Space of modular forms of level 91, weight 8, and Character 91.h

• Label: 91.8.h
• Level: $91$
• Weight: $8$
• Character orbit: 91.h
• Rep. character: $\chi_{91}(16,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $126$
• Newform subspaces: $1$
• Sturm bound: $74$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.h (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(74\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(91, [\chi])\).

	Total	New	Old
Modular forms	134	134	0
Cusp forms	126	126	0
Eisenstein series	8	8	0

Trace form

\( 126 q - 2 q^{2} - 80 q^{3} + 7678 q^{4} - 2 q^{5} - 258 q^{6} + 953 q^{7} - 264 q^{8} - 41707 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(91, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
91.8.h.a	$91$	$8$	91.h	91.h	$3$	$126$	$63$	$28.427$		None		$2$	$0$	\(-2\)	\(-80\)	\(-2\)	\(953\)		$\mathrm{SU}(2)[C_{3}]$