Properties

Label 2240.2.bl
Level $2240$
Weight $2$
Character orbit 2240.bl
Rep. character $\chi_{2240}(1583,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $144$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2240.bl (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2240, [\chi])\).

Total New Old
Modular forms 800 144 656
Cusp forms 736 144 592
Eisenstein series 64 0 64

Trace form

\( 144q + 144q^{9} + O(q^{10}) \) \( 144q + 144q^{9} - 16q^{19} + 16q^{51} - 32q^{61} + 32q^{69} + 16q^{73} + 24q^{75} + 144q^{81} + 80q^{83} + 112q^{87} + 80q^{95} + 64q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2240, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2240, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 3}\)