Space of modular forms of level 64, weight 8, and Character 64.i

• Label: 64.8.i
• Level: $64$
• Weight: $8$
• Character orbit: 64.i
• Rep. character: $\chi_{64}(5,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $440$
• Newform subspaces: $1$
• Sturm bound: $64$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	64.i (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 64 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(64\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(64, [\chi])\).

	Total	New	Old
Modular forms	456	456	0
Cusp forms	440	440	0
Eisenstein series	16	16	0

Trace form

\( 440 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(64, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
64.8.i.a	$64$	$8$	64.i	64.i	$16$	$440$	$55$	$19.993$		None		$2$	$0$	\(-8\)	\(-8\)	\(-8\)	\(-8\)		$\mathrm{SU}(2)[C_{16}]$