Properties

Label 1575.2.cx
Level 1575
Weight 2
Character orbit cx
Rep. character \(\chi_{1575}(8,\cdot)\)
Character field \(\Q(\zeta_{20})\)
Dimension 480
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.cx (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 75 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1984 480 1504
Cusp forms 1856 480 1376
Eisenstein series 128 0 128

Trace form

\( 480q + O(q^{10}) \) \( 480q - 32q^{10} + 8q^{13} + 120q^{16} + 80q^{19} + 96q^{22} + 16q^{25} + 40q^{34} - 8q^{37} + 56q^{40} - 80q^{43} - 72q^{52} + 32q^{55} + 56q^{58} - 320q^{64} - 64q^{67} - 16q^{70} - 120q^{73} - 160q^{79} + 120q^{82} - 40q^{85} - 80q^{88} + 160q^{94} - 24q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database