Properties

Label 1575.2.cj
Level 1575
Weight 2
Character orbit cj
Rep. character \(\chi_{1575}(643,\cdot)\)
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.cj (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

\( 560q + 4q^{2} + 2q^{7} + 32q^{8} + O(q^{10}) \) \( 560q + 4q^{2} + 2q^{7} + 32q^{8} + 248q^{16} + 8q^{18} - 24q^{21} - 12q^{22} + 12q^{23} + 32q^{28} - 48q^{32} + 16q^{36} + 16q^{37} - 38q^{42} + 4q^{43} + 64q^{46} + 8q^{51} - 64q^{53} - 4q^{56} + 112q^{57} + 44q^{58} - 24q^{63} + 4q^{67} + 32q^{71} + 20q^{72} - 26q^{77} - 76q^{78} + 80q^{81} - 184q^{86} + 60q^{88} - 16q^{91} + 68q^{92} - 88q^{93} + 120q^{98} + O(q^{100}) \)

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