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Properties

Label 2240.4.fk
Level $2240$
Weight $4$
Character orbit 2240.fk
Rep. character $\chi_{2240}(67,\cdot)$
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.fk (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

\( 18368 q - 8 q^{2} - 8 q^{3} - 8 q^{5} - 64 q^{6} - 16 q^{7} - 32 q^{8} + O(q^{10}) \) \( 18368 q - 8 q^{2} - 8 q^{3} - 8 q^{5} - 64 q^{6} - 16 q^{7} - 32 q^{8} - 8 q^{10} - 16 q^{11} - 8 q^{12} - 32 q^{13} - 832 q^{14} - 32 q^{15} - 16 q^{16} - 8 q^{18} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 8 q^{23} - 8 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 2264 q^{30} - 32 q^{31} - 8 q^{32} - 256 q^{34} - 16 q^{35} - 64 q^{36} - 8 q^{37} - 8 q^{38} + 1144 q^{40} - 64 q^{41} - 16 q^{42} - 32 q^{43} - 224 q^{45} - 16 q^{46} - 16 q^{47} - 32 q^{48} - 32 q^{50} - 16 q^{51} - 8 q^{52} - 8 q^{53} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 4040 q^{58} - 8 q^{60} - 16 q^{61} + 96 q^{62} - 16 q^{65} - 5488 q^{66} - 8 q^{67} - 1032 q^{68} - 16 q^{70} - 960 q^{71} - 8 q^{72} - 8 q^{73} - 8 q^{75} - 64 q^{76} - 16 q^{77} - 23440 q^{78} - 8 q^{80} - 16 q^{81} - 6968 q^{82} - 32 q^{83} - 2032 q^{85} - 16 q^{86} - 8 q^{87} - 624 q^{88} - 32 q^{90} - 32 q^{91} + 11056 q^{92} + 424 q^{93} + 256 q^{94} - 16 q^{95} - 16 q^{96} + 6360 q^{98} + O(q^{100}) \)

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.