Properties

Label 1575.2.bu
Level 1575
Weight 2
Character orbit bu
Rep. character \(\chi_{1575}(314,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 320
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.bu (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 525 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 992 320 672
Cusp forms 928 320 608
Eisenstein series 64 0 64

Trace form

\( 320q - 80q^{4} + O(q^{10}) \) \( 320q - 80q^{4} - 80q^{16} + 40q^{22} - 16q^{25} - 60q^{28} + 56q^{46} - 16q^{49} + 120q^{58} - 32q^{64} - 52q^{70} + 16q^{79} + 8q^{85} + 68q^{91} + O(q^{100}) \)

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