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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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	13	103
8034.2.a.x	$8034$	$2$	8034.a	1.a	$1$	$13$	$13$	$64.152$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$0$	\(-13\)	\(13\)	\(1\)	\(-1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+\beta _{3}q^{7}+\cdots\)
8034.2.a.y	$8034$	$2$	8034.a	1.a	$1$	$13$	$13$	$64.152$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$0$	\(13\)	\(-13\)	\(3\)	\(5\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+\beta _{8}q^{5}-q^{6}+\beta _{1}q^{7}+\cdots\)