Space of modular forms of level 197, weight 4, and Character 197.e

• Label: 197.4.e
• Level: $197$
• Weight: $4$
• Character orbit: 197.e
• Rep. character: $\chi_{197}(6,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $288$
• Newform subspaces: $1$
• Sturm bound: $66$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	197.e (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 197 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(66\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(197, [\chi])\).

	Total	New	Old
Modular forms	300	300	0
Cusp forms	288	288	0
Eisenstein series	12	12	0

Trace form

\( 288 q - 7 q^{2} - 7 q^{3} + 159 q^{4} - 7 q^{5} + 26 q^{6} - 53 q^{7} + 49 q^{8} + 391 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(197, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
197.4.e.a	$197$	$4$	197.e	197.e	$14$	$288$	$48$	$11.623$		None		✓	✓	✓	197.4.e.a	$2$	$0$	\(-7\)	\(-7\)	\(-7\)	\(-53\)		$\mathrm{SU}(2)[C_{14}]$