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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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Results (4 matches)

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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	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
171.2.a.a	$171$	$2$	171.a	1.a	$1$	$1$	$1$	$1.365$	\(\Q\)	None	✓				57.2.a.c	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+2q^{5}+3q^{8}-2q^{10}+\cdots\)
171.2.a.c	$171$	$2$	171.a	1.a	$1$	$1$	$1$	$1.365$	\(\Q\)	None	✓				57.2.a.b	$1$	$0$	\(2\)	\(0\)	\(-1\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}+3q^{7}-2q^{10}+\cdots\)
171.2.a.d	$171$	$2$	171.a	1.a	$1$	$1$	$1$	$1.365$	\(\Q\)	None	✓				57.2.a.a	$1$	$0$	\(2\)	\(0\)	\(3\)	\(-5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+3q^{5}-5q^{7}+6q^{10}+\cdots\)
171.2.a.e	$171$	$2$	171.a	1.a	$1$	$4$	$4$	$1.365$	4.4.13068.1	None	✓	✓	✓	✓	171.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{3})q^{4}+(\beta _{1}+\beta _{2})q^{5}+\cdots\)

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