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Properties

Label 1520.2.ch
Level $1520$
Weight $2$
Character orbit 1520.ch
Rep. character $\chi_{1520}(83,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $944$
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.ch (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1520 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 976 976 0
Cusp forms 944 944 0
Eisenstein series 32 32 0

Trace form

\( 944 q - 2 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 16 q^{7} + 4 q^{8} - 456 q^{9} + O(q^{10}) \) \( 944 q - 2 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 16 q^{7} + 4 q^{8} - 456 q^{9} - 10 q^{10} - 16 q^{11} + 4 q^{12} + 24 q^{15} - 8 q^{16} - 4 q^{17} + 40 q^{18} + 8 q^{19} + 4 q^{20} - 4 q^{21} - 26 q^{22} - 4 q^{23} - 12 q^{24} - 48 q^{26} + 8 q^{27} + 12 q^{28} + 4 q^{30} + 8 q^{32} - 4 q^{33} + 16 q^{34} - 16 q^{35} + 44 q^{36} - 6 q^{38} + 12 q^{40} - 10 q^{42} + 16 q^{44} + 24 q^{45} - 48 q^{46} + 24 q^{47} - 4 q^{48} + 4 q^{51} - 18 q^{52} - 4 q^{53} - 36 q^{54} - 4 q^{55} - 16 q^{56} + 12 q^{57} + 68 q^{58} + 18 q^{60} - 36 q^{61} + 12 q^{62} + 24 q^{63} + 64 q^{64} - 16 q^{65} - 36 q^{66} + 4 q^{68} - 40 q^{69} + 50 q^{70} - 8 q^{71} - 36 q^{72} - 8 q^{74} + 116 q^{75} - 8 q^{76} - 128 q^{77} - 52 q^{78} - 8 q^{80} - 416 q^{81} - 96 q^{83} + 48 q^{84} - 22 q^{85} + 28 q^{86} - 128 q^{87} + 8 q^{88} - 38 q^{90} - 4 q^{91} - 48 q^{92} + 32 q^{94} + 80 q^{95} + 24 q^{96} - 4 q^{97} + 28 q^{98} - 8 q^{99} + O(q^{100}) \)

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.