Properties

Label 1512.2.cq
Level 1512
Weight 2
Character orbit cq
Rep. character \(\chi_{1512}(37,\cdot)\)
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.cq (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

\( 184q + 2q^{2} - 2q^{4} - 2q^{7} + 8q^{8} + O(q^{10}) \) \( 184q + 2q^{2} - 2q^{4} - 2q^{7} + 8q^{8} + 2q^{10} + 4q^{14} - 2q^{16} + 4q^{17} - 6q^{20} + 2q^{22} - 2q^{23} + 78q^{25} + 4q^{26} - 8q^{28} - 4q^{31} + 2q^{32} + 5q^{38} - 4q^{40} + 4q^{41} - 17q^{44} - 6q^{46} + 84q^{47} - 2q^{49} + 31q^{50} + 9q^{52} + 4q^{55} + 16q^{56} + 5q^{58} - 32q^{62} - 8q^{64} + 44q^{65} + 12q^{68} + 5q^{70} + 16q^{71} - 4q^{73} - 19q^{74} - 6q^{76} - 4q^{79} + 11q^{80} + 23q^{86} - 7q^{88} - 4q^{89} + 48q^{92} - 18q^{94} + 44q^{95} - 4q^{97} + 83q^{98} + O(q^{100}) \)

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