Properties

Label 3150.2.ci
Level 3150
Weight 2
Character orbit ci
Rep. character \(\chi_{3150}(407,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 432
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.ci (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 45 \)
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 432 2544
Cusp forms 2784 432 2352
Eisenstein series 192 0 192

Trace form

\( 432q + 8q^{3} + O(q^{10}) \) \( 432q + 8q^{3} - 48q^{11} - 8q^{12} + 216q^{16} - 8q^{18} - 16q^{21} - 24q^{23} - 16q^{27} - 8q^{33} + 16q^{36} - 48q^{37} + 72q^{38} + 192q^{41} + 96q^{47} + 16q^{48} + 176q^{51} + 32q^{57} + 8q^{63} + 88q^{66} - 24q^{67} - 16q^{72} - 32q^{78} + 240q^{81} - 96q^{82} + 120q^{83} + 72q^{86} + 40q^{87} + 96q^{91} - 24q^{92} + 32q^{93} - 72q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database