Properties

Label 1575.2.cz
Level 1575
Weight 2
Character orbit cz
Rep. character \(\chi_{1575}(164,\cdot)\)
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.cz (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

\( 1888q - 15q^{3} - 470q^{4} - 12q^{5} + 12q^{6} - 3q^{9} + O(q^{10}) \) \( 1888q - 15q^{3} - 470q^{4} - 12q^{5} + 12q^{6} - 3q^{9} - 24q^{10} - 9q^{11} - 15q^{12} - 9q^{14} - 54q^{15} - 446q^{16} - 18q^{19} + 6q^{20} + 9q^{21} - 10q^{22} - 15q^{23} + 18q^{24} + 4q^{25} + 12q^{26} - 18q^{29} - 38q^{30} - 15q^{33} + 12q^{34} - 75q^{35} - 40q^{36} - 10q^{37} - 15q^{38} + 17q^{39} + 15q^{40} + 20q^{42} + 60q^{44} + 84q^{45} + 2q^{46} - 30q^{47} + 30q^{48} - 8q^{49} - 60q^{50} + 28q^{51} - 15q^{52} + 3q^{54} - 60q^{56} + 5q^{58} - 18q^{59} - 10q^{60} - 180q^{62} + 35q^{63} - 436q^{64} + 9q^{66} - 10q^{67} + 45q^{69} + 20q^{70} + 75q^{72} - 30q^{73} - 87q^{75} + 48q^{76} + 105q^{77} + 10q^{78} + 18q^{79} - 216q^{80} + 49q^{81} - 116q^{84} - 3q^{85} + 51q^{86} - 15q^{87} + 5q^{88} + 45q^{89} + 162q^{90} + 30q^{91} - 210q^{92} + 87q^{96} + 30q^{98} - 66q^{99} + O(q^{100}) \)

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