Properties

Label 1512.2.bm
Level 1512
Weight 2
Character orbit bm
Rep. character \(\chi_{1512}(107,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 256
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.bm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 168 \)
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 600 256 344
Cusp forms 552 256 296
Eisenstein series 48 0 48

Trace form

\( 256q + O(q^{10}) \) \( 256q + 16q^{16} + 44q^{22} - 128q^{25} - 10q^{28} - 40q^{34} + 26q^{40} + 6q^{46} - 8q^{49} - 14q^{52} - 36q^{58} + 12q^{64} + 64q^{67} + 114q^{70} + 8q^{73} - 48q^{76} - 94q^{82} + 8q^{88} + 24q^{91} - 6q^{94} - 16q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1512, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database