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Properties

Label 2240.2.eg
Level $2240$
Weight $2$
Character orbit 2240.eg
Rep. character $\chi_{2240}(267,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $2304$
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.eg (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 320 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 3104 2304 800
Cusp forms 3040 2304 736
Eisenstein series 64 0 64

Trace form

\( 2304 q + O(q^{10}) \) \( 2304 q + 64 q^{12} - 64 q^{22} - 32 q^{24} + 80 q^{30} - 112 q^{38} + 80 q^{40} + 208 q^{48} + 208 q^{50} + 64 q^{51} - 96 q^{56} - 112 q^{60} + 112 q^{68} - 128 q^{69} - 240 q^{72} - 128 q^{76} + 64 q^{79} + 160 q^{82} - 224 q^{87} + 304 q^{92} - 256 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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