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

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

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

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