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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	11
1089.2.a.n	$1089$	$2$	1089.a	1.a	$1$	$2$	$2$	$8.696$	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-3}) \)	✓	✓			1089.2.a.n	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}-\beta q^{7}+4\beta q^{13}+4q^{16}-3\beta q^{19}+\cdots\)
1089.2.a.v	$1089$	$2$	1089.a	1.a	$1$	$4$	$4$	$8.696$	4.4.4400.1	None	✓		✓		99.2.f.c	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{1}q^{5}+(-3+\cdots)q^{7}+\cdots\)

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