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Properties

Label 3640.2.fu
Level $3640$
Weight $2$
Character orbit 3640.fu
Rep. character $\chi_{3640}(3221,\cdot)$
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.fu (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

\( 672 q + 36 q^{6} + 336 q^{9} + O(q^{10}) \) \( 672 q + 36 q^{6} + 336 q^{9} - 24 q^{12} - 48 q^{23} - 48 q^{24} + 672 q^{25} + 4 q^{26} + 16 q^{30} + 60 q^{32} - 28 q^{36} + 40 q^{38} + 96 q^{39} + 56 q^{48} + 336 q^{49} + 116 q^{52} + 108 q^{54} + 96 q^{58} - 16 q^{62} + 24 q^{64} + 24 q^{66} + 76 q^{68} + 264 q^{72} - 108 q^{74} + 216 q^{76} - 136 q^{78} - 48 q^{80} - 336 q^{81} + 20 q^{82} + 84 q^{84} + 48 q^{87} - 44 q^{88} + 8 q^{92} + 56 q^{94} + 64 q^{95} + O(q^{100}) \)

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

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