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Properties

Label 3640.2.ej
Level $3640$
Weight $2$
Character orbit 3640.ej
Rep. character $\chi_{3640}(309,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $1008$
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.ej (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 520 \)
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 1008 352
Cusp forms 1328 1008 320
Eisenstein series 32 0 32

Trace form

\( 1008 q - 504 q^{9} + O(q^{10}) \) \( 1008 q - 504 q^{9} - 8 q^{10} - 16 q^{16} - 48 q^{24} - 8 q^{25} + 24 q^{26} + 8 q^{30} + 16 q^{36} + 4 q^{40} - 24 q^{41} - 504 q^{49} - 30 q^{50} + 156 q^{54} + 32 q^{55} - 48 q^{64} - 28 q^{65} - 32 q^{66} - 16 q^{74} - 60 q^{76} - 160 q^{79} - 504 q^{81} - 40 q^{90} + 48 q^{94} + 40 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)