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Properties

Label 3640.2.ce
Level $3640$
Weight $2$
Character orbit 3640.ce
Rep. character $\chi_{3640}(57,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $252$
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.ce (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(i)\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 1376 252 1124
Cusp forms 1312 252 1060
Eisenstein series 64 0 64

Trace form

\( 252 q + 8 q^{5} + O(q^{10}) \) \( 252 q + 8 q^{5} - 16 q^{13} + 8 q^{15} - 12 q^{17} - 16 q^{23} - 20 q^{25} - 16 q^{31} + 48 q^{33} - 16 q^{39} - 20 q^{41} + 44 q^{45} - 252 q^{49} + 12 q^{53} + 96 q^{55} - 48 q^{57} - 16 q^{63} + 4 q^{65} - 96 q^{67} + 32 q^{69} + 24 q^{71} + 8 q^{73} - 220 q^{81} + 4 q^{85} + 20 q^{89} - 80 q^{97} + 24 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(455, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(910, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1820, [\chi])\)\(^{\oplus 2}\)