Space of modular forms of level 32, weight 8, and Character 32.g

• Label: 32.8.g
• Level: $32$
• Weight: $8$
• Character orbit: 32.g
• Rep. character: $\chi_{32}(5,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $108$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	32.g (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 32 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(32, [\chi])\).

	Total	New	Old
Modular forms	116	116	0
Cusp forms	108	108	0
Eisenstein series	8	8	0

Trace form

\( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(32, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
32.8.g.a	$32$	$8$	32.g	32.g	$8$	$108$	$27$	$9.996$		None		$2$	$0$	\(-4\)	\(-4\)	\(-4\)	\(-4\)		$\mathrm{SU}(2)[C_{8}]$