Space of modular forms of level 91, weight 6, and Character 91.k

• Label: 91.6.k
• Level: $91$
• Weight: $6$
• Character orbit: 91.k
• Rep. character: $\chi_{91}(4,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $90$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	91.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(56\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(91, [\chi])\).

	Total	New	Old
Modular forms	98	98	0
Cusp forms	90	90	0
Eisenstein series	8	8	0

Trace form

\( 90 q - 26 q^{3} - 1410 q^{4} - 6 q^{6} + 121 q^{7} - 3291 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(91, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
91.6.k.a	$91$	$6$	91.k	91.k	$6$	$90$	$45$	$14.595$		None		✓	✓	✓	91.6.k.a	$2$	$0$	\(0\)	\(-26\)	\(0\)	\(121\)		$\mathrm{SU}(2)[C_{6}]$