Properties

Label 3150.2.el
Level 3150
Weight 2
Character orbit el
Rep. character \(\chi_{3150}(103,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 3840
Sturm bound 1440

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.el (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

\( 3840q + O(q^{10}) \) \( 3840q + 12q^{15} + 960q^{16} - 36q^{17} + 8q^{18} - 8q^{23} - 36q^{27} - 12q^{30} - 48q^{35} + 80q^{39} - 4q^{42} + 192q^{45} + 16q^{50} + 40q^{53} - 48q^{57} + 12q^{58} + 16q^{60} + 112q^{63} - 16q^{65} - 144q^{68} - 420q^{69} + 8q^{72} + 384q^{75} - 96q^{77} + 16q^{78} + 672q^{83} + 60q^{84} + 36q^{87} + 300q^{89} - 144q^{90} - 8q^{92} + 48q^{93} + 128q^{95} + 48q^{98} + O(q^{100}) \)

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