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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		8009	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8009.2.a.a	$8009$	$2$	8009.a	1.a	$1$	$306$	$306$	$63.952$		None	✓	✓	✓	✓	8009.2.a.a	$1$	$1$	\(-13\)	\(-25\)	\(-25\)	\(-102\)		$+$	$+$		$\mathrm{SU}(2)$
8009.2.a.b	$8009$	$2$	8009.a	1.a	$1$	$361$	$361$	$63.952$		None	✓	✓	✓	✓	8009.2.a.b	$1$	$0$	\(10\)	\(23\)	\(21\)	\(106\)		$-$	$-$		$\mathrm{SU}(2)$

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