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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	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	19
513.2.a.a	$513$	$2$	513.a	1.a	$1$	$1$	$1$	$4.096$	\(\Q\)	None	✓	✓			513.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{7}+3q^{8}+5q^{11}+\cdots\)
513.2.a.b	$513$	$2$	513.a	1.a	$1$	$1$	$1$	$4.096$	\(\Q\)	None	✓	✓			513.2.a.a	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-2q^{7}-3q^{8}-5q^{11}+\cdots\)
513.2.a.e	$513$	$2$	513.a	1.a	$1$	$3$	$3$	$4.096$	3.3.321.1	None	✓	✓	✓		513.2.a.e	$1$	$1$	\(-1\)	\(0\)	\(-5\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots\)

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