Properties

Label 1575.2.v
Level 1575
Weight 2
Character orbit v
Rep. character \(\chi_{1575}(299,\cdot)\)
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.v (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

\( 280q - 138q^{4} - 12q^{6} + 10q^{9} + O(q^{10}) \) \( 280q - 138q^{4} - 12q^{6} + 10q^{9} + 18q^{14} - 130q^{16} + 12q^{19} - 6q^{21} + 24q^{24} - 12q^{26} - 24q^{29} - 6q^{31} + 12q^{34} + 36q^{39} + 12q^{41} - 84q^{44} + 16q^{46} - 22q^{49} + 6q^{51} + 90q^{54} + 120q^{56} + 6q^{59} - 42q^{61} + 248q^{64} - 18q^{66} + 24q^{69} - 2q^{79} - 34q^{81} - 66q^{84} + 114q^{89} - 36q^{91} + 6q^{94} - 42q^{96} - 34q^{99} + O(q^{100}) \)

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