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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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3639.1.d.b	$3639$	$1$	3639.d	3639.d	$2$	$1$	$1$	$1.816$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3639}) \)	\(\Q(\sqrt{1213}) \)	✓	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)	$1$		\(q-q^{3}-q^{4}-2q^{7}+q^{9}+q^{12}-2q^{13}+\cdots\)