Space of modular forms of level 991, weight 1, and Character 991.b

• Label: 991.1.b
• Level: $991$
• Weight: $1$
• Character orbit: 991.b
• Rep. character: $\chi_{991}(990,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $82$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 991 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	991.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 991 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(82\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(991, [\chi])\).

	Total	New	Old
Modular forms	9	9	0
Cusp forms	8	8	0
Eisenstein series	1	1	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q - q^{2} + 7 q^{4} - q^{5} - 2 q^{8} + 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(991, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
991.1.b.a	$991$	$1$	991.b	991.b	$2$	$8$	$8$	$0.495$	\(\Q(\zeta_{34})^+\)	$D_{17}$	\(\Q(\sqrt{-991}) \)	None	✓	✓	✓	✓	991.1.b.a	$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+\beta _{6}q^{2}+(1-\beta _{5})q^{4}+\beta _{2}q^{5}+(-\beta _{1}+\cdots)q^{8}+\cdots\)