^{80} - 23328 q^{81} + 5840 q^{82} - 3600 q^{84} + 480 q^{85} - 5440 q^{86} + 1528 q^{88} - 648 q^{90} - 5744 q^{92} - 5032 q^{94} + 15456 q^{95} - 8264 q^{98} + 720 q^{99} + O(q^{100}) \)

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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

\( S_{4}^{\mathrm{old}}(624, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)