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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
847.1.d.a	$847$	$1$	847.d	7.b	$2$	$2$	$2$	$0.423$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$2$		$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{4}+q^{7}-q^{8}+\cdots$
847.1.d.b	$847$	$1$	847.d	7.b	$2$	$2$	$2$	$0.423$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$-2$		$1$		$q+(1-\beta )q^{2}+(1-\beta )q^{4}-q^{7}+q^{8}+\cdots$
847.1.j.a	$847$	$1$	847.j	77.j	$10$	$4$	$1$	$0.423$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-3$	$0$	$0$	$1$		$1$		$q+(-1-\zeta_{10}^{4})q^{2}+(1-\zeta_{10}^{3}+\zeta_{10}^{4}+\cdots)q^{4}+\cdots$
847.1.j.b	$847$	$1$	847.j	77.j	$10$	$4$	$1$	$0.423$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$1$		$1$		$q+(\zeta_{10}+\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{4}+\cdots$
847.1.j.c	$847$	$1$	847.j	77.j	$10$	$4$	$1$	$0.423$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$3$	$0$	$0$	$-1$		$1$		$q+(1+\zeta_{10}^{4})q^{2}+(1-\zeta_{10}^{3}+\zeta_{10}^{4}+\cdots)q^{4}+\cdots$
847.1.o.a	$847$	$1$	847.o	847.o	$22$	$10$	$1$	$0.423$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$		$1$		$q+(-\zeta_{22}^{9}+\zeta_{22}^{10})q^{2}+(-\zeta_{22}^{7}+\cdots)q^{4}+\cdots$
847.1.bb.a	$847$	$1$	847.bb	847.ab	$110$	$40$	$1$	$0.423$	$\Q(\zeta_{55})$	$D_{55}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$1$		$1$		$q+(\zeta_{110}^{8}-\zeta_{110}^{49})q^{2}+(\zeta_{110}^{2}+\zeta_{110}^{16}+\cdots)q^{4}+\cdots$
847.2.a.a	$847$	$2$	847.a	1.a	$1$	$1$	$1$	$6.763$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$2$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}-q^{4}-2q^{5}-2q^{6}+q^{7}+\cdots$
847.2.a.b	$847$	$2$	847.a	1.a	$1$	$1$	$1$	$6.763$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-2q^{4}-q^{5}+q^{7}+6q^{9}+6q^{12}+\cdots$
847.2.a.c	$847$	$2$	847.a	1.a	$1$	$1$	$1$	$6.763$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+3q^{5}-q^{7}-2q^{9}-2q^{12}+\cdots$
847.2.a.d	$847$	$2$	847.a	1.a	$1$	$2$	$2$	$6.763$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-3$	$-1$	$2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+(-1+\beta )q^{3}+3\beta q^{4}+\cdots$
847.2.a.e	$847$	$2$	847.a	1.a	$1$	$2$	$2$	$6.763$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-\beta q^{3}+(1+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots$
847.2.a.f	$847$	$2$	847.a	1.a	$1$	$2$	$2$	$6.763$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-4$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1-\beta )q^{3}+3q^{4}-2q^{5}+(5+\cdots)q^{6}+\cdots$
847.2.a.g	$847$	$2$	847.a	1.a	$1$	$2$	$2$	$6.763$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$-1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-\beta q^{3}+(1+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots$
847.2.a.h	$847$	$2$	847.a	1.a	$1$	$2$	$2$	$6.763$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$3$	$-1$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(-1+\beta )q^{3}+3\beta q^{4}+\cdots$
847.2.a.i	$847$	$2$	847.a	1.a	$1$	$3$	$3$	$6.763$	3.3.568.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$-1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-\beta _{1}q^{3}+(3+\beta _{2})q^{4}+\cdots$
847.2.a.j	$847$	$2$	847.a	1.a	$1$	$3$	$3$	$6.763$	3.3.568.1	$_{}$	None	None	✓	$1$	$0$	$2$	$-1$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-\beta _{1}q^{3}+(3+\beta _{2})q^{4}+\cdots$
847.2.a.k	$847$	$2$	847.a	1.a	$1$	$4$	$4$	$6.763$	4.4.2525.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$-2$	$-6$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
847.2.a.l	$847$	$2$	847.a	1.a	$1$	$4$	$4$	$6.763$	4.4.2525.1	$_{}$	None	None	✓	$1$	$1$	$2$	$-2$	$-6$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
847.2.a.m	$847$	$2$	847.a	1.a	$1$	$6$	$6$	$6.763$	6.6.7674048.1	$_{}$	None	None	✓	$1$	$1$	$-4$	$-2$	$-4$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+\beta _{5}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
847.2.a.n	$847$	$2$	847.a	1.a	$1$	$6$	$6$	$6.763$	6.6.7674048.1	$_{}$	None	None	✓	$1$	$0$	$4$	$-2$	$-4$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+\beta _{5}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
847.2.a.o	$847$	$2$	847.a	1.a	$1$	$8$	$8$	$6.763$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-1$	$4$	$10$	$-8$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1-\beta _{4}-\beta _{7})q^{3}+(1+\beta _{5}+\cdots)q^{4}+\cdots$
847.2.a.p	$847$	$2$	847.a	1.a	$1$	$8$	$8$	$6.763$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$1$	$4$	$10$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1-\beta _{4}-\beta _{7})q^{3}+(1+\beta _{5}+\cdots)q^{4}+\cdots$
847.2.b.a	$847$	$2$	847.b	77.b	$2$	$8$	$8$	$6.763$	8.0.$\cdots$.11	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{2}+\beta _{4})q^{2}-\beta _{3}q^{3}+(-2+\beta _{6}+\cdots)q^{4}+\cdots$
847.2.b.b	$847$	$2$	847.b	77.b	$2$	$8$	$8$	$6.763$	8.0.37515625.1	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 11^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots$
847.2.b.c	$847$	$2$	847.b	77.b	$2$	$8$	$8$	$6.763$	8.0.4956160000.2	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{3}+\beta _{5})q^{2}+\beta _{6}q^{3}+(-1-\beta _{4}+\cdots)q^{4}+\cdots$
847.2.b.d	$847$	$2$	847.b	77.b	$2$	$8$	$8$	$6.763$	8.0.$\cdots$.2	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}-\beta _{1}q^{4}+\beta _{7}q^{5}+(-\beta _{3}-\beta _{5}+\cdots)q^{7}+\cdots$
847.2.b.e	$847$	$2$	847.b	77.b	$2$	$16$	$16$	$6.763$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{3}+\beta _{10})q^{2}+(-\beta _{5}+\beta _{14}+\beta _{15})q^{3}+\cdots$
847.2.b.f	$847$	$2$	847.b	77.b	$2$	$16$	$16$	$6.763$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{5})q^{2}-\beta _{14}q^{3}+(1-\beta _{6}-\beta _{8}+\cdots)q^{4}+\cdots$
847.2.e.a	$847$	$2$	847.e	7.c	$3$	$4$	$2$	$6.763$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$-1$	$-2$	$0$	$10$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots$
847.2.e.b	$847$	$2$	847.e	7.c	$3$	$4$	$2$	$6.763$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$1$	$-2$	$0$	$-10$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots$
847.2.e.c	$847$	$2$	847.e	7.c	$3$	$6$	$3$	$6.763$	$\Q(\zeta_{18})$	$_{}$	None	None		$2$	$0$	$0$	$-3$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\zeta_{18}-\zeta_{18}^{2}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots$
847.2.e.d	$847$	$2$	847.e	7.c	$3$	$6$	$3$	$6.763$	6.0.1783323.2	$_{}$	None	None		$2$	$0$	$0$	$1$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{3}-\beta _{5})q^{2}+\beta _{1}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots$
847.2.e.e	$847$	$2$	847.e	7.c	$3$	$12$	$6$	$6.763$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$2$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{2}-\beta _{6}q^{3}+(-1-\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots$
847.2.e.f	$847$	$2$	847.e	7.c	$3$	$14$	$7$	$6.763$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-3$	$-4$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(\beta _{4}+\beta _{10})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
847.2.e.g	$847$	$2$	847.e	7.c	$3$	$14$	$7$	$6.763$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-3$	$-4$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{4}+\beta _{10})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
847.2.e.h	$847$	$2$	847.e	7.c	$3$	$20$	$10$	$6.763$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$2$	$0$	$-1$	$3$	$2$	$11$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+\beta _{17}q^{3}+(-1-\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots$
847.2.e.i	$847$	$2$	847.e	7.c	$3$	$20$	$10$	$6.763$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$2$	$0$	$1$	$3$	$2$	$-11$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+\beta _{17}q^{3}+(-1-\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots$
847.2.e.j	$847$	$2$	847.e	7.c	$3$	$28$	$14$	$6.763$		$_{}$	None	None		$4$	$0$	$0$	$6$	$8$	$0$			$\mathrm{SU}(2)[C_{3}]$
847.2.f.a	$847$	$2$	847.f	11.c	$5$	$4$	$1$	$6.763$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$-5$	$-6$	$2$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
847.2.f.b	$847$	$2$	847.f	11.c	$5$	$4$	$1$	$6.763$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$-5$	$4$	$2$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
847.2.f.c	$847$	$2$	847.f	11.c	$5$	$4$	$1$	$6.763$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$-4$	$3$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2+\zeta_{10}-\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots$
847.2.f.d	$847$	$2$	847.f	11.c	$5$	$4$	$1$	$6.763$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$-1$	$-2$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-2\zeta_{10}+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\cdots$
847.2.f.e	$847$	$2$	847.f	11.c	$5$	$4$	$1$	$6.763$	$\Q(\zeta_{10})$	$_{}$	None	None		$4$	$0$	$-1$	$-2$	$2$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
847.2.f.f	$847$	$2$	847.f	11.c	$5$	$4$	$1$	$6.763$	$\Q(\zeta_{10})$	$_{}$	None	None		$4$	$0$	$0$	$-1$	$-3$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}^{2}q^{3}+2\zeta_{10}^{3}q^{4}-3\zeta_{10}q^{5}+\cdots$
847.2.f.g	$847$	$2$	847.f	11.c	$5$	$4$	$1$	$6.763$	$\Q(\zeta_{10})$	$_{}$	None	None		$4$	$0$	$0$	$-1$	$-3$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}^{2}q^{3}+2\zeta_{10}^{3}q^{4}-3\zeta_{10}q^{5}+\cdots$
847.2.f.h	$847$	$2$	847.f	11.c	$5$	$4$	$1$	$6.763$	$\Q(\zeta_{10})$	$_{}$	None	None		$4$	$0$	$0$	$3$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-3\zeta_{10}^{2}q^{3}+2\zeta_{10}^{3}q^{4}+\zeta_{10}q^{5}+\cdots$
847.2.f.i	$847$	$2$	847.f	11.c	$5$	$4$	$1$	$6.763$	$\Q(\zeta_{10})$	$_{}$	None	None		$4$	$0$	$0$	$3$	$1$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-3\zeta_{10}^{2}q^{3}+2\zeta_{10}^{3}q^{4}+\zeta_{10}q^{5}+\cdots$
847.2.f.j	$847$	$2$	847.f	11.c	$5$	$4$	$1$	$6.763$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$1$	$-2$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
847.2.f.k	$847$	$2$	847.f	11.c	$5$	$4$	$1$	$6.763$	$\Q(\zeta_{10})$	$_{}$	None	None		$4$	$0$	$1$	$-2$	$2$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+2\zeta_{10}^{2}q^{3}+\cdots$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.