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Properties

Label 3640.2.g
Level $3640$
Weight $2$
Character orbit 3640.g
Rep. character $\chi_{3640}(1821,\cdot)$
Character field $\Q$
Dimension $288$
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.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
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 680 288 392
Cusp forms 664 288 376
Eisenstein series 16 0 16

Trace form

\( 288 q - 4 q^{2} - 4 q^{4} - 8 q^{6} - 8 q^{7} - 4 q^{8} - 288 q^{9} + O(q^{10}) \) \( 288 q - 4 q^{2} - 4 q^{4} - 8 q^{6} - 8 q^{7} - 4 q^{8} - 288 q^{9} + 8 q^{10} + 4 q^{14} + 16 q^{15} + 28 q^{16} + 20 q^{18} - 16 q^{22} + 16 q^{23} + 8 q^{24} - 288 q^{25} - 20 q^{28} - 32 q^{31} - 4 q^{32} + 32 q^{33} - 24 q^{34} + 12 q^{36} - 32 q^{40} - 32 q^{41} + 288 q^{49} + 4 q^{50} + 32 q^{54} + 4 q^{56} - 32 q^{57} + 16 q^{58} - 8 q^{60} + 24 q^{62} + 40 q^{63} - 52 q^{64} + 24 q^{68} - 16 q^{71} + 20 q^{72} - 24 q^{74} + 24 q^{76} - 48 q^{79} + 320 q^{81} - 24 q^{82} + 16 q^{88} - 32 q^{90} + 32 q^{92} - 8 q^{96} - 4 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)