Properties

Label 1512.2.bf
Level 1512
Weight 2
Character orbit bf
Rep. character \(\chi_{1512}(451,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 184
Sturm bound 576

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Defining parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.bf (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

\( 184q + 2q^{2} - 2q^{4} + 8q^{8} + O(q^{10}) \) \( 184q + 2q^{2} - 2q^{4} + 8q^{8} - 6q^{10} - 2q^{11} - 2q^{14} - 2q^{16} + 12q^{17} - 12q^{19} - 24q^{20} - 6q^{22} - 74q^{25} + 42q^{32} - 6q^{34} + 18q^{35} + 33q^{38} + 12q^{40} - 4q^{43} + 21q^{44} + 2q^{46} - 2q^{49} - 19q^{50} + 21q^{52} + 2q^{56} + 5q^{58} - 8q^{64} - 36q^{65} - 4q^{67} - 12q^{68} + 21q^{70} - 12q^{73} - 47q^{74} - 12q^{76} + 63q^{80} - 12q^{82} - 60q^{83} + 31q^{86} + 9q^{88} + 36q^{89} + 20q^{91} + 32q^{92} - 27q^{98} + O(q^{100}) \)

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