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Properties

Label 3640.2.r
Level $3640$
Weight $2$
Character orbit 3640.r
Rep. character $\chi_{3640}(2549,\cdot)$
Character field $\Q$
Dimension $432$
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.r (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 680 432 248
Cusp forms 664 432 232
Eisenstein series 16 0 16

Trace form

\( 432 q - 8 q^{4} + 8 q^{6} + 432 q^{9} + O(q^{10}) \) \( 432 q - 8 q^{4} + 8 q^{6} + 432 q^{9} + 8 q^{10} - 24 q^{16} + 28 q^{20} + 64 q^{24} + 32 q^{31} - 24 q^{34} + 8 q^{36} + 32 q^{39} - 20 q^{40} - 80 q^{44} - 432 q^{49} - 8 q^{50} + 32 q^{54} + 32 q^{55} - 24 q^{56} + 68 q^{60} - 8 q^{64} + 104 q^{66} - 112 q^{71} + 80 q^{74} - 24 q^{76} + 32 q^{79} - 128 q^{80} + 432 q^{81} - 16 q^{86} + 20 q^{90} + 88 q^{94} - 64 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)