↑

Properties

Label 3640.2.bp
Level $3640$
Weight $2$
Character orbit 3640.bp
Rep. character $\chi_{3640}(1721,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $224$
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.bp (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
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 224 1152
Cusp forms 1312 224 1088
Eisenstein series 64 0 64

Trace form

\( 224 q - 8 q^{7} - 224 q^{9} + O(q^{10}) \) \( 224 q - 8 q^{7} - 224 q^{9} + 8 q^{11} - 24 q^{21} + 16 q^{29} - 8 q^{35} + 16 q^{37} + 40 q^{39} + 112 q^{53} - 16 q^{57} + 24 q^{63} + 24 q^{65} + 32 q^{67} - 88 q^{71} + 288 q^{81} - 32 q^{91} + 112 q^{93} - 16 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 6}\)