Space of modular forms of level 85, weight 4, and Character 85.r

• Label: 85.4.r
• Level: $85$
• Weight: $4$
• Character orbit: 85.r
• Rep. character: $\chi_{85}(12,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $200$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	85.r (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 85 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(85, [\chi])\).

	Total	New	Old
Modular forms	232	232	0
Cusp forms	200	200	0
Eisenstein series	32	32	0

Trace form

\( 200 q - 8 q^{2} - 8 q^{3} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 72 q^{8} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(85, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
85.4.r.a	$85$	$4$	85.r	85.r	$16$	$200$	$25$	$5.015$		None		$2$	$0$	\(-8\)	\(-8\)	\(-8\)	\(-8\)		$\mathrm{SU}(2)[C_{16}]$