Properties

Label 1575.2.cq
Level 1575
Weight 2
Character orbit cq
Rep. character \(\chi_{1575}(121,\cdot)\)
Character field \(\Q(\zeta_{15})\)
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.cq (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 1575 \)
Character field: \(\Q(\zeta_{15})\)
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

\( 1888q - 6q^{2} - 3q^{3} - 470q^{4} + 4q^{5} - 8q^{6} - 8q^{7} - 16q^{8} - 3q^{9} + O(q^{10}) \) \( 1888q - 6q^{2} - 3q^{3} - 470q^{4} + 4q^{5} - 8q^{6} - 8q^{7} - 16q^{8} - 3q^{9} - 4q^{10} + 3q^{11} + 25q^{12} - 6q^{13} - 27q^{14} - 42q^{15} - 446q^{16} - 12q^{17} - 6q^{19} - 2q^{20} - 3q^{21} + 2q^{22} + 11q^{23} + 22q^{24} + 4q^{25} + 76q^{26} + 18q^{27} - 20q^{28} - 6q^{29} - 26q^{30} - 6q^{31} - 8q^{32} + 15q^{33} - 10q^{34} - 49q^{35} + 20q^{36} - 6q^{37} + 11q^{38} - 11q^{39} + 11q^{40} - 38q^{41} + 4q^{42} - 16q^{43} + 6q^{44} - 32q^{45} + 2q^{46} - 6q^{47} + 44q^{48} - 8q^{49} - 28q^{50} - 44q^{51} + 7q^{52} + 14q^{53} + q^{54} - 34q^{55} + 12q^{56} - 144q^{57} + 23q^{58} + 90q^{59} + 74q^{60} - 6q^{61} - 52q^{62} + 43q^{63} - 436q^{64} - 38q^{65} - 37q^{66} - 6q^{67} + 128q^{68} - 27q^{69} + 68q^{70} - 42q^{71} - 15q^{72} - 6q^{73} + 16q^{74} - 149q^{75} - 16q^{76} - 17q^{77} + 40q^{78} - 30q^{79} + 94q^{80} + 49q^{81} - 20q^{82} - 48q^{83} - 44q^{84} - 13q^{85} + 11q^{86} - 41q^{87} + 11q^{88} - 39q^{89} - 178q^{90} + 30q^{91} - 30q^{92} - 4q^{93} + 26q^{94} - 36q^{95} - 55q^{96} - 6q^{97} - 142q^{98} - 30q^{99} + O(q^{100}) \)

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