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Properties

Label 3640.2.dg
Level $3640$
Weight $2$
Character orbit 3640.dg
Rep. character $\chi_{3640}(1101,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $896$
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.dg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 728 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3640, [\chi])\).

Total New Old
Modular forms 1360 896 464
Cusp forms 1328 896 432
Eisenstein series 32 0 32

Trace form

\( 896 q - 896 q^{9} + O(q^{10}) \) \( 896 q - 896 q^{9} - 8 q^{14} + 4 q^{16} - 4 q^{20} - 12 q^{22} + 48 q^{24} + 448 q^{25} - 2 q^{26} - 14 q^{28} - 20 q^{32} + 64 q^{34} - 20 q^{36} + 64 q^{42} - 4 q^{44} - 10 q^{46} - 40 q^{48} + 32 q^{49} + 12 q^{52} + 32 q^{55} + 8 q^{56} - 64 q^{57} + 48 q^{64} + 20 q^{66} + 20 q^{68} - 8 q^{70} + 32 q^{71} + 112 q^{72} - 16 q^{73} + 28 q^{74} - 44 q^{78} + 896 q^{81} - 20 q^{82} - 18 q^{84} + 26 q^{86} + 96 q^{87} + 36 q^{90} + 60 q^{92} - 12 q^{94} - 72 q^{96} - 32 q^{97} + 38 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3640, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)