Properties

Label 1575.2.cm
Level 1575
Weight 2
Character orbit cm
Rep. character \(\chi_{1575}(107,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 192
Sturm bound 480

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1575.cm (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 105 \)
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 1056 192 864
Cusp forms 864 192 672
Eisenstein series 192 0 192

Trace form

\( 192q - 8q^{7} + O(q^{10}) \) \( 192q - 8q^{7} + 96q^{16} + 48q^{22} - 88q^{28} + 16q^{31} + 16q^{37} + 16q^{43} + 80q^{52} + 88q^{58} - 56q^{61} + 32q^{67} + 88q^{73} + 320q^{76} + 56q^{82} - 120q^{88} - 104q^{91} - 208q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database