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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad \(p\)	Char.	Primitive character	Character order	Coefficient field

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

\(Nk^2\)	Coefficient ring index	Coefficient ring gens.	Projective image	Projective image type

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	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	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		31	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
31.6.a.a	$31$	$6$	31.a	1.a	$1$	$5$	$5$	$4.972$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓	31.6.a.a	$1$	$1$	\(-9\)	\(-20\)	\(-72\)	\(-108\)		$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{2}+(-4-\beta _{1}-\beta _{3})q^{3}+\cdots\)

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