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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	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
38.8.a.a	$38$	$8$	38.a	1.a	$1$	$1$	$1$	$11.871$	\(\Q\)	None	✓	$1$	$0$	\(-8\)	\(77\)	\(440\)	\(951\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-8q^{2}+77q^{3}+2^{6}q^{4}+440q^{5}+\cdots\)
38.8.a.b	$38$	$8$	38.a	1.a	$1$	$2$	$2$	$11.871$	\(\Q(\sqrt{2737}) \)	None	✓	$1$	$0$	\(-16\)	\(-61\)	\(175\)	\(-2592\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-8q^{2}+(-30-\beta )q^{3}+2^{6}q^{4}+(95+\cdots)q^{5}+\cdots\)

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