Properties

Label 2240.4.r
Level $2240$
Weight $4$
Character orbit 2240.r
Rep. character $\chi_{2240}(433,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $568$
Sturm bound $1536$

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Defining parameters

Level: \( N \) \(=\) \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2240.r (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 560 \)
Character field: \(\Q(i)\)
Sturm bound: \(1536\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2240, [\chi])\).

Total New Old
Modular forms 2336 584 1752
Cusp forms 2272 568 1704
Eisenstein series 64 16 48

Trace form

\( 568 q - 4968 q^{9} + O(q^{10}) \) \( 568 q - 4968 q^{9} + 8 q^{11} + 8 q^{15} - 4 q^{21} - 20 q^{35} - 8 q^{37} - 432 q^{39} + 8 q^{51} + 216 q^{57} + 1376 q^{63} - 8 q^{65} + 40808 q^{81} + 496 q^{85} + 852 q^{91} + 208 q^{93} + 7736 q^{95} - 216 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(2240, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2240, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2240, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 3}\)