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Properties

Label 3640.2.bg
Level $3640$
Weight $2$
Character orbit 3640.bg
Rep. character $\chi_{3640}(841,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $168$
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.bg (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 1376 168 1208
Cusp forms 1312 168 1144
Eisenstein series 64 0 64

Trace form

\( 168 q - 84 q^{9} + O(q^{10}) \) \( 168 q - 84 q^{9} - 8 q^{23} + 168 q^{25} - 16 q^{31} - 12 q^{35} - 4 q^{39} - 32 q^{43} + 112 q^{47} - 84 q^{49} - 8 q^{51} - 48 q^{53} - 8 q^{55} + 48 q^{57} + 24 q^{59} - 8 q^{67} - 8 q^{69} + 4 q^{71} - 32 q^{77} - 64 q^{79} - 84 q^{81} + 16 q^{87} - 16 q^{91} - 16 q^{93} + 24 q^{97} - 24 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)