Space of modular forms of level 91, weight 11, and Character 91.b

• Label: 91.11.b
• Level: $91$
• Weight: $11$
• Character orbit: 91.b
• Rep. character: $\chi_{91}(90,\cdot)$
• Character field: $\Q$
• Dimension: $90$
• Newform subspaces: $3$
• Sturm bound: $102$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 11 \)
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:			\(102\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(91, [\chi])\).

	Total	New	Old
Modular forms	94	94	0
Cusp forms	90	90	0
Eisenstein series	4	4	0

Trace form

\( 90 q - 43012 q^{4} - 1534590 q^{9} + O(q^{10}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(91, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
91.11.b.a	$91$	$11$	91.b	91.b	$2$	$1$	$1$	$57.818$	\(\Q\)	\(\Q(\sqrt{-91}) \)	✓	✓			91.11.b.a	$2$	$0$	\(0\)	\(0\)	\(-6243\)	\(16807\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{10}q^{4}-6243q^{5}+7^{5}q^{7}+3^{10}q^{9}+\cdots\)
91.11.b.b	$91$	$11$	91.b	91.b	$2$	$1$	$1$	$57.818$	\(\Q\)	\(\Q(\sqrt{-91}) \)	✓	✓			91.11.b.a	$2$	$0$	\(0\)	\(0\)	\(6243\)	\(-16807\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{10}q^{4}+6243q^{5}-7^{5}q^{7}+3^{10}q^{9}+\cdots\)
91.11.b.c	$91$	$11$	91.b	91.b	$2$	$88$	$88$	$57.818$		None		✓	✓		91.11.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$