Properties

Label 1512.2.bt
Level 1512
Weight 2
Character orbit bt
Rep. character \(\chi_{1512}(611,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 184
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.bt (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 504 \)
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 600 200 400
Cusp forms 552 184 368
Eisenstein series 48 16 32

Trace form

\( 184q - 2q^{4} + O(q^{10}) \) \( 184q - 2q^{4} - 6q^{10} + 6q^{11} - 12q^{14} - 2q^{16} - 4q^{19} + 6q^{20} + 2q^{22} - 74q^{25} + 6q^{26} - 4q^{34} - 30q^{35} - 39q^{38} + 6q^{40} + 12q^{41} - 4q^{43} - 9q^{44} - 6q^{46} - 2q^{49} + 21q^{50} + 9q^{52} + 24q^{56} - 3q^{58} - 8q^{64} - 4q^{67} + 42q^{68} - 3q^{70} - 4q^{73} - 27q^{74} + 2q^{76} - 87q^{80} - 4q^{82} + 72q^{83} + 27q^{86} - 7q^{88} + 24q^{89} - 36q^{91} + 36q^{92} - 18q^{94} - 4q^{97} - 57q^{98} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database