Space of modular forms of level 91, weight 5, and Character 91.y

• Label: 91.5.y
• Level: $91$
• Weight: $5$
• Character orbit: 91.y
• Rep. character: $\chi_{91}(15,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $112$
• Newform subspaces: $1$
• Sturm bound: $46$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	91.y (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(46\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(91, [\chi])\).

	Total	New	Old
Modular forms	160	112	48
Cusp forms	144	112	32
Eisenstein series	16	0	16

Trace form

\( 112 q - 24 q^{5} + 132 q^{6} - 252 q^{8} - 1512 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(91, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
91.5.y.a	$91$	$5$	91.y	13.f	$12$	$112$	$28$	$9.407$		None		✓	✓	✓	91.5.y.a	$2$	$0$	\(0\)	\(0\)	\(-24\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{5}^{\mathrm{old}}(91, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(91, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)