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Properties

Label 3640.2.ls
Level $3640$
Weight $2$
Character orbit 3640.ls
Rep. character $\chi_{3640}(787,\cdot)$
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.ls (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

\( 2656 q - 12 q^{3} + O(q^{10}) \) \( 2656 q - 12 q^{3} - 6 q^{10} - 8 q^{11} - 24 q^{14} - 8 q^{16} - 24 q^{17} - 2 q^{18} + 24 q^{20} - 4 q^{22} + 36 q^{24} - 12 q^{26} + 30 q^{28} - 14 q^{30} - 12 q^{33} + 24 q^{34} - 4 q^{35} - 24 q^{36} + 48 q^{40} - 2 q^{42} - 24 q^{43} - 8 q^{44} - 4 q^{46} - 36 q^{48} + 32 q^{50} + 18 q^{52} + 24 q^{54} - 12 q^{56} + 18 q^{58} + 96 q^{59} + 24 q^{60} - 12 q^{62} - 24 q^{65} - 24 q^{66} - 12 q^{67} - 30 q^{70} + 10 q^{72} - 24 q^{75} - 48 q^{76} - 82 q^{78} - 60 q^{80} + 1208 q^{81} + 18 q^{82} + 88 q^{84} + 24 q^{86} - 94 q^{88} - 108 q^{90} + 16 q^{91} - 12 q^{96} - 6 q^{98} - 24 q^{99} + O(q^{100}) \)

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.