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Level	Weight	Analytic conductor	\(Nk^2\)	Dim.

Bad \(p\)	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	5	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
80.4.a.c	$80$	$4$	80.a	1.a	$1$	$1$	$1$	$4.720$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-4\)	\(5\)	\(16\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{3}+5q^{5}+2^{4}q^{7}-11q^{9}+60q^{11}+\cdots\)
80.4.a.f	$80$	$4$	80.a	1.a	$1$	$1$	$1$	$4.720$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(8\)	\(5\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+8q^{3}+5q^{5}+4q^{7}+37q^{9}-12q^{11}+\cdots\)

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