Properties

Label 3640.2.b
Level $3640$
Weight $2$
Character orbit 3640.b
Rep. character $\chi_{3640}(3249,\cdot)$
Character field $\Q$
Dimension $128$
Sturm bound $1344$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3640.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 688 128 560
Cusp forms 656 128 528
Eisenstein series 32 0 32

Trace form

\( 128 q - 136 q^{9} + O(q^{10}) \) \( 128 q - 136 q^{9} + 4 q^{25} - 32 q^{29} + 28 q^{39} + 128 q^{49} + 72 q^{51} - 48 q^{55} + 40 q^{61} - 4 q^{65} + 16 q^{69} - 40 q^{75} - 16 q^{79} + 128 q^{81} + 4 q^{95} + O(q^{100}) \)

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

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