Space of modular forms of level 91, weight 10, and Character 91.i

• Label: 91.10.i
• Level: $91$
• Weight: $10$
• Character orbit: 91.i
• Rep. character: $\chi_{91}(34,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $164$
• Newform subspaces: $1$
• Sturm bound: $93$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	91.i (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(93\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(91, [\chi])\).

	Total	New	Old
Modular forms	172	172	0
Cusp forms	164	164	0
Eisenstein series	8	8	0

Trace form

\( 164 q - 4 q^{2} - 1142 q^{7} + 2044 q^{8} - 1023524 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(91, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
91.10.i.a	$91$	$10$	91.i	91.i	$4$	$164$	$82$	$46.868$		None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(-1142\)		$\mathrm{SU}(2)[C_{4}]$