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Properties

Label 624.4.bm
Level $624$
Weight $4$
Character orbit 624.bm
Rep. character $\chi_{624}(317,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $664$
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.bm (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 624 \)
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 680 680 0
Cusp forms 664 664 0
Eisenstein series 16 16 0

Trace form

\( 664 q - 4 q^{3} - 16 q^{6} + O(q^{10}) \) \( 664 q - 4 q^{3} - 16 q^{6} + 8 q^{10} - 4 q^{13} - 4 q^{15} - 8 q^{16} + 168 q^{18} - 8 q^{19} + 104 q^{21} - 224 q^{22} + 312 q^{24} + 15800 q^{25} - 4 q^{27} - 224 q^{28} - 500 q^{30} - 8 q^{31} - 4 q^{33} - 216 q^{34} - 284 q^{36} - 8 q^{37} - 1568 q^{40} - 344 q^{42} - 432 q^{43} - 504 q^{45} - 1112 q^{46} - 24 q^{48} - 64 q^{52} - 336 q^{54} - 108 q^{57} - 8 q^{58} - 464 q^{60} - 8 q^{61} + 1368 q^{63} + 1872 q^{64} + 1096 q^{66} - 8 q^{67} - 2360 q^{70} - 4236 q^{72} - 500 q^{75} + 1960 q^{76} + 3828 q^{78} - 16 q^{79} - 8 q^{81} + 1656 q^{82} - 1104 q^{84} - 1008 q^{85} + 4096 q^{88} - 468 q^{90} + 3168 q^{91} + 4160 q^{93} - 4688 q^{94} - 3584 q^{96} - 8 q^{97} + O(q^{100}) \)

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.