Properties

Label 1575.2.bm
Level 1575
Weight 2
Character orbit bm
Rep. character \(\chi_{1575}(776,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 292
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.bm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 63 \)
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 504 316 188
Cusp forms 456 292 164
Eisenstein series 48 24 24

Trace form

\( 292q + 6q^{2} + 142q^{4} + 12q^{9} + O(q^{10}) \) \( 292q + 6q^{2} + 142q^{4} + 12q^{9} - 24q^{11} - 18q^{14} - 138q^{16} + 2q^{18} + 6q^{21} + 10q^{22} + 12q^{23} - 8q^{28} - 30q^{29} + 12q^{32} + 78q^{36} + 12q^{37} + 30q^{42} - 6q^{43} + 8q^{46} - 4q^{49} - 30q^{51} - 114q^{56} - 18q^{57} - 2q^{58} + 28q^{63} - 240q^{64} + 16q^{67} - 116q^{72} - 24q^{74} + 78q^{77} + 144q^{78} + 10q^{79} - 48q^{81} + 54q^{84} - 72q^{86} - 34q^{88} - 4q^{91} - 6q^{92} - 42q^{93} - 84q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database