Properties

Label 1575.2.ca
Level 1575
Weight 2
Character orbit ca
Rep. character \(\chi_{1575}(418,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 560
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.ca (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1008 592 416
Cusp forms 912 560 352
Eisenstein series 96 32 64

Trace form

\( 560q + 4q^{2} + 6q^{3} + 2q^{7} + 8q^{8} + O(q^{10}) \) \( 560q + 4q^{2} + 6q^{3} + 2q^{7} + 8q^{8} + 12q^{11} + 18q^{12} - 520q^{16} + 30q^{17} - 22q^{18} - 24q^{21} + 12q^{22} + 6q^{23} - 24q^{26} + 36q^{27} - 4q^{28} + 60q^{32} + 6q^{33} - 80q^{36} + 4q^{37} + 6q^{38} - 24q^{41} + 40q^{42} + 4q^{43} + 16q^{46} - 18q^{48} - 76q^{51} - 42q^{52} - 16q^{53} - 76q^{56} - 8q^{57} - 22q^{58} + 6q^{63} - 12q^{66} + 4q^{67} - 90q^{68} + 32q^{71} - 106q^{72} + 12q^{73} + 48q^{76} - 74q^{77} + 62q^{78} + 116q^{81} + 24q^{82} + 84q^{83} + 92q^{86} - 12q^{87} - 42q^{88} - 16q^{91} + 8q^{92} - 58q^{93} + 84q^{96} - 120q^{98} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database