Properties

Label 1512.2.ca
Level 1512
Weight 2
Character orbit ca
Rep. character \(\chi_{1512}(341,\cdot)\)
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.ca (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

\( 184q - 2q^{4} - 2q^{7} + O(q^{10}) \) \( 184q - 2q^{4} - 2q^{7} - 6q^{10} + 18q^{14} - 2q^{16} - 6q^{22} + 6q^{23} + 78q^{25} + 6q^{26} - 8q^{28} + 6q^{34} + 33q^{38} - 18q^{40} + 9q^{44} + 2q^{46} + 12q^{47} - 2q^{49} - 9q^{50} + 21q^{52} - 18q^{56} - 3q^{58} - 12q^{62} - 8q^{64} + 18q^{68} - 27q^{70} - 12q^{73} + 57q^{74} + 12q^{76} - 4q^{79} + 57q^{80} + 27q^{86} + 9q^{88} + 24q^{89} + 36q^{92} + 45q^{98} + O(q^{100}) \)

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