Space of modular forms of level 791, weight 1, and Character 791.x

• Label: 791.1.x
• Level: $791$
• Weight: $1$
• Character orbit: 791.x
• Rep. character: $\chi_{791}(111,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $76$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 791 = 7 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	791.x (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 791 \)
Character field:			\(\Q(\zeta_{28})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(76\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(791, [\chi])\).

	Total	New	Old
Modular forms	36	36	0
Cusp forms	12	12	0
Eisenstein series	24	24	0

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

\( 12 q - 12 q^{4} - 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(791, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
791.1.x.a	$791$	$1$	791.x	791.x	$28$	$12$	$1$	$0.395$	\(\Q(\zeta_{28})\)	$D_{28}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+(-\zeta_{28}^{3}+\zeta_{28}^{7})q^{2}+(-1+\zeta_{28}^{6}+\cdots)q^{4}+\cdots\)