Space of modular forms of level 391, weight 1, and Character 391.c

• Label: 391.1.c
• Level: $391$
• Weight: $1$
• Character orbit: 391.c
• Rep. character: $\chi_{391}(390,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $36$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 391 = 17 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	391.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 391 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(36\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(391, [\chi])\).

	Total	New	Old
Modular forms	8	8	0
Cusp forms	6	6	0
Eisenstein series	2	2	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

\( 6 q - 2 q^{2} + 4 q^{4} - 4 q^{8} + 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(391, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
391.1.c.a	$391$	$1$	391.c	391.c	$2$	$3$	$3$	$0.195$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-391}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(-1\)	$1$		\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{5}+(-1+\cdots)q^{7}+\cdots\)
391.1.c.b	$391$	$1$	391.c	391.c	$2$	$3$	$3$	$0.195$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-391}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(1\)	\(1\)	$1$		\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{1}q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)