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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	5
675.2.a.g	$675$	$2$	675.a	1.a	$1$	$1$	$1$	$5.390$	\(\Q\)	None	✓	✓			675.2.a.b	$1$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-3q^{8}-5q^{11}-5q^{13}+\cdots\)
675.2.a.j	$675$	$2$	675.a	1.a	$1$	$2$	$2$	$5.390$	\(\Q(\sqrt{5}) \)	\(\Q(\sqrt{-15}) \)	✓				135.2.b.a	$2$	$1$	\(-3\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+(-1-\beta )q^{2}+3\beta q^{4}+(-1-4\beta )q^{8}+\cdots\)
675.2.a.l	$675$	$2$	675.a	1.a	$1$	$2$	$2$	$5.390$	\(\Q(\sqrt{2}) \)	None	✓				135.2.b.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-3q^{7}-2\beta q^{8}-3\beta q^{11}-3q^{13}+\cdots\)

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