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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	5	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
315.10.a.n	$315$	$10$	315.a	1.a	$1$	$8$	$8$	$162.236$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓	✓	✓	315.10.a.n	$1$	$1$	\(-25\)	\(0\)	\(5000\)	\(19208\)		$+$	$-$	$-$	$+$	$2^{10}\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q+(-3-\beta _{1})q^{2}+(233+5\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

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