Properties

Label 1575.2.bi
Level 1575
Weight 2
Character orbit bi
Rep. character \(\chi_{1575}(274,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 216
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.bi (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 45 \)
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 504 216 288
Cusp forms 456 216 240
Eisenstein series 48 0 48

Trace form

\( 216q + 108q^{4} + 12q^{9} + O(q^{10}) \) \( 216q + 108q^{4} + 12q^{9} - 20q^{11} + 8q^{14} - 108q^{16} + 4q^{21} - 4q^{24} + 64q^{26} + 16q^{29} + 12q^{31} - 24q^{34} + 60q^{36} + 20q^{39} - 16q^{41} + 16q^{44} - 48q^{46} + 108q^{49} - 8q^{51} - 16q^{54} - 24q^{56} - 48q^{59} - 168q^{64} + 76q^{66} + 60q^{69} + 104q^{71} + 44q^{74} + 24q^{76} + 12q^{79} - 28q^{81} + 32q^{84} - 8q^{86} - 80q^{89} + 24q^{91} + 48q^{94} - 228q^{96} - 104q^{99} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database