Properties

Label 3150.2.s
Level 3150
Weight 2
Character orbit s
Rep. character \(\chi_{3150}(299,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 288
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.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 315 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 1488 288 1200
Cusp forms 1392 288 1104
Eisenstein series 96 0 96

Trace form

\( 288q - 144q^{4} - 12q^{9} + O(q^{10}) \) \( 288q - 144q^{4} - 12q^{9} - 12q^{14} - 144q^{16} - 8q^{21} - 12q^{24} + 12q^{29} - 12q^{39} - 12q^{41} + 24q^{44} - 12q^{46} + 24q^{49} + 20q^{51} + 36q^{61} + 288q^{64} + 48q^{66} - 84q^{69} - 12q^{79} + 76q^{81} + 28q^{84} - 72q^{89} + 12q^{96} + 72q^{99} + O(q^{100}) \)

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