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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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3467.1.b.a	$3467$	$1$	3467.b	3467.b	$2$	$9$	$9$	$1.730$	\(\Q(\zeta_{38})^+\)	$D_{19}$	\(\Q(\sqrt{-3467}) \)	None	✓	✓	✓	✓	3467.1.b.a	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)		$1$		\(q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots\)
3467.2.a.a	$3467$	$2$	3467.a	1.a	$1$	$1$	$1$	$27.684$	\(\Q\)	$_{}$	None	None	✓	✓			3467.2.a.a	$1$	$0$	\(0\)	\(1\)	\(0\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+2q^{7}-2q^{9}-4q^{11}+\cdots\)
3467.2.a.b	$3467$	$2$	3467.a	1.a	$1$	$126$	$126$	$27.684$		$_{}$	None	None	✓	✓	✓	✓	3467.2.a.b	$1$	$1$	\(-11\)	\(-25\)	\(-32\)	\(-27\)	$+$		$\mathrm{SU}(2)$
3467.2.a.c	$3467$	$2$	3467.a	1.a	$1$	$162$	$162$	$27.684$		$_{}$	None	None	✓	✓	✓		3467.2.a.c	$1$	$0$	\(9\)	\(24\)	\(32\)	\(23\)	$-$		$\mathrm{SU}(2)$

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