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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad \(p\)	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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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					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		197	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
197.2.a.a	$197$	$2$	197.a	1.a	$1$	$1$	$1$	$1.573$	\(\Q\)	None	✓	✓			197.2.a.a	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(-3\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-3q^{7}-3q^{9}+4q^{11}+\cdots\)
197.2.a.b	$197$	$2$	197.a	1.a	$1$	$5$	$5$	$1.573$	5.5.24217.1	None	✓	✓	✓		197.2.a.b	$1$	$1$	\(0\)	\(-8\)	\(-4\)	\(-10\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{2}+(-2+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)

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