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Properties

Label 1512.2.cj
Level $1512$
Weight $2$
Character orbit 1512.cj
Rep. character $\chi_{1512}(109,\cdot)$
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.cj (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
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

\( 256 q + O(q^{10}) \) \( 256 q - 16 q^{16} - 20 q^{22} + 128 q^{25} + 22 q^{28} + 40 q^{34} + 6 q^{40} + 26 q^{46} - 8 q^{49} - 26 q^{52} - 36 q^{58} + 36 q^{64} + 90 q^{70} - 8 q^{73} - 48 q^{76} + 64 q^{79} + 98 q^{82} - 16 q^{88} + 30 q^{94} + 48 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{2}^{\mathrm{old}}(1512, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)