Properties

Label 2240.2.fg
Level $2240$
Weight $2$
Character orbit 2240.fg
Rep. character $\chi_{2240}(109,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $6080$
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.fg (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2240 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(768\)

Dimensions

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

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

Trace form

\( 6080q - 16q^{4} - 8q^{5} - 64q^{6} - 16q^{9} + O(q^{10}) \) \( 6080q - 16q^{4} - 8q^{5} - 64q^{6} - 16q^{9} - 8q^{10} - 16q^{11} - 32q^{14} - 32q^{15} - 16q^{16} - 16q^{19} - 32q^{20} - 32q^{21} - 16q^{24} - 8q^{25} - 16q^{26} - 64q^{29} - 88q^{30} - 64q^{34} - 16q^{35} - 384q^{36} - 16q^{39} - 8q^{40} - 64q^{41} - 16q^{44} - 8q^{45} - 16q^{46} - 32q^{49} - 80q^{50} - 16q^{51} - 16q^{54} - 32q^{55} - 32q^{56} - 80q^{59} - 104q^{60} - 16q^{61} - 256q^{64} - 16q^{65} - 48q^{66} - 64q^{69} - 16q^{70} - 192q^{71} - 112q^{74} - 8q^{75} - 64q^{76} - 16q^{79} + 16q^{80} - 16q^{81} + 80q^{84} - 32q^{85} - 16q^{86} - 16q^{89} - 32q^{90} - 32q^{91} - 16q^{94} - 16q^{96} + 32q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2240, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.