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Properties

Label 2240.2.dh
Level $2240$
Weight $2$
Character orbit 2240.dh
Rep. character $\chi_{2240}(529,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $368$
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.dh (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 560 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 1600 400 1200
Cusp forms 1472 368 1104
Eisenstein series 128 32 96

Trace form

\( 368 q - 2 q^{5} + O(q^{10}) \) \( 368 q - 2 q^{5} + 4 q^{11} + 16 q^{15} + 4 q^{19} + 4 q^{21} - 16 q^{29} + 56 q^{31} - 18 q^{35} - 16 q^{45} - 16 q^{49} + 28 q^{51} - 12 q^{59} - 4 q^{61} - 4 q^{65} + 8 q^{69} - 10 q^{75} + 8 q^{79} + 112 q^{81} - 28 q^{85} + 80 q^{91} - 20 q^{95} + 112 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)