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

• Label: 91.11.s
• Level: $91$
• Weight: $11$
• Character orbit: 91.s
• Rep. character: $\chi_{91}(12,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $184$
• Newform subspaces: $1$
• Sturm bound: $102$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	91.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(102\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	192	192	0
Cusp forms	184	184	0
Eisenstein series	8	8	0

Trace form

\( 184 q + 480 q^{3} + 47102 q^{4} + 1692048 q^{9} + O(q^{10}) \)

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.s.a	$91$	$11$	91.s	91.s	$6$	$184$	$92$	$57.818$		None		✓	✓	✓	91.11.s.a	$4$	$0$	\(0\)	\(480\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$