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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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3145.1.x.a	$3145$	$1$	3145.x	3145.x	$4$	$4$	$2$	$1.570$	\(\Q(\zeta_{8})\)	$D_{4}$	None	\(\Q(\sqrt{629}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{9}-q^{16}+\cdots\)