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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	3	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
252.8.a.g	$252$	$8$	252.a	1.a	$1$	$4$	$4$	$78.721$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓	✓	✓	252.8.a.g	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-1372\)		$-$	$+$	$+$	$-$	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}-7^{3}q^{7}+(-5\beta _{1}+\beta _{3})q^{11}+\cdots\)

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