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Properties

Label 3640.2.ma
Level $3640$
Weight $2$
Character orbit 3640.ma
Rep. character $\chi_{3640}(37,\cdot)$
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.ma (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

\( 2656 q - 16 q^{6} - 4 q^{7} + O(q^{10}) \) \( 2656 q - 16 q^{6} - 4 q^{7} - 14 q^{10} + 36 q^{12} + 24 q^{14} - 40 q^{15} - 8 q^{16} - 2 q^{18} - 4 q^{22} - 12 q^{24} - 4 q^{26} - 34 q^{28} + 2 q^{30} - 8 q^{31} - 12 q^{33} - 8 q^{34} - 24 q^{36} - 8 q^{38} - 24 q^{40} - 32 q^{41} - 2 q^{42} - 8 q^{44} - 4 q^{46} - 8 q^{47} + 8 q^{48} + 32 q^{50} + 82 q^{52} - 32 q^{54} - 8 q^{55} - 12 q^{56} - 30 q^{58} + 8 q^{60} - 52 q^{62} - 12 q^{63} + 16 q^{65} - 8 q^{66} - 68 q^{68} + 46 q^{70} - 64 q^{71} + 10 q^{72} - 74 q^{78} - 56 q^{80} + 1208 q^{81} + 2 q^{82} + 88 q^{84} + 40 q^{86} + 40 q^{87} + 82 q^{88} - 48 q^{90} - 32 q^{92} + 48 q^{94} - 76 q^{96} - 24 q^{97} - 6 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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