Space of modular forms of level 32, weight 5, and Character 32.h

• Label: 32.5.h
• Level: $32$
• Weight: $5$
• Character orbit: 32.h
• Rep. character: $\chi_{32}(3,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $60$
• Newform subspaces: $1$
• Sturm bound: $20$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	32.h (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 32 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(20\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(32, [\chi])\).

	Total	New	Old
Modular forms	68	68	0
Cusp forms	60	60	0
Eisenstein series	8	8	0

Trace form

\( 60 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(32, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
32.5.h.a	$32$	$5$	32.h	32.h	$8$	$60$	$15$	$3.308$		None		✓	32.5.h.a	$2$	$0$	\(-4\)	\(-4\)	\(-4\)	\(-4\)		$\mathrm{SU}(2)[C_{8}]$