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Properties

Label 3640.2.id
Level $3640$
Weight $2$
Character orbit 3640.id
Rep. character $\chi_{3640}(739,\cdot)$
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.id (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

\( 2656 q - 12 q^{4} - 8 q^{6} - 2608 q^{9} + O(q^{10}) \) \( 2656 q - 12 q^{4} - 8 q^{6} - 2608 q^{9} - 8 q^{11} - 32 q^{14} + 4 q^{16} - 8 q^{19} - 16 q^{20} + 8 q^{24} - 4 q^{26} - 40 q^{34} - 4 q^{35} + 12 q^{36} - 24 q^{40} - 32 q^{41} - 44 q^{44} - 60 q^{46} - 24 q^{49} - 36 q^{50} + 144 q^{51} + 28 q^{54} + 96 q^{56} + 56 q^{59} - 4 q^{60} - 4 q^{65} - 20 q^{66} - 16 q^{70} + 4 q^{74} + 60 q^{75} - 20 q^{80} + 2432 q^{81} + 116 q^{84} + 52 q^{86} - 8 q^{89} - 48 q^{91} - 8 q^{94} + 156 q^{96} - 80 q^{99} + O(q^{100}) \)

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.