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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	7	37	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
518.2.a.b	$518$	$2$	518.a	1.a	$1$	$2$	$2$	$4.136$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓	✓	518.2.a.b	$1$	$1$	\(2\)	\(-3\)	\(-3\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-2+\beta )q^{5}+\cdots\)

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