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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	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	11	17
6171.2.a.bd	$6171$	$2$	6171.a	1.a	$1$	$7$	$7$	$49.276$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	6171.2.a.bd	$1$	$1$	\(-3\)	\(7\)	\(0\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
6171.2.a.be	$6171$	$2$	6171.a	1.a	$1$	$7$	$7$	$49.276$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	6171.2.a.bd	$1$	$0$	\(3\)	\(7\)	\(0\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)