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Properties

Label 3640.2.ge
Level $3640$
Weight $2$
Character orbit 3640.ge
Rep. character $\chi_{3640}(2809,\cdot)$
Character field $\Q(\zeta_{6})$
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.ge (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
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 1376 288 1088
Cusp forms 1312 288 1024
Eisenstein series 64 0 64

Trace form

\( 288 q + 140 q^{9} + O(q^{10}) \) \( 288 q + 140 q^{9} - 8 q^{15} + 24 q^{19} + 20 q^{21} + 4 q^{25} - 24 q^{29} - 8 q^{31} + 44 q^{35} - 72 q^{41} + 16 q^{45} + 36 q^{49} - 12 q^{51} + 24 q^{55} + 88 q^{59} + 12 q^{61} + 56 q^{69} + 16 q^{71} + 24 q^{75} + 40 q^{79} - 144 q^{81} + 88 q^{85} - 36 q^{89} + 48 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(455, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(910, [\chi])\)\(^{\oplus 3}\)