Space of modular forms of level 197, weight 3, and Character 197.i

• Label: 197.3.i
• Level: $197$
• Weight: $3$
• Character orbit: 197.i
• Rep. character: $\chi_{197}(2,\cdot)$
• Character field: $\Q(\zeta_{196})$
• Dimension: $2688$
• Newform subspaces: $1$
• Sturm bound: $49$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	197.i (of order \(196\) and degree \(84\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 197 \)
Character field:			\(\Q(\zeta_{196})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(49\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(197, [\chi])\).

	Total	New	Old
Modular forms	2856	2856	0
Cusp forms	2688	2688	0
Eisenstein series	168	168	0

Trace form

\( 2688 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 84 q^{5} - 98 q^{6} - 84 q^{7} - 140 q^{8} - 84 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(197, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
197.3.i.a	$197$	$3$	197.i	197.i	$196$	$2688$	$32$	$5.368$		None		✓	✓	✓	197.3.i.a	$2$	$0$	\(-84\)	\(-84\)	\(-84\)	\(-84\)		$\mathrm{SU}(2)[C_{196}]$