Properties

Label 1575.2.bg
Level 1575
Weight 2
Character orbit bg
Rep. character \(\chi_{1575}(424,\cdot)\)
Character field \(\Q(\zeta_{6})\)
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.bg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 35 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 116q + 58q^{4} + O(q^{10}) \) \( 116q + 58q^{4} + 8q^{11} - 10q^{14} - 50q^{16} - 12q^{19} - 18q^{26} - 8q^{29} + 14q^{31} + 64q^{34} + 52q^{41} - 24q^{44} + 40q^{46} + 24q^{49} + 114q^{56} + 18q^{59} + 38q^{61} - 168q^{64} - 76q^{71} + 38q^{74} - 148q^{76} + 26q^{79} - 60q^{86} + 56q^{89} - 106q^{91} + 6q^{94} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database