Properties

Label 3150.2.eb
Level 3150
Weight 2
Character orbit eb
Rep. character \(\chi_{3150}(187,\cdot)\)
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.eb (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

\( 3840q + O(q^{10}) \) \( 3840q + 12q^{15} - 480q^{16} - 36q^{17} - 16q^{18} + 16q^{23} + 36q^{27} - 12q^{30} + 60q^{33} - 48q^{35} - 40q^{39} - 4q^{42} + 36q^{45} + 16q^{50} + 40q^{53} - 48q^{57} - 24q^{58} - 8q^{60} - 92q^{63} + 8q^{65} + 420q^{69} + 8q^{72} + 240q^{77} + 16q^{78} - 672q^{83} - 120q^{84} + 300q^{89} + 144q^{90} - 8q^{92} + 60q^{93} - 64q^{95} + 48q^{98} + O(q^{100}) \)

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