Properties

Label 1575.2.ch
Level 1575
Weight 2
Character orbit ch
Rep. character \(\chi_{1575}(82,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 232
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.ch (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 35 \)
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 248 808
Cusp forms 864 232 632
Eisenstein series 192 16 176

Trace form

\( 232q - 2q^{2} + 2q^{7} - 28q^{8} + O(q^{10}) \) \( 232q - 2q^{2} + 2q^{7} - 28q^{8} + 4q^{11} + 84q^{16} + 12q^{17} + 8q^{22} + 2q^{23} + 36q^{26} + 70q^{28} + 12q^{31} + 6q^{32} + 16q^{37} + 28q^{43} - 8q^{46} - 36q^{47} - 24q^{52} - 4q^{53} + 8q^{56} - 66q^{58} + 48q^{61} - 18q^{67} + 120q^{68} + 64q^{71} - 48q^{73} + 40q^{77} - 18q^{82} + 112q^{86} - 16q^{88} - 52q^{91} - 92q^{92} - 54q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database