Properties

Label 1575.2.do
Level 1575
Weight 2
Character orbit do
Rep. character \(\chi_{1575}(89,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 640
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.do (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 525 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1984 640 1344
Cusp forms 1856 640 1216
Eisenstein series 128 0 128

Trace form

\( 640q + 80q^{4} + O(q^{10}) \) \( 640q + 80q^{4} + 12q^{10} + 80q^{16} + 80q^{22} - 20q^{25} + 60q^{28} - 36q^{31} - 96q^{40} + 64q^{46} + 16q^{49} - 120q^{58} - 64q^{64} + 88q^{70} + 240q^{73} + 8q^{79} + 88q^{85} - 180q^{88} - 68q^{91} - 96q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database