Properties

Label 3640.2.jp
Level $3640$
Weight $2$
Character orbit 3640.jp
Rep. character $\chi_{3640}(747,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2656$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3640.jp (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3640 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3640, [\chi])\).

Total New Old
Modular forms 2720 2720 0
Cusp forms 2656 2656 0
Eisenstein series 64 64 0

Trace form

\( 2656 q + 2 q^{2} - 16 q^{8} + O(q^{10}) \) \( 2656 q + 2 q^{2} - 16 q^{8} - 12 q^{10} - 8 q^{11} - 24 q^{14} + 4 q^{16} - 12 q^{17} + 42 q^{18} - 24 q^{20} - 4 q^{22} - 36 q^{24} - 12 q^{26} - 6 q^{28} - 16 q^{30} + 2 q^{32} + 24 q^{34} + 56 q^{35} - 24 q^{36} + 48 q^{40} - 68 q^{42} - 24 q^{43} - 16 q^{44} - 4 q^{46} + 36 q^{48} + 24 q^{50} + 48 q^{52} - 12 q^{56} - 56 q^{57} - 96 q^{59} + 58 q^{60} - 12 q^{62} + 16 q^{65} - 24 q^{66} - 8 q^{67} - 6 q^{68} - 26 q^{70} - 24 q^{73} - 12 q^{75} + 48 q^{76} - 122 q^{78} + 108 q^{80} - 2416 q^{81} - 12 q^{82} - 40 q^{84} - 84 q^{86} - 32 q^{88} + 108 q^{90} + 16 q^{91} - 12 q^{96} - 12 q^{98} + 24 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3640, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.