Properties

Label 3150.2.cl
Level 3150
Weight 2
Character orbit cl
Rep. character \(\chi_{3150}(893,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 576
Sturm bound 1440

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Defining parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.cl (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3150, [\chi])\).

Total New Old
Modular forms 2976 576 2400
Cusp forms 2784 576 2208
Eisenstein series 192 0 192

Trace form

\( 576q - 16q^{6} + O(q^{10}) \) \( 576q - 16q^{6} - 48q^{11} - 576q^{16} + 36q^{17} + 8q^{18} - 24q^{23} - 36q^{27} - 40q^{33} - 24q^{41} + 4q^{42} + 24q^{46} - 48q^{51} + 24q^{56} + 48q^{57} + 12q^{58} + 48q^{61} + 52q^{63} + 36q^{68} - 8q^{72} - 96q^{77} + 16q^{78} - 32q^{81} - 76q^{87} + 24q^{92} + 16q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database