Space of modular forms of level 8, weight 16, and Character 8.b

• Label: 8.16.b
• Level: $8$
• Weight: $16$
• Character orbit: 8.b
• Rep. character: $\chi_{8}(5,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 16 \)
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:			\(16\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(8, [\chi])\).

	Total	New	Old
Modular forms	16	16	0
Cusp forms	14	14	0
Eisenstein series	2	2	0

Trace form

\( 14 q - 90 q^{2} + 51444 q^{4} - 189428 q^{6} - 1647088 q^{7} + 1889640 q^{8} - 57395630 q^{9} + O(q^{10}) \)

Decomposition of \(S_{16}^{\mathrm{new}}(8, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
8.16.b.a	$8$	$16$	8.b	8.b	$2$	$14$	$14$	$11.415$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(-90\)	\(0\)	\(0\)	\(-1647088\)	$2^{91}\cdot 3^{6}\cdot 5^{4}\cdot 31^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-6-\beta _{1})q^{2}+\beta _{2}q^{3}+(3672+5\beta _{1}+\cdots)q^{4}+\cdots\)