Properties

Label 1520.2.cz
Level $1520$
Weight $2$
Character orbit 1520.cz
Rep. character $\chi_{1520}(387,\cdot)$
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.cz (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

\( 944q - 2q^{2} - 4q^{4} - 2q^{5} - 4q^{6} - 16q^{7} + 4q^{8} + 456q^{9} + O(q^{10}) \) \( 944q - 2q^{2} - 4q^{4} - 2q^{5} - 4q^{6} - 16q^{7} + 4q^{8} + 456q^{9} + 6q^{10} - 16q^{11} - 20q^{12} - 4q^{13} - 24q^{15} - 8q^{16} - 4q^{17} - 40q^{18} - 8q^{19} - 20q^{20} - 4q^{21} + 22q^{22} - 4q^{23} + 12q^{24} - 48q^{26} - 20q^{30} + 8q^{32} - 4q^{33} - 16q^{34} - 36q^{35} + 44q^{36} - 16q^{37} + 26q^{38} + 4q^{40} - 18q^{42} - 4q^{43} - 16q^{44} - 48q^{46} - 24q^{47} - 56q^{50} + 4q^{51} + 14q^{52} + 36q^{54} - 4q^{55} - 16q^{56} - 12q^{57} - 84q^{58} + 10q^{60} - 36q^{61} - 8q^{62} - 24q^{63} - 64q^{64} - 16q^{65} - 36q^{66} - 52q^{67} + 4q^{68} + 40q^{69} + 66q^{70} - 8q^{71} + 8q^{74} + 92q^{75} - 8q^{76} + 8q^{78} - 36q^{80} - 416q^{81} - 60q^{82} - 48q^{84} + 18q^{85} + 28q^{86} - 128q^{87} - 24q^{88} + 58q^{90} - 4q^{91} + 12q^{92} + 8q^{93} - 32q^{94} - 80q^{95} + 24q^{96} - 4q^{97} + 28q^{98} + 8q^{99} + O(q^{100}) \)

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

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