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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
19.6.a.b	$19$	$6$	19.a	1.a	$1$	$1$	$1$	$3.047$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(-1\)	\(-24\)	\(-167\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}-28q^{4}-24q^{5}+2q^{6}+\cdots\)
19.6.a.c	$19$	$6$	19.a	1.a	$1$	$2$	$2$	$3.047$	\(\Q(\sqrt{177}) \)	None	✓	$1$	$1$	\(-7\)	\(-7\)	\(-133\)	\(72\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-3-\beta )q^{2}+(-5+3\beta )q^{3}+(21+\cdots)q^{4}+\cdots\)

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