Properties

Label 1575.2.p
Level 1575
Weight 2
Character orbit p
Rep. character \(\chi_{1575}(118,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 116
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.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 35 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 528 124 404
Cusp forms 432 116 316
Eisenstein series 96 8 88

Trace form

\( 116q - 4q^{2} + 4q^{7} + 16q^{8} + O(q^{10}) \) \( 116q - 4q^{2} + 4q^{7} + 16q^{8} - 16q^{11} - 144q^{16} + 28q^{22} - 32q^{23} + 8q^{28} + 48q^{32} + 8q^{37} - 4q^{43} - 52q^{46} + 28q^{53} - 20q^{56} - 12q^{58} - 60q^{67} + 104q^{71} - 28q^{77} + 140q^{86} - 56q^{88} - 56q^{91} - 40q^{92} - 108q^{98} + O(q^{100}) \)

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