Properties

Label 1575.2.u
Level 1575
Weight 2
Character orbit u
Rep. character \(\chi_{1575}(101,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 292
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.u (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1575, [\chi])\).

Total New Old
Modular forms 504 316 188
Cusp forms 456 292 164
Eisenstein series 48 24 24

Trace form

\( 292q + 3q^{3} - 278q^{4} - 6q^{6} + 3q^{9} + O(q^{10}) \) \( 292q + 3q^{3} - 278q^{4} - 6q^{6} + 3q^{9} - 3q^{11} - 18q^{12} - 3q^{13} + 12q^{14} + 246q^{16} - 9q^{17} + 2q^{18} + 6q^{19} + 9q^{21} - 2q^{22} + 24q^{23} + 42q^{24} - 18q^{26} + 9q^{27} + 10q^{28} + 24q^{29} + 3q^{33} + 18q^{34} - 60q^{36} + 3q^{37} + 33q^{38} - 15q^{39} - 6q^{41} + 24q^{42} + 6q^{43} - 15q^{44} - 4q^{46} + 42q^{47} + 45q^{48} - 4q^{49} - 36q^{51} + 39q^{52} + 24q^{53} - 39q^{54} - 48q^{56} + 21q^{57} + q^{58} - 24q^{59} + 24q^{62} + 91q^{63} - 180q^{64} - 72q^{66} + 16q^{67} + 54q^{68} - 48q^{69} - 32q^{72} + 6q^{73} - 21q^{74} - 48q^{76} + 6q^{77} + 9q^{78} + 28q^{79} - 21q^{81} + 30q^{83} - 21q^{84} - 117q^{86} - 15q^{87} + 11q^{88} + 27q^{89} + 5q^{91} - 42q^{92} - 66q^{93} - 135q^{96} - 3q^{97} - 33q^{98} - 6q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database