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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	5	89
4005.2.a.i	$4005$	$2$	4005.a	1.a	$1$	$3$	$3$	$31.980$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(1+\beta _{2})q^{7}+\cdots\)
4005.2.a.j	$4005$	$2$	4005.a	1.a	$1$	$3$	$3$	$31.980$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(-3\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)