Properties

Label 3150.2.ch
Level 3150
Weight 2
Character orbit ch
Rep. character \(\chi_{3150}(643,\cdot)\)
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.ch (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

\( 576q + O(q^{10}) \) \( 576q - 16q^{11} + 288q^{16} + 8q^{18} - 8q^{23} - 16q^{36} + 44q^{42} - 96q^{46} + 160q^{53} + 8q^{56} - 88q^{57} - 24q^{58} + 48q^{63} - 32q^{71} - 16q^{72} + 16q^{77} + 16q^{78} + 16q^{81} + 32q^{86} - 8q^{92} + 120q^{93} + 48q^{98} + O(q^{100}) \)

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