Properties

Label 1575.2.dg
Level 1575
Weight 2
Character orbit dg
Rep. character \(\chi_{1575}(206,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 640
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.dg (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 525 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1984 640 1344
Cusp forms 1856 640 1216
Eisenstein series 128 0 128

Trace form

\( 640q - 80q^{4} + 8q^{7} + O(q^{10}) \) \( 640q - 80q^{4} + 8q^{7} + 12q^{10} + 80q^{16} + 32q^{22} + 4q^{25} + 100q^{28} + 36q^{31} + 16q^{37} - 24q^{40} + 16q^{43} - 64q^{46} + 16q^{49} + 96q^{58} + 256q^{64} + 32q^{67} + 120q^{70} - 168q^{73} + 8q^{79} - 264q^{82} - 8q^{85} - 84q^{88} + 68q^{91} - 96q^{94} + O(q^{100}) \)

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