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Properties

Label 2240.4.fi
Level $2240$
Weight $4$
Character orbit 2240.fi
Rep. character $\chi_{2240}(221,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $12288$
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.fi (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 448 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(1536\)

Dimensions

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

Total New Old
Modular forms 18496 12288 6208
Cusp forms 18368 12288 6080
Eisenstein series 128 0 128

Trace form

\( 12288 q + O(q^{10}) \) \( 12288 q - 1888 q^{22} + 4000 q^{24} - 1520 q^{28} + 1760 q^{38} + 6320 q^{42} + 2000 q^{44} + 6624 q^{52} + 2752 q^{59} + 12096 q^{64} - 5472 q^{66} - 8160 q^{67} - 896 q^{71} - 752 q^{74} - 28224 q^{78} + 4144 q^{84} - 18720 q^{90} + 25840 q^{96} - 24208 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2240, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)