Properties

Label 1575.2.cr
Level 1575
Weight 2
Character orbit cr
Rep. character \(\chi_{1575}(16,\cdot)\)
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.cr (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

\( 1888q + 3q^{2} - 3q^{3} + 235q^{4} - 8q^{5} - 8q^{6} - 8q^{7} - 16q^{8} - 3q^{9} + O(q^{10}) \) \( 1888q + 3q^{2} - 3q^{3} + 235q^{4} - 8q^{5} - 8q^{6} - 8q^{7} - 16q^{8} - 3q^{9} - 4q^{10} - 6q^{11} - 23q^{12} - 6q^{13} + 9q^{14} - 42q^{15} + 223q^{16} - 12q^{17} - 6q^{19} - 2q^{20} - 30q^{21} + 2q^{22} - 22q^{23} - 26q^{24} - 8q^{25} + 76q^{26} + 18q^{27} - 20q^{28} - 6q^{29} + 25q^{30} + 3q^{31} + 4q^{32} + 6q^{33} - 10q^{34} - 49q^{35} + 20q^{36} - 6q^{37} - 22q^{38} + 7q^{39} - 22q^{40} - 38q^{41} - 26q^{42} - 16q^{43} + 6q^{44} + 73q^{45} + 2q^{46} + 3q^{47} + 44q^{48} - 8q^{49} - 28q^{50} - 8q^{51} - 14q^{52} + 14q^{53} - 11q^{54} - 34q^{55} - 48q^{56} - 144q^{57} - 46q^{58} - 45q^{59} + 53q^{60} + 3q^{61} - 52q^{62} - 11q^{63} - 436q^{64} + 19q^{65} + 5q^{66} + 3q^{67} - 256q^{68} - 27q^{69} + 8q^{70} - 42q^{71} - 15q^{72} - 6q^{73} - 32q^{74} + 97q^{75} - 16q^{76} - 23q^{77} + 40q^{78} + 15q^{79} + 94q^{80} + q^{81} - 20q^{82} - 48q^{83} - 125q^{84} - 13q^{85} - 22q^{86} - 41q^{87} - 22q^{88} - 39q^{89} - 178q^{90} + 30q^{91} - 30q^{92} + 50q^{93} - 13q^{94} + 18q^{95} + 23q^{96} - 6q^{97} - 142q^{98} - 30q^{99} + O(q^{100}) \)

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