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Properties

Label 912.3.bj
Level $912$
Weight $3$
Character orbit 912.bj
Rep. character $\chi_{912}(335,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 912.bj (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 228 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(912, [\chi])\).

Total New Old
Modular forms 664 160 504
Cusp forms 616 160 456
Eisenstein series 48 0 48

Trace form

\( 160 q + 12 q^{9} + O(q^{10}) \) \( 160 q + 12 q^{9} + 24 q^{13} + 400 q^{25} - 180 q^{33} - 1136 q^{49} + 96 q^{57} - 56 q^{61} - 32 q^{73} - 564 q^{81} + 48 q^{85} - 1080 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(912, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{3}^{\mathrm{old}}(912, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)