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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	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
2847.1.g.a	$2847$	$1$	2847.g	2847.g	$2$	$1$	$1$	$1.421$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2847}) \)	\(\Q(\sqrt{949}) \)	✓	$4$	$0$	\(0\)	\(1\)	\(0\)	\(-2\)	$1$		\(q+q^{3}-q^{4}-2q^{7}+q^{9}-q^{12}+q^{13}+\cdots\)
2847.1.g.b	$2847$	$1$	2847.g	2847.g	$2$	$1$	$1$	$1.421$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2847}) \)	\(\Q(\sqrt{949}) \)	✓	$4$	$0$	\(0\)	\(1\)	\(0\)	\(2\)	$1$		\(q+q^{3}-q^{4}+2q^{7}+q^{9}-q^{12}-q^{13}+\cdots\)

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