Space of modular forms of level 943, weight 1, and Character 943.f

• Label: 943.1.f
• Level: $943$
• Weight: $1$
• Character orbit: 943.f
• Rep. character: $\chi_{943}(91,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $84$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 943 = 23 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	943.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 943 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(84\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(943, [\chi])\).

	Total	New	Old
Modular forms	10	10	0
Cusp forms	6	6	0
Eisenstein series	4	4	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

\( 6 q - 6 q^{4} + 6 q^{6} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(943, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
943.1.f.a	$943$	$1$	943.f	943.f	$4$	$2$	$1$	$0.471$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-23}) \)	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q+iq^{2}+(-1-i)q^{3}-3q^{4}+(2-2i+\cdots)q^{6}+\cdots\)
943.1.f.b	$943$	$1$	943.f	943.f	$4$	$4$	$2$	$0.471$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-23}) \)	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q+\zeta_{12}^{3}q^{2}+(-\zeta_{12}+\zeta_{12}^{2})q^{3}+(-\zeta_{12}^{4}+\cdots)q^{6}+\cdots\)