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Properties

Label 3640.2.lz
Level $3640$
Weight $2$
Character orbit 3640.lz
Rep. character $\chi_{3640}(1397,\cdot)$
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.lz (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

\( 2656 q - 4 q^{2} - 16 q^{6} - 12 q^{7} - 16 q^{8} + O(q^{10}) \) \( 2656 q - 4 q^{2} - 16 q^{6} - 12 q^{7} - 16 q^{8} + 2 q^{10} + 36 q^{12} - 24 q^{14} + 8 q^{15} - 8 q^{16} - 42 q^{18} - 4 q^{22} + 12 q^{24} - 4 q^{26} - 6 q^{28} - 14 q^{30} - 8 q^{31} - 4 q^{32} - 44 q^{33} + 8 q^{34} - 24 q^{36} + 8 q^{38} - 24 q^{40} - 32 q^{41} + 22 q^{42} + 8 q^{44} - 4 q^{46} + 8 q^{48} + 24 q^{50} + 2 q^{52} + 32 q^{54} - 8 q^{55} - 12 q^{56} - 56 q^{57} - 78 q^{58} - 68 q^{60} + 28 q^{62} - 84 q^{63} - 24 q^{65} - 8 q^{66} - 68 q^{68} + 118 q^{70} - 64 q^{71} - 54 q^{72} - 8 q^{73} - 34 q^{78} + 96 q^{80} + 1208 q^{81} - 14 q^{82} - 88 q^{84} + 40 q^{86} + 40 q^{87} + 50 q^{88} + 48 q^{90} - 32 q^{92} - 48 q^{94} - 76 q^{96} - 8 q^{97} + 114 q^{98} + O(q^{100}) \)

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.