Properties

Label 1575.2.ck
Level 1575
Weight 2
Character orbit ck
Rep. character \(\chi_{1575}(218,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 432
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.ck (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 45 \)
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 432 576
Cusp forms 912 432 480
Eisenstein series 96 0 96

Trace form

\( 432q - 4q^{3} + O(q^{10}) \) \( 432q - 4q^{3} + 24q^{11} + 16q^{12} + 216q^{16} + 64q^{18} + 8q^{21} + 24q^{23} + 32q^{27} + 60q^{32} + 16q^{33} + 32q^{36} + 24q^{37} - 72q^{38} - 96q^{41} + 40q^{42} + 96q^{46} - 12q^{47} - 104q^{48} - 88q^{51} + 4q^{57} - 8q^{63} + 40q^{66} + 12q^{67} + 64q^{72} + 48q^{76} - 72q^{78} - 184q^{81} + 96q^{82} - 120q^{83} - 72q^{86} - 116q^{87} + 48q^{88} - 48q^{91} - 156q^{92} + 44q^{93} + 192q^{96} + 60q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database