Properties

Label 1575.2.dw
Level 1575
Weight 2
Character orbit dw
Rep. character \(\chi_{1575}(131,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 1888
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.dw (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 1575 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1952 1952 0
Cusp forms 1888 1888 0
Eisenstein series 64 64 0

Trace form

\( 1888q - 9q^{3} + 458q^{4} - 12q^{5} - 12q^{6} - 8q^{7} - 3q^{9} + O(q^{10}) \) \( 1888q - 9q^{3} + 458q^{4} - 12q^{5} - 12q^{6} - 8q^{7} - 3q^{9} - 24q^{10} - 9q^{11} - 21q^{12} - 9q^{14} + 16q^{15} - 462q^{16} - 18q^{17} - 32q^{18} - 18q^{19} - 6q^{20} - 21q^{21} - 14q^{22} + 15q^{23} - 18q^{24} + 4q^{25} - 12q^{26} + 36q^{27} - 28q^{28} - 18q^{29} - 22q^{30} - 9q^{33} - 12q^{34} + 75q^{35} + 32q^{36} - 6q^{37} - 9q^{38} + 5q^{39} - 39q^{40} + 8q^{42} - 16q^{43} + 36q^{44} + 84q^{45} - 14q^{46} - 18q^{47} + 60q^{48} - 8q^{49} - 36q^{50} - 44q^{51} + 39q^{52} - 21q^{54} + 42q^{56} - 72q^{57} + 7q^{58} - 18q^{59} - 34q^{60} - 132q^{62} + 13q^{63} + 420q^{64} - 27q^{66} - 6q^{67} - 312q^{68} + 81q^{69} - 48q^{70} - 87q^{72} - 18q^{73} - 48q^{74} - 129q^{75} + 63q^{77} + 4q^{78} + 18q^{79} + 240q^{80} - 55q^{81} - 60q^{82} - 36q^{84} - 13q^{85} - 69q^{86} - 27q^{87} + 27q^{88} + 45q^{89} - 18q^{90} - 54q^{91} + 78q^{92} - 100q^{93} - 33q^{96} + 18q^{98} - 66q^{99} + O(q^{100}) \)

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