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Properties

Label 3040.2.gl
Level $3040$
Weight $2$
Character orbit 3040.gl
Rep. character $\chi_{3040}(13,\cdot)$
Character field $\Q(\zeta_{72})$
Dimension $11424$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 3040 = 2^{5} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3040.gl (of order \(72\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3040 \)
Character field: \(\Q(\zeta_{72})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3040, [\chi])\).

Total New Old
Modular forms 11616 11616 0
Cusp forms 11424 11424 0
Eisenstein series 192 192 0

Trace form

\( 11424 q - 24 q^{2} - 24 q^{3} - 24 q^{5} - 48 q^{6} - 36 q^{8} + O(q^{10}) \) \( 11424 q - 24 q^{2} - 24 q^{3} - 24 q^{5} - 48 q^{6} - 36 q^{8} - 60 q^{10} - 24 q^{11} - 36 q^{12} - 24 q^{13} - 48 q^{14} - 48 q^{16} - 48 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 24 q^{26} - 36 q^{27} - 72 q^{28} - 96 q^{30} - 144 q^{31} + 36 q^{32} - 48 q^{33} - 84 q^{35} - 48 q^{36} - 192 q^{38} + 36 q^{40} - 48 q^{41} - 96 q^{42} - 24 q^{43} - 12 q^{45} - 72 q^{46} - 24 q^{48} + 5424 q^{49} - 36 q^{50} - 96 q^{51} - 24 q^{52} - 24 q^{53} - 24 q^{55} - 48 q^{58} - 24 q^{60} - 48 q^{61} - 48 q^{62} - 48 q^{63} - 72 q^{65} - 48 q^{66} - 24 q^{67} - 12 q^{68} - 108 q^{70} - 48 q^{71} + 72 q^{72} - 48 q^{76} - 216 q^{77} - 120 q^{78} - 144 q^{80} + 96 q^{82} - 12 q^{83} - 24 q^{85} - 48 q^{86} - 24 q^{87} - 36 q^{88} - 24 q^{90} - 48 q^{91} - 24 q^{92} - 60 q^{93} - 48 q^{95} - 288 q^{96} - 48 q^{97} - 84 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3040, [\chi])\) into newform subspaces

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