Properties

Label 3150.2.ei
Level 3150
Weight 2
Character orbit ei
Rep. character \(\chi_{3150}(13,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 3840
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.ei (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 1575 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 11648 3840 7808
Cusp forms 11392 3840 7552
Eisenstein series 256 0 256

Trace form

\( 3840q + O(q^{10}) \) \( 3840q - 24q^{15} - 480q^{16} + 8q^{18} - 8q^{23} - 48q^{30} + 24q^{35} - 40q^{39} + 44q^{42} - 32q^{50} + 160q^{53} + 72q^{57} - 24q^{58} - 8q^{60} + 148q^{63} + 8q^{65} - 16q^{72} - 144q^{77} + 16q^{78} + 60q^{84} - 8q^{92} + 120q^{93} + 128q^{95} + 48q^{98} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database