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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				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1166.2.a.a	$1166$	$2$	1166.a	1.a	$1$	$1$	$1$	$9.311$	\(\Q\)	None	✓	✓			1166.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}-q^{8}-3q^{9}+2q^{10}+\cdots\)
1166.2.a.b	$1166$	$2$	1166.a	1.a	$1$	$1$	$1$	$9.311$	\(\Q\)	None	✓	✓			1166.2.a.b	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots\)
1166.2.a.c	$1166$	$2$	1166.a	1.a	$1$	$1$	$1$	$9.311$	\(\Q\)	None	✓	✓			1166.2.a.c	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
1166.2.a.d	$1166$	$2$	1166.a	1.a	$1$	$1$	$1$	$9.311$	\(\Q\)	None	✓	✓			1166.2.a.d	$1$	$0$	\(1\)	\(-1\)	\(-3\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+4q^{7}+\cdots\)
1166.2.a.e	$1166$	$2$	1166.a	1.a	$1$	$2$	$2$	$9.311$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓		1166.2.a.e	$1$	$1$	\(-2\)	\(-2\)	\(0\)	\(4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta )q^{3}+q^{4}+(1-\beta )q^{6}+\cdots\)
1166.2.a.f	$1166$	$2$	1166.a	1.a	$1$	$3$	$3$	$9.311$	3.3.148.1	None	✓	✓	✓	✓	1166.2.a.f	$1$	$1$	\(3\)	\(-3\)	\(-6\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta _{2})q^{3}+q^{4}-2q^{5}+\cdots\)
1166.2.a.g	$1166$	$2$	1166.a	1.a	$1$	$3$	$3$	$9.311$	\(\Q(\zeta_{14})^+\)	None	✓	✓			1166.2.a.g	$1$	$0$	\(3\)	\(4\)	\(4\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1+\beta _{1})q^{3}+q^{4}+(2-\beta _{1}+\beta _{2})q^{5}+\cdots\)
1166.2.a.h	$1166$	$2$	1166.a	1.a	$1$	$4$	$4$	$9.311$	4.4.6224.1	None	✓	✓	✓	✓	1166.2.a.h	$1$	$1$	\(-4\)	\(0\)	\(2\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{1}-\beta _{3})q^{5}+\cdots\)
1166.2.a.i	$1166$	$2$	1166.a	1.a	$1$	$4$	$4$	$9.311$	4.4.4352.1	None	✓	✓	✓	✓	1166.2.a.i	$1$	$1$	\(4\)	\(-4\)	\(-4\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
1166.2.a.j	$1166$	$2$	1166.a	1.a	$1$	$4$	$4$	$9.311$	4.4.67348.1	None	✓	✓	✓		1166.2.a.j	$1$	$0$	\(4\)	\(2\)	\(1\)	\(6\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+\beta _{3}q^{5}+(1+\cdots)q^{6}+\cdots\)
1166.2.a.k	$1166$	$2$	1166.a	1.a	$1$	$6$	$6$	$9.311$	6.6.390126348.1	None	✓	✓	✓		1166.2.a.k	$1$	$0$	\(-6\)	\(-1\)	\(-1\)	\(-2\)	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{3}q^{3}+q^{4}-\beta _{2}q^{5}-\beta _{3}q^{6}+\cdots\)
1166.2.a.l	$1166$	$2$	1166.a	1.a	$1$	$7$	$7$	$9.311$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓		1166.2.a.l	$1$	$0$	\(7\)	\(4\)	\(4\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{5})q^{5}+\cdots\)
1166.2.a.m	$1166$	$2$	1166.a	1.a	$1$	$8$	$8$	$9.311$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓	✓		1166.2.a.m	$1$	$0$	\(-8\)	\(-1\)	\(3\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots\)
1166.2.c.a	$1166$	$2$	1166.c	53.b	$2$	$2$	$2$	$9.311$	\(\Q(\sqrt{-1}) \)	None		✓			1166.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+i q^{3}-q^{4}-i q^{5}+q^{6}+\cdots\)
1166.2.c.b	$1166$	$2$	1166.c	53.b	$2$	$22$	$22$	$9.311$		None		✓			1166.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
1166.2.c.c	$1166$	$2$	1166.c	53.b	$2$	$22$	$22$	$9.311$		None		✓			1166.2.c.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)			$\mathrm{SU}(2)[C_{2}]$
1166.4.a.a	$1166$	$4$	1166.a	1.a	$1$	$13$	$13$	$68.796$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	✓	✓	✓	1166.4.a.a	$1$	$1$	\(-26\)	\(4\)	\(-5\)	\(5\)	$-$	$2^{4}\cdot 7$	$\mathrm{SU}(2)$	\(q-2q^{2}+\beta _{1}q^{3}+4q^{4}+\beta _{3}q^{5}-2\beta _{1}q^{6}+\cdots\)
1166.4.a.b	$1166$	$4$	1166.a	1.a	$1$	$13$	$13$	$68.796$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	✓	✓	✓	1166.4.a.b	$1$	$1$	\(26\)	\(-16\)	\(-35\)	\(-43\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-1-\beta _{1})q^{3}+4q^{4}+(-3+\cdots)q^{5}+\cdots\)
1166.4.a.c	$1166$	$4$	1166.a	1.a	$1$	$15$	$15$	$68.796$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	✓	✓	✓	1166.4.a.c	$1$	$1$	\(-30\)	\(1\)	\(5\)	\(-25\)	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q-2q^{2}+\beta _{1}q^{3}+4q^{4}+\beta _{2}q^{5}-2\beta _{1}q^{6}+\cdots\)
1166.4.a.d	$1166$	$4$	1166.a	1.a	$1$	$15$	$15$	$68.796$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	✓	✓	✓	1166.4.a.d	$1$	$1$	\(30\)	\(-13\)	\(-25\)	\(-45\)	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(-2+\cdots)q^{5}+\cdots\)
1166.4.a.e	$1166$	$4$	1166.a	1.a	$1$	$18$	$18$	$68.796$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓	✓	✓	1166.4.a.e	$1$	$0$	\(-36\)	\(1\)	\(-10\)	\(3\)	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(-1-\beta _{7}+\cdots)q^{5}+\cdots\)
1166.4.a.f	$1166$	$4$	1166.a	1.a	$1$	$18$	$18$	$68.796$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓	✓	✓	1166.4.a.f	$1$	$0$	\(36\)	\(17\)	\(20\)	\(39\)	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(1+\beta _{5}+\cdots)q^{5}+\cdots\)
1166.4.a.g	$1166$	$4$	1166.a	1.a	$1$	$19$	$19$	$68.796$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	✓	✓	✓	1166.4.a.g	$1$	$0$	\(-38\)	\(4\)	\(0\)	\(5\)	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q-2q^{2}+\beta _{1}q^{3}+4q^{4}+\beta _{9}q^{5}-2\beta _{1}q^{6}+\cdots\)
1166.4.a.h	$1166$	$4$	1166.a	1.a	$1$	$19$	$19$	$68.796$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	✓	✓	✓	1166.4.a.h	$1$	$0$	\(38\)	\(14\)	\(30\)	\(69\)	$+$	$2^{8}\cdot 3$	$\mathrm{SU}(2)$	\(q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(2+\beta _{3}+\cdots)q^{5}+\cdots\)

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