Space of modular forms of level 8, weight 22, and Character 8.b

• Label: 8.22.b
• Level: $8$
• Weight: $22$
• Character orbit: 8.b
• Rep. character: $\chi_{8}(5,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $22$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(22\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(8, [\chi])\).

	Total	New	Old
Modular forms	22	22	0
Cusp forms	20	20	0
Eisenstein series	2	2	0

Trace form

\( 20 q + 286 q^{2} + 409876 q^{4} + 118236748 q^{6} + 564950496 q^{7} + 3649699336 q^{8} - 62762119220 q^{9} + O(q^{10}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(8, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
8.22.b.a	$8$	$22$	8.b	8.b	$2$	$20$	$20$	$22.358$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(286\)	\(0\)	\(0\)	\(564950496\)	$2^{190}\cdot 3^{14}\cdot 5^{4}\cdot 7^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(14-\beta _{1})q^{2}+(1+3\beta _{1}-\beta _{2})q^{3}+\cdots\)