Properties

Label 2240.2.df
Level $2240$
Weight $2$
Character orbit 2240.df
Rep. character $\chi_{2240}(81,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $256$
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.df (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
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 256 1344
Cusp forms 1472 256 1216
Eisenstein series 128 0 128

Trace form

\( 256q + O(q^{10}) \) \( 256q - 8q^{11} - 32q^{29} + 16q^{37} - 16q^{43} - 80q^{47} + 40q^{51} - 16q^{53} - 16q^{59} + 40q^{67} + 128q^{81} + 80q^{83} + 32q^{91} + 80q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 3}\)