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Properties

Label 624.4.da
Level $624$
Weight $4$
Character orbit 624.da
Rep. character $\chi_{624}(245,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1328$
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.da (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 624 \)
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 1360 0
Cusp forms 1328 1328 0
Eisenstein series 32 32 0

Trace form

\( 1328 q - 2 q^{3} - 12 q^{4} + 10 q^{6} + O(q^{10}) \) \( 1328 q - 2 q^{3} - 12 q^{4} + 10 q^{6} - 116 q^{10} - 8 q^{13} - 8 q^{15} - 4 q^{16} + 384 q^{18} - 4 q^{19} - 116 q^{21} + 212 q^{22} + 624 q^{24} + 31600 q^{25} - 8 q^{27} + 212 q^{28} - 256 q^{30} - 16 q^{31} - 8 q^{33} + 204 q^{34} + 2432 q^{36} - 4 q^{37} + 1544 q^{40} + 386 q^{42} + 420 q^{43} - 252 q^{45} + 1100 q^{46} + 18 q^{48} - 24 q^{49} + 52 q^{52} + 2592 q^{54} - 3000 q^{55} + 108 q^{57} - 4108 q^{58} - 292 q^{60} - 4 q^{61} - 1380 q^{63} - 1872 q^{64} + 2192 q^{66} - 4 q^{67} - 6 q^{69} + 2360 q^{70} + 4230 q^{72} - 418 q^{75} - 1972 q^{76} + 9396 q^{78} - 32 q^{79} - 4 q^{81} - 5088 q^{82} + 7620 q^{84} - 504 q^{85} + 2036 q^{88} - 1032 q^{90} - 3180 q^{91} - 4328 q^{93} - 2344 q^{94} + 3884 q^{96} - 16 q^{97} + O(q^{100}) \)

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.