Properties

Label 3150.2.eh
Level 3150
Weight 2
Character orbit eh
Rep. character \(\chi_{3150}(113,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 2880
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.eh (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 225 \)
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 2880 8768
Cusp forms 11392 2880 8512
Eisenstein series 256 0 256

Trace form

\( 2880q + 8q^{3} + O(q^{10}) \) \( 2880q + 8q^{3} - 8q^{12} + 8q^{15} - 360q^{16} - 8q^{18} - 24q^{20} - 24q^{23} + 96q^{25} - 16q^{27} - 8q^{33} - 48q^{37} + 72q^{38} - 40q^{39} + 80q^{45} + 96q^{47} + 16q^{48} - 48q^{55} + 32q^{57} + 120q^{59} + 40q^{60} - 32q^{63} - 24q^{65} - 24q^{67} - 16q^{72} + 32q^{75} + 168q^{78} - 80q^{81} - 96q^{82} + 120q^{83} - 48q^{85} + 240q^{87} + 40q^{90} - 24q^{92} + 72q^{93} + 120q^{95} - 72q^{97} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database