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Properties

Label 624.4.v
Level $624$
Weight $4$
Character orbit 624.v
Rep. character $\chi_{624}(155,\cdot)$
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.v (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

\( 664 q - 4 q^{3} - 8 q^{4} + O(q^{10}) \) \( 664 q - 4 q^{3} - 8 q^{4} - 8 q^{10} + 152 q^{12} - 4 q^{13} - 8 q^{16} + 712 q^{22} + 260 q^{27} + 28 q^{30} - 768 q^{36} - 604 q^{39} + 1552 q^{40} + 1200 q^{42} + 424 q^{43} - 2468 q^{48} - 30200 q^{49} + 104 q^{51} - 1264 q^{52} + 272 q^{55} - 8 q^{61} - 1088 q^{64} - 4432 q^{66} + 104 q^{69} + 604 q^{75} - 3456 q^{78} - 8 q^{81} - 3952 q^{82} - 8 q^{87} - 6440 q^{88} - 5876 q^{90} + 3168 q^{91} + 4736 q^{94} + O(q^{100}) \)

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.