Properties

Label 3640.2.gw
Level $3640$
Weight $2$
Character orbit 3640.gw
Rep. character $\chi_{3640}(2661,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $672$
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.gw (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 104 \)
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 672 688
Cusp forms 1328 672 656
Eisenstein series 32 0 32

Trace form

\( 672 q - 12 q^{6} - 24 q^{8} + 336 q^{9} + O(q^{10}) \) \( 672 q - 12 q^{6} - 24 q^{8} + 336 q^{9} + 24 q^{12} + 48 q^{18} - 48 q^{23} - 16 q^{24} - 672 q^{25} + 4 q^{26} + 16 q^{30} - 20 q^{32} + 40 q^{34} + 4 q^{36} - 40 q^{38} - 96 q^{39} + 48 q^{44} + 64 q^{46} + 8 q^{48} - 336 q^{49} - 12 q^{52} + 4 q^{54} + 104 q^{58} + 32 q^{62} + 120 q^{64} - 232 q^{66} - 28 q^{68} + 72 q^{72} + 4 q^{74} + 40 q^{76} + 80 q^{78} + 48 q^{80} - 336 q^{81} - 100 q^{82} + 28 q^{84} - 176 q^{86} + 48 q^{87} - 124 q^{88} - 104 q^{92} - 88 q^{94} + 64 q^{95} + 56 q^{96} + O(q^{100}) \)

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

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