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Properties

Label 3640.2.nx
Level $3640$
Weight $2$
Character orbit 3640.nx
Rep. character $\chi_{3640}(997,\cdot)$
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.nx (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

\( 2656 q - 4 q^{2} - 4 q^{7} - 16 q^{8} + O(q^{10}) \) \( 2656 q - 4 q^{2} - 4 q^{7} - 16 q^{8} - 6 q^{10} - 12 q^{12} - 8 q^{15} - 24 q^{16} + 10 q^{18} - 24 q^{20} + 4 q^{22} - 8 q^{23} - 8 q^{25} - 12 q^{26} + 30 q^{28} + 12 q^{30} - 48 q^{31} - 4 q^{32} - 12 q^{33} + 24 q^{36} - 12 q^{38} - 72 q^{40} - 74 q^{42} - 8 q^{46} - 24 q^{47} + 36 q^{48} + 14 q^{50} - 30 q^{52} - 60 q^{55} - 20 q^{56} - 8 q^{57} - 30 q^{58} + 28 q^{60} - 12 q^{62} - 36 q^{63} - 4 q^{65} + 48 q^{66} + 10 q^{70} - 80 q^{71} - 38 q^{72} - 24 q^{73} - 96 q^{76} + 114 q^{78} - 114 q^{80} + 1208 q^{81} + 90 q^{82} + 12 q^{86} - 38 q^{88} + 72 q^{92} - 88 q^{95} - 24 q^{96} - 6 q^{98} + O(q^{100}) \)

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.