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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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
110.2.a.a	$110$	$2$	110.a	1.a	$1$	$1$	$1$	$0.878$	$\Q$	None	✓	✓	✓	✓	110.2.a.a	$1$	$0$	$-1$	$1$	$-1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+5q^{7}+\cdots$
110.2.a.b	$110$	$2$	110.a	1.a	$1$	$1$	$1$	$0.878$	$\Q$	None	✓	✓	✓	✓	110.2.a.b	$1$	$0$	$1$	$-1$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots$
110.2.a.c	$110$	$2$	110.a	1.a	$1$	$1$	$1$	$0.878$	$\Q$	None	✓	✓	✓	✓	110.2.a.c	$1$	$0$	$1$	$1$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
110.2.a.d	$110$	$2$	110.a	1.a	$1$	$2$	$2$	$0.878$	$\Q(\sqrt{33})$	None	✓	✓	✓	✓	110.2.a.d	$1$	$0$	$-2$	$-1$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+\beta q^{7}+\cdots$
110.2.b.a	$110$	$2$	110.b	5.b	$2$	$2$	$2$	$0.878$	$\Q(\sqrt{-1})$	None		✓			110.2.b.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+i q^{3}-q^{4}+(i-2)q^{5}+\cdots$
110.2.b.b	$110$	$2$	110.b	5.b	$2$	$2$	$2$	$0.878$	$\Q(\sqrt{-1})$	None		✓			110.2.b.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-2 i q^{3}-q^{4}+(-2 i+1)q^{5}+\cdots$
110.2.b.c	$110$	$2$	110.b	5.b	$2$	$2$	$2$	$0.878$	$\Q(\sqrt{-1})$	None		✓			110.2.b.c	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+3 i q^{3}-q^{4}+(-i+2)q^{5}+\cdots$
110.2.f.a	$110$	$2$	110.f	55.e	$4$	$4$	$2$	$0.878$	$\Q(\zeta_{8})$	None		✓			110.2.f.a	$4$	$0$	$0$	$-4$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
110.2.f.b	$110$	$2$	110.f	55.e	$4$	$4$	$2$	$0.878$	$\Q(\zeta_{8})$	None		✓			110.2.f.b	$2$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+(1-\zeta_{8}+\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
110.2.f.c	$110$	$2$	110.f	55.e	$4$	$4$	$2$	$0.878$	$\Q(\zeta_{8})$	None		✓			110.2.f.b	$2$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+(1+\zeta_{8}+\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
110.2.g.a	$110$	$2$	110.g	11.c	$5$	$4$	$1$	$0.878$	$\Q(\zeta_{10})$	None		✓			110.2.g.a	$2$	$0$	$-1$	$4$	$1$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
110.2.g.b	$110$	$2$	110.g	11.c	$5$	$4$	$1$	$0.878$	$\Q(\zeta_{10})$	None		✓			110.2.g.b	$2$	$0$	$1$	$4$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(\zeta_{10}+\cdots)q^{3}+\cdots$
110.2.g.c	$110$	$2$	110.g	11.c	$5$	$8$	$2$	$0.878$	8.0.682515625.5	None		✓	✓		110.2.g.c	$2$	$0$	$2$	$-4$	$-2$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{2}+\beta _{3}-\beta _{7})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$
110.2.j.a	$110$	$2$	110.j	55.j	$10$	$8$	$2$	$0.878$	$\Q(\zeta_{20})$	None		✓			110.2.j.a	$4$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\zeta_{20}q^{2}+(-2\zeta_{20}-2\zeta_{20}^{5})q^{3}+\cdots$
110.2.j.b	$110$	$2$	110.j	55.j	$10$	$16$	$4$	$0.878$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓		110.2.j.b	$4$	$0$	$0$	$0$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q-\beta _{6}q^{2}+(-\beta _{6}-\beta _{10}-\beta _{12})q^{3}+\cdots$
110.2.k.a	$110$	$2$	110.k	55.l	$20$	$48$	$6$	$0.878$		None		✓	✓	✓	110.2.k.a	$4$	$0$	$0$	$-4$	$-8$	$-20$			$\mathrm{SU}(2)[C_{20}]$
110.3.c.a	$110$	$3$	110.c	55.d	$2$	$4$	$4$	$2.997$	$\Q(\sqrt{2}, \sqrt{-13})$	None		✓			110.3.c.a	$4$	$0$	$0$	$0$	$20$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}+5q^{5}+2\beta _{3}q^{6}+\cdots$
110.3.c.b	$110$	$3$	110.c	55.d	$2$	$8$	$8$	$2.997$	8.0.$\cdots$.7	None		✓	✓		110.3.c.b	$4$	$0$	$0$	$0$	$-10$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+2q^{4}+(-1+\beta _{5}+\cdots)q^{5}+\cdots$
110.3.d.a	$110$	$3$	110.d	11.b	$2$	$8$	$8$	$2.997$	8.0.4956160000.2	None		✓	✓	✓	110.3.d.a	$2$	$0$	$0$	$-8$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(-1+\beta _{1}+\beta _{3})q^{3}-2q^{4}+\cdots$
110.3.e.a	$110$	$3$	110.e	5.c	$4$	$8$	$4$	$2.997$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓			110.3.e.a	$2$	$0$	$-8$	$6$	$12$	$-12$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{3})q^{2}+(1+\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots$
110.3.e.b	$110$	$3$	110.e	5.c	$4$	$12$	$6$	$2.997$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓		110.3.e.b	$2$	$0$	$12$	$-2$	$-4$	$12$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{2})q^{2}-\beta _{6}q^{3}+2\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
110.3.h.a	$110$	$3$	110.h	11.d	$10$	$16$	$4$	$2.997$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			110.3.h.a	$2$	$0$	$0$	$-6$	$20$	$10$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q-\beta _{8}q^{2}+(-1-\beta _{3}-\beta _{5}+\beta _{7}+\beta _{8}+\cdots)q^{3}+\cdots$
110.3.h.b	$110$	$3$	110.h	11.d	$10$	$16$	$4$	$2.997$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			110.3.h.b	$2$	$0$	$0$	$14$	$-20$	$-10$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{12}q^{2}+(-\beta _{1}+\beta _{4}+\beta _{6}+2\beta _{9}+\cdots)q^{3}+\cdots$
110.3.i.a	$110$	$3$	110.i	55.h	$10$	$48$	$12$	$2.997$		None		✓	✓	✓	110.3.i.a	$4$	$0$	$0$	$0$	$-10$	$0$			$\mathrm{SU}(2)[C_{10}]$
110.3.l.a	$110$	$3$	110.l	55.k	$20$	$48$	$6$	$2.997$		None		✓			110.3.l.a	$4$	$0$	$-12$	$2$	$4$	$38$			$\mathrm{SU}(2)[C_{20}]$
110.3.l.b	$110$	$3$	110.l	55.k	$20$	$48$	$6$	$2.997$		None		✓			110.3.l.b	$4$	$0$	$12$	$2$	$-12$	$14$			$\mathrm{SU}(2)[C_{20}]$
110.4.a.a	$110$	$4$	110.a	1.a	$1$	$1$	$1$	$6.490$	$\Q$	None	✓	✓			110.4.a.a	$1$	$0$	$-2$	$-7$	$5$	$-35$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-7q^{3}+4q^{4}+5q^{5}+14q^{6}+\cdots$
110.4.a.b	$110$	$4$	110.a	1.a	$1$	$1$	$1$	$6.490$	$\Q$	None	✓	✓	✓	✓	110.4.a.b	$1$	$1$	$-2$	$4$	$-5$	$-30$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots$
110.4.a.c	$110$	$4$	110.a	1.a	$1$	$1$	$1$	$6.490$	$\Q$	None	✓	✓			110.4.a.c	$1$	$0$	$-2$	$4$	$5$	$20$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{3}+4q^{4}+5q^{5}-8q^{6}+\cdots$
110.4.a.d	$110$	$4$	110.a	1.a	$1$	$1$	$1$	$6.490$	$\Q$	None	✓	✓			110.4.a.d	$1$	$0$	$2$	$-8$	$-5$	$26$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-8q^{3}+4q^{4}-5q^{5}-2^{4}q^{6}+\cdots$
110.4.a.e	$110$	$4$	110.a	1.a	$1$	$1$	$1$	$6.490$	$\Q$	None	✓	✓	✓	✓	110.4.a.e	$1$	$1$	$2$	$-4$	$-5$	$-22$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots$
110.4.a.f	$110$	$4$	110.a	1.a	$1$	$1$	$1$	$6.490$	$\Q$	None	✓	✓			110.4.a.f	$1$	$0$	$2$	$1$	$5$	$23$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+4q^{4}+5q^{5}+2q^{6}+\cdots$
110.4.a.g	$110$	$4$	110.a	1.a	$1$	$1$	$1$	$6.490$	$\Q$	None	✓	✓			110.4.a.g	$1$	$0$	$2$	$7$	$-5$	$11$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+7q^{3}+4q^{4}-5q^{5}+14q^{6}+\cdots$
110.4.a.h	$110$	$4$	110.a	1.a	$1$	$1$	$1$	$6.490$	$\Q$	None	✓	✓			110.4.a.h	$1$	$0$	$2$	$8$	$5$	$-12$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+8q^{3}+4q^{4}+5q^{5}+2^{4}q^{6}+\cdots$
110.4.a.i	$110$	$4$	110.a	1.a	$1$	$2$	$2$	$6.490$	$\Q(\sqrt{177})$	None	✓	✓	✓	✓	110.4.a.i	$1$	$0$	$-4$	$7$	$-10$	$27$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(4-\beta )q^{3}+4q^{4}-5q^{5}+(-8+\cdots)q^{6}+\cdots$
110.4.b.a	$110$	$4$	110.b	5.b	$2$	$2$	$2$	$6.490$	$\Q(\sqrt{-1})$	None		✓			110.4.b.a	$2$	$0$	$0$	$0$	$-20$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{2}+9 i q^{3}-4 q^{4}+(-5 i-10)q^{5}+\cdots$
110.4.b.b	$110$	$4$	110.b	5.b	$2$	$4$	$4$	$6.490$	$\Q(i, \sqrt{89})$	None		✓			110.4.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-\beta _{2}q^{3}-4q^{4}+(3\beta _{2}+\beta _{3})q^{5}+\cdots$
110.4.b.c	$110$	$4$	110.b	5.b	$2$	$8$	$8$	$6.490$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓	✓		110.4.b.c	$2$	$0$	$0$	$0$	$16$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-4q^{4}+(2+\beta _{2}+\cdots)q^{5}+\cdots$
110.4.f.a	$110$	$4$	110.f	55.e	$4$	$36$	$18$	$6.490$		None		✓	✓	✓	110.4.f.a	$4$	$0$	$0$	$-8$	$-32$	$0$			$\mathrm{SU}(2)[C_{4}]$
110.4.g.a	$110$	$4$	110.g	11.c	$5$	$8$	$2$	$6.490$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓			110.4.g.a	$2$	$0$	$4$	$-7$	$-10$	$-15$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+2\beta _{4}q^{2}+(-2\beta _{2}-2\beta _{3}+\beta _{7})q^{3}+\cdots$
110.4.g.b	$110$	$4$	110.g	11.c	$5$	$12$	$3$	$6.490$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			110.4.g.b	$2$	$0$	$-6$	$15$	$15$	$15$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+2\beta _{4}q^{2}+(2-\beta _{1}+2\beta _{4})q^{3}-4\beta _{7}q^{4}+\cdots$
110.4.g.c	$110$	$4$	110.g	11.c	$5$	$12$	$3$	$6.490$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			110.4.g.c	$2$	$0$	$6$	$-1$	$15$	$38$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(2-2\beta _{2}-2\beta _{5}-2\beta _{8})q^{2}-\beta _{4}q^{3}+\cdots$
110.4.g.d	$110$	$4$	110.g	11.c	$5$	$16$	$4$	$6.490$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓		110.4.g.d	$2$	$0$	$-8$	$-3$	$-20$	$-38$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q-2\beta _{8}q^{2}+(-1-\beta _{2}-\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots$
110.4.j.a	$110$	$4$	110.j	55.j	$10$	$72$	$18$	$6.490$		None		✓	✓	✓	110.4.j.a	$4$	$0$	$0$	$0$	$24$	$0$			$\mathrm{SU}(2)[C_{10}]$
110.4.k.a	$110$	$4$	110.k	55.l	$20$	$144$	$18$	$6.490$		None		✓	✓	✓	110.4.k.a	$4$	$0$	$0$	$8$	$32$	$-40$			$\mathrm{SU}(2)[C_{20}]$
110.5.c.a	$110$	$5$	110.c	55.d	$2$	$24$	$24$	$11.371$		None		✓	✓	✓	110.5.c.a	$4$	$0$	$0$	$0$	$-42$	$0$			$\mathrm{SU}(2)[C_{2}]$
110.5.d.a	$110$	$5$	110.d	11.b	$2$	$16$	$16$	$11.371$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓	✓	110.5.d.a	$2$	$0$	$0$	$16$	$0$	$0$		$2^{24}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+(1-\beta _{2})q^{3}-8q^{4}-\beta _{6}q^{5}+\cdots$
110.5.e.a	$110$	$5$	110.e	5.c	$4$	$20$	$10$	$11.371$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓			110.5.e.a	$2$	$0$	$-40$	$-26$	$8$	$-48$		$2^{9}\cdot 5^{5}\cdot 11^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2-2\beta _{3})q^{2}+(-1+\beta _{3}+\beta _{6}+\cdots)q^{3}+\cdots$
110.5.e.b	$110$	$5$	110.e	5.c	$4$	$20$	$10$	$11.371$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓			110.5.e.b	$2$	$0$	$40$	$6$	$40$	$48$		$2^{9}\cdot 5^{3}\cdot 11^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(2-2\beta _{2})q^{2}+\beta _{3}q^{3}-8\beta _{2}q^{4}+(2+\cdots)q^{5}+\cdots$
110.5.h.a	$110$	$5$	110.h	11.d	$10$	$32$	$8$	$11.371$		None		✓			110.5.h.a	$2$	$0$	$0$	$-18$	$-200$	$-60$			$\mathrm{SU}(2)[C_{10}]$

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