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Properties

Label 3640.2.ke
Level $3640$
Weight $2$
Character orbit 3640.ke
Rep. character $\chi_{3640}(627,\cdot)$
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.ke (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

\( 2656 q + 2 q^{2} - 8 q^{3} - 8 q^{6} - 16 q^{8} + O(q^{10}) \) \( 2656 q + 2 q^{2} - 8 q^{3} - 8 q^{6} - 16 q^{8} - 4 q^{10} - 16 q^{11} + 8 q^{12} - 4 q^{16} + 4 q^{17} + 10 q^{18} + 4 q^{20} - 12 q^{22} - 8 q^{25} - 20 q^{26} - 8 q^{27} + 14 q^{28} + 16 q^{30} + 2 q^{32} - 104 q^{33} - 4 q^{35} + 24 q^{36} + 4 q^{38} + 16 q^{40} - 16 q^{41} - 48 q^{42} - 8 q^{43} + 4 q^{46} - 16 q^{48} + 14 q^{50} - 16 q^{51} + 112 q^{52} + 12 q^{56} - 8 q^{57} - 36 q^{58} - 36 q^{60} + 28 q^{62} - 4 q^{65} + 16 q^{66} - 8 q^{67} - 30 q^{68} + 14 q^{70} + 76 q^{72} - 8 q^{73} + 4 q^{75} + 24 q^{76} + 10 q^{78} + 28 q^{80} - 2416 q^{81} - 68 q^{82} - 32 q^{83} + 44 q^{86} - 84 q^{88} - 28 q^{90} + 16 q^{91} + 40 q^{92} - 152 q^{96} - 8 q^{97} - 104 q^{98} + O(q^{100}) \)

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.