Properties

Label 912.3.ce
Level $912$
Weight $3$
Character orbit 912.ce
Rep. character $\chi_{912}(143,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $480$
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.ce (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 228 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1992 480 1512
Cusp forms 1848 480 1368
Eisenstein series 144 0 144

Trace form

\( 480 q - 36 q^{9} + O(q^{10}) \) \( 480 q - 36 q^{9} - 24 q^{13} + 180 q^{33} + 1680 q^{49} - 336 q^{61} - 552 q^{73} + 252 q^{81} - 144 q^{85} + 1080 q^{97} + O(q^{100}) \)

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

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