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Properties

Label 3640.2.gk
Level $3640$
Weight $2$
Character orbit 3640.gk
Rep. character $\chi_{3640}(1661,\cdot)$
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.gk (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

\( 896 q + 448 q^{9} + O(q^{10}) \) \( 896 q + 448 q^{9} - 8 q^{14} + 8 q^{16} - 12 q^{20} + 12 q^{22} - 448 q^{25} + 6 q^{26} + 36 q^{28} + 20 q^{36} + 40 q^{38} - 32 q^{42} - 12 q^{44} - 40 q^{48} - 16 q^{49} + 24 q^{52} - 32 q^{55} - 22 q^{56} + 48 q^{64} + 20 q^{66} + 40 q^{68} - 48 q^{73} - 56 q^{74} + 44 q^{78} - 448 q^{81} - 10 q^{82} + 54 q^{84} - 54 q^{86} + 192 q^{87} - 36 q^{90} - 52 q^{92} - 30 q^{94} + 96 q^{97} - 30 q^{98} + O(q^{100}) \)

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

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