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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	3	7	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3822.2.a.bn	$3822$	$2$	3822.a	1.a	$1$	$2$	$2$	$30.519$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(2\)	\(-2\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+(-2+\beta )q^{5}-q^{6}+\cdots\)
3822.2.a.bq	$3822$	$2$	3822.a	1.a	$1$	$2$	$2$	$30.519$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(2\)	\(-2\)	\(2\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)

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