Properties

Label 1575.2.db
Level 1575
Weight 2
Character orbit db
Rep. character \(\chi_{1575}(4,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 1888
Sturm bound 480

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1575.db (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

\( 1888q + 5q^{2} - 5q^{3} - 229q^{4} - 8q^{5} - 16q^{6} - 40q^{8} - 3q^{9} + O(q^{10}) \) \( 1888q + 5q^{2} - 5q^{3} - 229q^{4} - 8q^{5} - 16q^{6} - 40q^{8} - 3q^{9} - 12q^{10} - 6q^{11} - 5q^{12} - 10q^{13} - 15q^{14} + 16q^{15} + 231q^{16} - 10q^{17} - 6q^{19} + 2q^{20} + 18q^{21} - 10q^{22} - 10q^{23} - 22q^{24} - 8q^{25} - 108q^{26} - 50q^{27} - 6q^{29} + 29q^{30} + 3q^{31} + 20q^{33} - 2q^{34} - 19q^{35} - 28q^{36} - 10q^{37} - 10q^{38} + 31q^{39} - 26q^{40} + 26q^{41} - 40q^{42} + 14q^{44} + 93q^{45} - 14q^{46} + 5q^{47} - 30q^{48} - 8q^{49} - 44q^{50} - 8q^{51} + 30q^{52} - 10q^{53} + 5q^{54} - 10q^{55} + 10q^{56} - 10q^{58} - 45q^{59} - 9q^{60} + 3q^{61} - 100q^{62} - 95q^{63} + 420q^{64} + 13q^{65} + 13q^{66} + 5q^{67} - 39q^{69} + 24q^{70} - 6q^{71} - 45q^{72} - 10q^{73} - q^{75} - 32q^{76} + 215q^{77} + 10q^{78} + 15q^{79} - 98q^{80} - 7q^{81} - 80q^{83} - 147q^{84} - 3q^{85} + 10q^{86} - 5q^{87} - 10q^{88} - 39q^{89} + 30q^{90} - 54q^{91} + 50q^{92} + 19q^{94} + 42q^{95} - 29q^{96} - 10q^{97} - 30q^{98} - 30q^{99} + O(q^{100}) \)

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