Properties

Label 1575.2.s
Level 1575
Weight 2
Character orbit s
Rep. character \(\chi_{1575}(499,\cdot)\)
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.s (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

\( 280q - 268q^{4} - 20q^{6} + 14q^{9} + O(q^{10}) \) \( 280q - 268q^{4} - 20q^{6} + 14q^{9} + 6q^{11} + 14q^{14} + 244q^{16} + 4q^{19} - 8q^{21} + 56q^{24} + 24q^{26} + 24q^{29} - 4q^{31} - 40q^{36} + 54q^{39} + 24q^{41} - 24q^{46} - 10q^{49} + 62q^{51} - 38q^{54} - 96q^{56} + 100q^{59} + 20q^{61} - 184q^{64} - 24q^{66} + 60q^{69} - 60q^{71} - 50q^{74} - 4q^{76} + 4q^{79} - 54q^{81} - 4q^{84} - 54q^{86} - 26q^{89} + 20q^{91} + 84q^{94} - 190q^{96} + 50q^{99} + O(q^{100}) \)

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