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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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2947.1.b.a	$2947$	$1$	2947.b	2947.b	$2$	$1$	$1$	$1.471$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2947}) \)	\(\Q(\sqrt{421}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$		\(q+q^{4}+q^{7}+q^{9}-2q^{11}+q^{16}+q^{25}+\cdots\)
2947.1.b.b	$2947$	$1$	2947.b	2947.b	$2$	$2$	$2$	$1.471$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-2947}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+q^{4}-q^{7}+q^{9}-\beta q^{13}+q^{16}+\beta q^{19}+\cdots\)