Properties

Label 1512.2.y
Level 1512
Weight 2
Character orbit y
Rep. character \(\chi_{1512}(773,\cdot)\)
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.y (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

\( 184q + 3q^{2} + q^{4} - 2q^{7} + O(q^{10}) \) \( 184q + 3q^{2} + q^{4} - 2q^{7} - 6q^{10} + 3q^{14} + q^{16} - 6q^{22} - 156q^{25} - 6q^{26} - 8q^{28} - 6q^{31} + 33q^{32} - 6q^{34} + 66q^{38} - 9q^{44} + 2q^{46} + 6q^{47} - 2q^{49} - 9q^{50} - 60q^{56} + 6q^{58} + 12q^{62} - 8q^{64} + 6q^{65} + 36q^{68} + 30q^{70} - 12q^{73} - 12q^{76} + 2q^{79} - 57q^{80} - 18q^{88} - 24q^{89} + 36q^{92} - 3q^{94} - 54q^{95} - 45q^{98} + O(q^{100}) \)

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