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

• Label: 91.10.w
• Level: $91$
• Weight: $10$
• Character orbit: 91.w
• Rep. character: $\chi_{91}(19,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $328$
• Newform subspaces: $1$
• Sturm bound: $93$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	91.w (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{12})\)
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	344	344	0
Cusp forms	328	328	0
Eisenstein series	16	16	0

Trace form

\( 328 q - 2 q^{2} - 6 q^{4} - 6 q^{5} + 3072 q^{6} + 1136 q^{7} + 1016 q^{8} - 2047036 q^{9} + O(q^{10}) \)

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.w.a	$91$	$10$	91.w	91.w	$12$	$328$	$82$	$46.868$		None		$2$	$0$	\(-2\)	\(0\)	\(-6\)	\(1136\)		$\mathrm{SU}(2)[C_{12}]$