Properties

Label 1575.2.ed
Level 1575
Weight 2
Character orbit ed
Rep. character \(\chi_{1575}(53,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 1280
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.ed (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 525 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 3968 1280 2688
Cusp forms 3712 1280 2432
Eisenstein series 256 0 256

Trace form

\( 1280q - 8q^{7} + O(q^{10}) \) \( 1280q - 8q^{7} - 8q^{10} - 160q^{16} - 112q^{22} + 16q^{25} + 32q^{28} + 16q^{37} + 40q^{40} + 16q^{43} + 80q^{52} + 32q^{55} + 88q^{58} + 32q^{67} - 48q^{70} + 88q^{73} + 216q^{82} - 16q^{85} + 120q^{88} + 352q^{97} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database