Properties

Label 1575.2.dy
Level 1575
Weight 2
Character orbit dy
Rep. character \(\chi_{1575}(184,\cdot)\)
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.dy (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

\( 1888q - 10q^{2} - 5q^{3} + 458q^{4} + 4q^{5} - 16q^{6} - 40q^{8} - 3q^{9} + O(q^{10}) \) \( 1888q - 10q^{2} - 5q^{3} + 458q^{4} + 4q^{5} - 16q^{6} - 40q^{8} - 3q^{9} - 12q^{10} + 3q^{11} - 5q^{12} - 10q^{13} + 21q^{14} + 16q^{15} - 462q^{16} - 10q^{17} - 6q^{19} + 2q^{20} - 9q^{21} - 10q^{22} + 5q^{23} - 22q^{24} + 4q^{25} - 108q^{26} - 50q^{27} - 6q^{29} - 10q^{30} - 6q^{31} - 55q^{33} - 2q^{34} - 19q^{35} - 28q^{36} - 10q^{37} + 5q^{38} - 23q^{39} + 13q^{40} + 26q^{41} - 40q^{42} + 14q^{44} - 72q^{45} - 14q^{46} - 10q^{47} - 30q^{48} - 8q^{49} - 44q^{50} + 28q^{51} - 15q^{52} - 10q^{53} - 7q^{54} - 10q^{55} + 46q^{56} + 5q^{58} + 90q^{59} + 66q^{60} - 6q^{61} - 100q^{62} + 85q^{63} + 420q^{64} - 26q^{65} - 17q^{66} - 10q^{67} - 39q^{69} - 96q^{70} - 6q^{71} + 75q^{72} - 10q^{73} + 53q^{75} - 32q^{76} - 115q^{77} + 10q^{78} - 30q^{79} - 98q^{80} - 55q^{81} - 80q^{83} + 36q^{84} - 3q^{85} - 5q^{86} - 5q^{87} + 5q^{88} - 39q^{89} + 30q^{90} - 54q^{91} + 50q^{92} - 38q^{94} - 84q^{95} - 23q^{96} - 10q^{97} - 30q^{98} - 30q^{99} + O(q^{100}) \)

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