Properties

Label 2240.4.dp
Level $2240$
Weight $4$
Character orbit 2240.dp
Rep. character $\chi_{2240}(17,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1136$
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.dp (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 560 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1536\)

Dimensions

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

Total New Old
Modular forms 4672 1168 3504
Cusp forms 4544 1136 3408
Eisenstein series 128 32 96

Trace form

\( 1136 q + 12 q^{3} - 6 q^{5} + 4968 q^{9} + O(q^{10}) \) \( 1136 q + 12 q^{3} - 6 q^{5} + 4968 q^{9} + 4 q^{11} + 16 q^{15} - 12 q^{17} - 8 q^{21} + 24 q^{31} - 12 q^{33} + 26 q^{35} - 4 q^{37} - 216 q^{39} - 168 q^{45} + 12 q^{47} + 4 q^{51} - 216 q^{57} - 2064 q^{59} - 12 q^{61} - 1364 q^{63} - 4 q^{65} + 6 q^{75} - 40832 q^{81} - 508 q^{85} + 324 q^{87} - 840 q^{91} - 220 q^{93} + 3868 q^{95} + 216 q^{99} + O(q^{100}) \)

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

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