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Properties

Label 3640.2.fp
Level $3640$
Weight $2$
Character orbit 3640.fp
Rep. character $\chi_{3640}(289,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $336$
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.fp (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 455 \)
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 336 1040
Cusp forms 1312 336 976
Eisenstein series 64 0 64

Trace form

\( 336 q + 168 q^{9} + O(q^{10}) \) \( 336 q + 168 q^{9} + 2 q^{11} - 8 q^{15} - 2 q^{19} + 6 q^{35} - 4 q^{39} + 12 q^{41} - 6 q^{49} + 24 q^{51} + 16 q^{59} - 24 q^{61} + 28 q^{65} + 32 q^{69} + 12 q^{71} - 40 q^{75} + 24 q^{79} - 192 q^{81} - 24 q^{85} + 24 q^{89} + 14 q^{91} + 32 q^{95} + 44 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(455, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(910, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1820, [\chi])\)\(^{\oplus 2}\)