Properties

Label 1575.2.cf
Level 1575
Weight 2
Character orbit cf
Rep. character \(\chi_{1575}(32,\cdot)\)
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.cf (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

\( 560q + 6q^{2} + 2q^{3} + 2q^{7} + O(q^{10}) \) \( 560q + 6q^{2} + 2q^{3} + 2q^{7} + 22q^{12} + 4q^{13} + 260q^{16} + 18q^{17} + 10q^{18} - 64q^{21} - 4q^{22} + 32q^{27} + 4q^{28} + 4q^{31} + 90q^{32} - 32q^{33} - 16q^{36} + 4q^{37} - 14q^{42} + 4q^{43} - 32q^{46} + 6q^{47} - 38q^{48} - 52q^{51} + 52q^{52} + 156q^{56} - 32q^{57} + 12q^{58} + 28q^{61} - 14q^{63} + 244q^{66} - 2q^{67} + 46q^{72} + 4q^{73} - 24q^{76} - 42q^{77} - 54q^{78} - 52q^{81} + 8q^{82} + 12q^{83} + 28q^{87} - 12q^{88} - 16q^{91} - 72q^{92} - 4q^{93} + 36q^{96} + 4q^{97} - 12q^{98} + O(q^{100}) \)

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