Space of modular forms of level 912, weight 1, and Character 912.ce

• Label: 912.1.ce
• Level: $912$
• Weight: $1$
• Character orbit: 912.ce
• Rep. character: $\chi_{912}(143,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $160$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	912.ce (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 228 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(160\)
Trace bound:			\(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(912, [\chi])\).

	Total	New	Old
Modular forms	84	12	72
Cusp forms	12	12	0
Eisenstein series	72	0	72

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(912, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
912.1.ce.a	$912$	$1$	912.ce	228.u	$18$	$6$	$1$	$0.455$	\(\Q(\zeta_{18})\)	$D_{18}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{18}^{8}q^{3}+(\zeta_{18}^{2}-\zeta_{18}^{4})q^{7}-\zeta_{18}^{7}q^{9}+\cdots\)
912.1.ce.b	$912$	$1$	912.ce	228.u	$18$	$6$	$1$	$0.455$	\(\Q(\zeta_{18})\)	$D_{18}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{18}^{8}q^{3}+(-\zeta_{18}^{2}+\zeta_{18}^{4})q^{7}+\cdots\)