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Properties

Label 2240.2.dk
Level $2240$
Weight $2$
Character orbit 2240.dk
Rep. character $\chi_{2240}(767,\cdot)$
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.dk (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
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 1632 400 1232
Cusp forms 1440 368 1072
Eisenstein series 192 32 160

Trace form

\( 368 q + 4 q^{5} + O(q^{10}) \) \( 368 q + 4 q^{5} + 16 q^{13} - 4 q^{17} + 16 q^{21} - 4 q^{25} - 28 q^{33} + 4 q^{37} - 32 q^{41} + 44 q^{45} + 4 q^{53} + 8 q^{57} + 8 q^{61} - 4 q^{65} - 4 q^{73} + 84 q^{77} + 144 q^{81} + 112 q^{85} + 28 q^{93} + 48 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)