Properties

Label 1575.2.bp
Level 1575
Weight 2
Character orbit bp
Rep. character \(\chi_{1575}(949,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 280
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.bp (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 315 \)
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 504 296 208
Cusp forms 456 280 176
Eisenstein series 48 16 32

Trace form

\( 280q + 134q^{4} - 20q^{6} + 2q^{9} + O(q^{10}) \) \( 280q + 134q^{4} - 20q^{6} + 2q^{9} - 12q^{11} - 10q^{14} - 122q^{16} + 4q^{19} + 10q^{21} - 28q^{24} + 24q^{26} + 24q^{29} + 2q^{31} - 40q^{36} + 24q^{41} - 24q^{46} + 26q^{49} - 10q^{51} - 26q^{54} + 12q^{56} - 50q^{59} - 10q^{61} - 184q^{64} + 102q^{66} + 60q^{69} - 60q^{71} + 100q^{74} - 4q^{76} - 2q^{79} + 78q^{81} + 38q^{84} + 108q^{86} - 26q^{89} + 20q^{91} - 42q^{94} - 58q^{96} + 50q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database