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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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3851.1.b.a	$3851$	$1$	3851.b	3851.b	$2$	$2$	$2$	$1.922$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-3851}) \)	None	✓	$2$	$0$	\(0\)	\(-1\)	\(4\)	\(0\)	$1$		\(q+(-1+\beta )q^{3}+q^{4}+2q^{5}+(1-\beta )q^{9}+\cdots\)
3851.1.b.b	$3851$	$1$	3851.b	3851.b	$2$	$10$	$10$	$1.922$	\(\Q(\zeta_{50})^+\)	$D_{25}$	\(\Q(\sqrt{-3851}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(-5\)	\(0\)	$1$		\(q-\beta _{1}q^{3}+q^{4}+(-1+\beta _{5})q^{5}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)