Properties

Label 1575.2.ep
Level 1575
Weight 2
Character orbit ep
Rep. character \(\chi_{1575}(52,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 3776
Sturm bound 480

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Defining parameters

Level: \( N \) = \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1575.ep (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 1575 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1575, [\chi])\).

Total New Old
Modular forms 3904 3904 0
Cusp forms 3776 3776 0
Eisenstein series 128 128 0

Trace form

\( 3776q - 16q^{2} - 24q^{3} - 20q^{4} - 24q^{5} - 8q^{7} - 72q^{8} - 10q^{9} + O(q^{10}) \) \( 3776q - 16q^{2} - 24q^{3} - 20q^{4} - 24q^{5} - 8q^{7} - 72q^{8} - 10q^{9} - 48q^{10} + 6q^{11} - 12q^{12} - 10q^{14} - 38q^{15} + 884q^{16} - 30q^{17} - 32q^{18} - 60q^{19} - 48q^{20} - 12q^{21} - 8q^{22} + 16q^{23} + 8q^{25} - 96q^{26} + 36q^{27} - 44q^{28} - 20q^{29} + 4q^{30} + 40q^{32} - 24q^{33} + 4q^{35} - 40q^{36} - 16q^{37} - 24q^{38} - 90q^{39} - 24q^{40} + 20q^{42} - 16q^{43} - 20q^{44} - 216q^{45} - 12q^{46} + 42q^{48} + 8q^{50} - 16q^{51} - 72q^{52} - 36q^{53} - 30q^{54} - 70q^{56} + 32q^{57} - 12q^{58} + 4q^{60} - 64q^{63} - 80q^{64} + 32q^{65} - 18q^{66} - 16q^{67} + 240q^{68} + 210q^{69} - 28q^{70} - 48q^{71} - 116q^{72} - 48q^{73} - 216q^{75} - 48q^{76} - 4q^{77} - 38q^{78} - 20q^{79} - 72q^{80} - 6q^{81} - 36q^{82} - 336q^{83} - 140q^{84} - 16q^{85} + 6q^{86} - 42q^{87} - 32q^{88} - 210q^{89} + 144q^{90} - 24q^{91} - 12q^{92} - 68q^{93} - 120q^{95} + 54q^{96} - 140q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database