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Properties

Label 2240.4.eg
Level $2240$
Weight $4$
Character orbit 2240.eg
Rep. character $\chi_{2240}(267,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $6912$
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.eg (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 320 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(1536\)

Dimensions

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

Total New Old
Modular forms 9248 6912 2336
Cusp forms 9184 6912 2272
Eisenstein series 64 0 64

Trace form

\( 6912 q + O(q^{10}) \) \( 6912 q - 192 q^{12} - 1728 q^{22} - 1824 q^{24} - 2320 q^{30} - 4816 q^{38} + 3280 q^{40} - 9776 q^{48} - 8528 q^{50} + 5952 q^{51} + 672 q^{56} - 12208 q^{60} + 5936 q^{68} + 4224 q^{69} + 5520 q^{72} - 11904 q^{76} + 11328 q^{79} - 11680 q^{82} + 5152 q^{87} - 25232 q^{92} + 21248 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{4}^{\mathrm{old}}(2240, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)