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Properties

Label 1520.2.eg
Level $1520$
Weight $2$
Character orbit 1520.eg
Rep. character $\chi_{1520}(53,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $2832$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1520.eg (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1520 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1520, [\chi])\).

Total New Old
Modular forms 2928 2928 0
Cusp forms 2832 2832 0
Eisenstein series 96 96 0

Trace form

\( 2832 q - 12 q^{2} - 24 q^{3} + 12 q^{4} - 12 q^{5} - 24 q^{6} - 18 q^{8} + O(q^{10}) \) \( 2832 q - 12 q^{2} - 24 q^{3} + 12 q^{4} - 12 q^{5} - 24 q^{6} - 18 q^{8} - 12 q^{10} - 12 q^{11} - 18 q^{12} - 24 q^{13} - 24 q^{15} - 12 q^{16} - 24 q^{17} - 24 q^{20} - 24 q^{21} - 36 q^{24} + 36 q^{26} - 36 q^{27} + 48 q^{28} - 6 q^{30} - 72 q^{31} + 18 q^{32} - 24 q^{33} - 48 q^{34} + 18 q^{35} - 72 q^{36} - 114 q^{38} + 132 q^{40} - 48 q^{42} - 6 q^{45} - 36 q^{46} - 24 q^{47} - 96 q^{48} - 18 q^{50} - 48 q^{51} - 12 q^{52} + 48 q^{54} + 120 q^{58} - 78 q^{60} - 24 q^{61} - 84 q^{62} + 60 q^{63} - 48 q^{64} - 36 q^{65} - 24 q^{66} - 6 q^{68} - 144 q^{69} - 12 q^{70} + 120 q^{72} + 144 q^{74} - 24 q^{76} + 54 q^{78} + 90 q^{80} - 48 q^{81} - 252 q^{82} - 12 q^{83} - 216 q^{84} - 12 q^{85} - 24 q^{86} - 18 q^{88} - 66 q^{90} - 24 q^{91} - 12 q^{92} - 60 q^{93} - 24 q^{95} + 48 q^{96} - 24 q^{97} + 18 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1520, [\chi])\) into newform subspaces

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