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Properties

Label 2240.4.fg
Level $2240$
Weight $4$
Character orbit 2240.fg
Rep. character $\chi_{2240}(109,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $18368$
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.fg (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2240 \)
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 18496 0
Cusp forms 18368 18368 0
Eisenstein series 128 128 0

Trace form

\( 18368 q - 16 q^{4} - 8 q^{5} - 64 q^{6} - 16 q^{9} + O(q^{10}) \) \( 18368 q - 16 q^{4} - 8 q^{5} - 64 q^{6} - 16 q^{9} - 8 q^{10} - 16 q^{11} - 32 q^{14} - 32 q^{15} - 16 q^{16} - 16 q^{19} - 32 q^{20} - 32 q^{21} - 16 q^{24} - 8 q^{25} - 16 q^{26} - 64 q^{29} + 2312 q^{30} - 64 q^{34} - 16 q^{35} + 3456 q^{36} - 16 q^{39} - 8 q^{40} - 64 q^{41} - 16 q^{44} - 8 q^{45} - 16 q^{46} - 32 q^{49} - 5744 q^{50} - 16 q^{51} - 16 q^{54} - 32 q^{55} - 32 q^{56} + 2736 q^{59} + 4888 q^{60} - 16 q^{61} + 12032 q^{64} - 16 q^{65} + 5712 q^{66} - 64 q^{69} - 16 q^{70} + 832 q^{71} - 4528 q^{74} - 8 q^{75} - 64 q^{76} - 16 q^{79} + 5008 q^{80} - 16 q^{81} + 4112 q^{84} - 32 q^{85} - 16 q^{86} - 16 q^{89} - 32 q^{90} - 32 q^{91} - 16 q^{94} - 16 q^{96} + 800 q^{99} + O(q^{100}) \)

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.