Properties

Label 1512.2.cs
Level 1512
Weight 2
Character orbit cs
Rep. character \(\chi_{1512}(253,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 144
Sturm bound 576

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.cs (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1512, [\chi])\).

Total New Old
Modular forms 600 144 456
Cusp forms 552 144 408
Eisenstein series 48 0 48

Trace form

\( 144q - 12q^{8} + O(q^{10}) \) \( 144q - 12q^{8} - 14q^{20} - 24q^{23} + 72q^{25} + 56q^{26} + 10q^{32} + 12q^{34} + 28q^{38} + 12q^{40} + 8q^{41} + 64q^{44} + 24q^{46} - 72q^{49} - 46q^{50} - 18q^{52} + 18q^{58} - 48q^{62} - 60q^{64} - 78q^{68} + 112q^{71} - 12q^{76} - 88q^{80} - 36q^{82} + 42q^{86} - 24q^{88} - 66q^{92} + 6q^{94} + 64q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1512, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1512, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1512, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database