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Properties

Label 2240.2.fl
Level $2240$
Weight $2$
Character orbit 2240.fl
Rep. character $\chi_{2240}(117,\cdot)$
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.fl (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

\( 6080 q - 8 q^{2} - 24 q^{3} - 24 q^{5} - 16 q^{7} - 32 q^{8} + O(q^{10}) \) \( 6080 q - 8 q^{2} - 24 q^{3} - 24 q^{5} - 16 q^{7} - 32 q^{8} - 24 q^{10} - 16 q^{11} - 24 q^{12} + 64 q^{14} - 32 q^{15} - 16 q^{16} - 48 q^{17} - 8 q^{18} - 32 q^{21} - 32 q^{22} - 8 q^{23} - 8 q^{25} - 48 q^{26} - 16 q^{28} - 72 q^{30} - 8 q^{32} - 16 q^{35} - 64 q^{36} - 8 q^{37} - 24 q^{38} - 24 q^{40} - 16 q^{42} - 32 q^{43} - 96 q^{45} - 16 q^{46} - 48 q^{47} - 32 q^{50} - 16 q^{51} - 24 q^{52} - 8 q^{53} - 32 q^{56} - 32 q^{57} - 72 q^{58} - 8 q^{60} - 48 q^{61} - 32 q^{63} - 16 q^{65} - 336 q^{66} - 8 q^{67} - 24 q^{68} - 16 q^{70} - 192 q^{71} - 8 q^{72} - 24 q^{73} - 24 q^{75} - 16 q^{77} - 336 q^{78} - 24 q^{80} - 16 q^{81} + 216 q^{82} - 112 q^{85} - 16 q^{86} - 24 q^{87} + 80 q^{88} - 32 q^{91} - 176 q^{92} + 40 q^{93} - 48 q^{96} - 8 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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