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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1231.1.b.a	$1231$	$1$	1231.b	1231.b	$2$	$1$	$1$	$0.614$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1231}) \)	None	✓	✓			1231.1.b.a	$2$	$0$	\(-1\)	\(0\)	\(2\)	\(-1\)		$1$		\(q-q^{2}+2q^{5}-q^{7}+q^{8}+q^{9}-2q^{10}+\cdots\)
1231.1.b.b	$1231$	$1$	1231.b	1231.b	$2$	$3$	$3$	$0.614$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-1231}) \)	None	✓	✓			1231.1.b.b	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)		$1$		\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{2}q^{7}+\cdots\)
1231.1.b.c	$1231$	$1$	1231.b	1231.b	$2$	$9$	$9$	$0.614$	\(\Q(\zeta_{54})^+\)	$D_{27}$	\(\Q(\sqrt{-1231}) \)	None	✓	✓	✓		1231.1.b.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{6}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
1231.2.a.a	$1231$	$2$	1231.a	1.a	$1$	$38$	$38$	$9.830$		$_{}$	None	None	✓	✓	✓	✓	1231.2.a.a	$1$	$1$	\(-6\)	\(-5\)	\(-23\)	\(-8\)	$+$		$\mathrm{SU}(2)$
1231.2.a.b	$1231$	$2$	1231.a	1.a	$1$	$64$	$64$	$9.830$		$_{}$	None	None	✓	✓	✓	✓	1231.2.a.b	$1$	$0$	\(7\)	\(5\)	\(27\)	\(4\)	$-$		$\mathrm{SU}(2)$
1231.4.a.a	$1231$	$4$	1231.a	1.a	$1$	$140$	$140$	$72.631$		$_{}$	None	None	✓	✓	✓	✓	1231.4.a.a	$1$	$1$	\(-17\)	\(-22\)	\(-141\)	\(-75\)	$-$		$\mathrm{SU}(2)$
1231.4.a.b	$1231$	$4$	1231.a	1.a	$1$	$167$	$167$	$72.631$		$_{}$	None	None	✓	✓	✓	✓	1231.4.a.b	$1$	$0$	\(15\)	\(20\)	\(139\)	\(65\)	$+$		$\mathrm{SU}(2)$

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