Space of modular forms of level 91, weight 9, and Character 91.b

• Label: 91.9.b
• Level: $91$
• Weight: $9$
• Character orbit: 91.b
• Rep. character: $\chi_{91}(90,\cdot)$
• Character field: $\Q$
• Dimension: $74$
• Newform subspaces: $3$
• Sturm bound: $84$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	91.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(84\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(91, [\chi])\).

	Total	New	Old
Modular forms	78	78	0
Cusp forms	74	74	0
Eisenstein series	4	4	0

Trace form

\( 74 q - 9732 q^{4} - 170478 q^{9} + O(q^{10}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(91, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
91.9.b.a	$91$	$9$	91.b	91.b	$2$	$1$	$1$	$37.071$	\(\Q\)	\(\Q(\sqrt{-91}) \)	✓	✓			91.9.b.a	$2$	$0$	\(0\)	\(0\)	\(-431\)	\(-2401\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{8}q^{4}-431q^{5}-7^{4}q^{7}+3^{8}q^{9}+\cdots\)
91.9.b.b	$91$	$9$	91.b	91.b	$2$	$1$	$1$	$37.071$	\(\Q\)	\(\Q(\sqrt{-91}) \)	✓	✓			91.9.b.a	$2$	$0$	\(0\)	\(0\)	\(431\)	\(2401\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{8}q^{4}+431q^{5}+7^{4}q^{7}+3^{8}q^{9}+\cdots\)
91.9.b.c	$91$	$9$	91.b	91.b	$2$	$72$	$72$	$37.071$		None		✓	✓		91.9.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$