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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
1064.1.p.a	$1064$	$1$	1064.p	1064.p	$2$	$2$	$2$	$0.531$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-266}) $	None	✓	$2$	$0$	$-2$	$-1$	$1$	$-2$		$1$		$q-q^{2}+(-1+\beta )q^{3}+q^{4}+\beta q^{5}+(1+\cdots)q^{6}+\cdots$
1064.1.p.b	$1064$	$1$	1064.p	1064.p	$2$	$2$	$2$	$0.531$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-266}) $	None	✓	$2$	$0$	$-2$	$1$	$-1$	$2$		$1$		$q-q^{2}+(1-\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots$
1064.1.p.c	$1064$	$1$	1064.p	1064.p	$2$	$2$	$2$	$0.531$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-266}) $	None	✓	$2$	$0$	$2$	$-1$	$-1$	$2$		$1$		$q+q^{2}+(-1+\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots$
1064.1.p.d	$1064$	$1$	1064.p	1064.p	$2$	$2$	$2$	$0.531$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-266}) $	None	✓	$2$	$0$	$2$	$1$	$1$	$-2$		$1$		$q+q^{2}+(1-\beta )q^{3}+q^{4}+\beta q^{5}+(1-\beta )q^{6}+\cdots$
1064.1.bg.a	$1064$	$1$	1064.bg	1064.ag	$6$	$2$	$1$	$0.531$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-14}) $	None		$4$	$0$	$-1$	$-2$	$1$	$2$		$1$		$q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\cdots$
1064.1.bg.b	$1064$	$1$	1064.bg	1064.ag	$6$	$2$	$1$	$0.531$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-14}) $	None		$4$	$0$	$-1$	$2$	$-1$	$2$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots$
1064.1.bg.c	$1064$	$1$	1064.bg	1064.ag	$6$	$4$	$2$	$0.531$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$2$	$0$	$0$	$-4$		$1$		$q-\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}+(-\zeta_{12}^{3}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots$
1064.1.br.a	$1064$	$1$	1064.br	1064.ar	$6$	$6$	$3$	$0.531$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{6}q^{2}+(-\zeta_{18}-\zeta_{18}^{5})q^{3}-\zeta_{18}^{3}q^{4}+\cdots$
1064.1.br.b	$1064$	$1$	1064.br	1064.ar	$6$	$6$	$3$	$0.531$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$3$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{6}q^{2}+(-\zeta_{18}^{2}-\zeta_{18}^{4})q^{3}+\cdots$
1064.1.br.c	$1064$	$1$	1064.br	1064.ar	$6$	$8$	$4$	$0.531$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{24}^{5}q^{2}+(-\zeta_{24}-\zeta_{24}^{7})q^{3}+\zeta_{24}^{10}q^{4}+\cdots$
1064.1.cd.a	$1064$	$1$	1064.cd	133.r	$6$	$4$	$2$	$0.531$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+(\beta _{1}-\beta _{3})q^{3}-\beta _{2}q^{7}+(1-\beta _{2})q^{9}+\cdots$
1064.1.ef.a	$1064$	$1$	1064.ef	1064.df	$18$	$6$	$1$	$0.531$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-14}) $	None		$4$	$0$	$0$	$0$	$-3$	$-3$		$1$		$q-\zeta_{18}^{5}q^{2}-\zeta_{18}^{2}q^{3}-\zeta_{18}q^{4}+(-\zeta_{18}^{3}+\cdots)q^{5}+\cdots$
1064.1.ef.b	$1064$	$1$	1064.ef	1064.df	$18$	$6$	$1$	$0.531$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-14}) $	None		$4$	$0$	$0$	$0$	$3$	$-3$		$1$		$q-\zeta_{18}^{5}q^{2}+\zeta_{18}^{2}q^{3}-\zeta_{18}q^{4}+(\zeta_{18}^{3}+\cdots)q^{5}+\cdots$
1064.1.ef.c	$1064$	$1$	1064.ef	1064.df	$18$	$12$	$2$	$0.531$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$0$	$0$	$0$	$6$		$1$		$q+\zeta_{36}^{10}q^{2}+(-\zeta_{36}-\zeta_{36}^{7})q^{3}+\cdots$
1064.2.a.a	$1064$	$2$	1064.a	1.a	$1$	$2$	$2$	$8.496$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(1-2\beta )q^{5}+q^{7}+(-1+\cdots)q^{9}+\cdots$
1064.2.a.b	$1064$	$2$	1064.a	1.a	$1$	$2$	$2$	$8.496$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-q^{5}-q^{7}+\beta q^{9}+(-1+\beta )q^{11}+\cdots$
1064.2.a.c	$1064$	$2$	1064.a	1.a	$1$	$2$	$2$	$8.496$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-1+2\beta )q^{5}+q^{7}+(-2+\cdots)q^{9}+\cdots$
1064.2.a.d	$1064$	$2$	1064.a	1.a	$1$	$2$	$2$	$8.496$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}-q^{7}+(-2+\beta )q^{9}+(1+\cdots)q^{11}+\cdots$
1064.2.a.e	$1064$	$2$	1064.a	1.a	$1$	$2$	$2$	$8.496$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$5$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(2+\beta )q^{5}+q^{7}+(-1+\cdots)q^{9}+\cdots$
1064.2.a.f	$1064$	$2$	1064.a	1.a	$1$	$3$	$3$	$8.496$	3.3.1101.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1+\beta _{2})q^{5}+q^{7}+(4-\beta _{1}+\cdots)q^{9}+\cdots$
1064.2.a.g	$1064$	$2$	1064.a	1.a	$1$	$4$	$4$	$8.496$	4.4.18097.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-3$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+(-1-\beta _{2}+\beta _{3})q^{5}-q^{7}+\cdots$
1064.2.a.h	$1064$	$2$	1064.a	1.a	$1$	$4$	$4$	$8.496$	4.4.25857.1	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+q^{7}+\cdots$
1064.2.a.i	$1064$	$2$	1064.a	1.a	$1$	$5$	$5$	$8.496$	5.5.10463409.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1-\beta _{4})q^{5}-q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots$
1064.2.m.a	$1064$	$2$	1064.m	133.c	$2$	$16$	$16$	$8.496$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{3}+(-\beta _{14}-\beta _{15})q^{5}+(\beta _{2}+\beta _{15})q^{7}+\cdots$
1064.2.m.b	$1064$	$2$	1064.m	133.c	$2$	$24$	$24$	$8.496$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{2}]$
1064.2.q.a	$1064$	$2$	1064.q	7.c	$3$	$2$	$1$	$8.496$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-1$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots$
1064.2.q.b	$1064$	$2$	1064.q	7.c	$3$	$2$	$1$	$8.496$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$-2$	$1$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots$
1064.2.q.c	$1064$	$2$	1064.q	7.c	$3$	$2$	$1$	$8.496$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$1$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots$
1064.2.q.d	$1064$	$2$	1064.q	7.c	$3$	$2$	$1$	$8.496$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-3\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$
1064.2.q.e	$1064$	$2$	1064.q	7.c	$3$	$2$	$1$	$8.496$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-3$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-3\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+(-5+\cdots)q^{11}+\cdots$
1064.2.q.f	$1064$	$2$	1064.q	7.c	$3$	$2$	$1$	$8.496$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$
1064.2.q.g	$1064$	$2$	1064.q	7.c	$3$	$2$	$1$	$8.496$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$3$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+3\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+(1+\cdots)q^{11}+\cdots$
1064.2.q.h	$1064$	$2$	1064.q	7.c	$3$	$2$	$1$	$8.496$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$-2$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots$
1064.2.q.i	$1064$	$2$	1064.q	7.c	$3$	$2$	$1$	$8.496$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+\cdots$
1064.2.q.j	$1064$	$2$	1064.q	7.c	$3$	$2$	$1$	$8.496$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$
1064.2.q.k	$1064$	$2$	1064.q	7.c	$3$	$4$	$2$	$8.496$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$0$	$-4$	$2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+(1+\beta _{2})q^{5}+\cdots$
1064.2.q.l	$1064$	$2$	1064.q	7.c	$3$	$4$	$2$	$8.496$	$\Q(\sqrt{-3}, \sqrt{-19})$	$_{}$	None	None		$2$	$0$	$0$	$4$	$2$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\beta _{2}q^{3}+(1-\beta _{2})q^{5}+(-\beta _{2}+\beta _{3})q^{7}+\cdots$
1064.2.q.m	$1064$	$2$	1064.q	7.c	$3$	$6$	$3$	$8.496$	6.0.31259952.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{5})q^{5}+\cdots$
1064.2.q.n	$1064$	$2$	1064.q	7.c	$3$	$16$	$8$	$8.496$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$1$	$5$		$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}+\beta _{10}q^{5}+\beta _{11}q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots$
1064.2.q.o	$1064$	$2$	1064.q	7.c	$3$	$22$	$11$	$8.496$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-3$	$-6$			$\mathrm{SU}(2)[C_{3}]$
1064.2.r.a	$1064$	$2$	1064.r	19.c	$3$	$2$	$1$	$8.496$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-3$	$3$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+3\zeta_{6})q^{3}+(3-3\zeta_{6})q^{5}+q^{7}+\cdots$
1064.2.r.b	$1064$	$2$	1064.r	19.c	$3$	$2$	$1$	$8.496$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-q^{7}+\cdots$
1064.2.r.c	$1064$	$2$	1064.r	19.c	$3$	$2$	$1$	$8.496$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+q^{7}+\cdots$
1064.2.r.d	$1064$	$2$	1064.r	19.c	$3$	$2$	$1$	$8.496$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$3$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(3-3\zeta_{6})q^{5}+q^{7}+3\zeta_{6}q^{9}+2q^{11}+\cdots$
1064.2.r.e	$1064$	$2$	1064.r	19.c	$3$	$2$	$1$	$8.496$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$-1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-q^{7}+\cdots$
1064.2.r.f	$1064$	$2$	1064.r	19.c	$3$	$4$	$2$	$8.496$	$\Q(\sqrt{-3}, \sqrt{17})$	$_{}$	None	None		$2$	$0$	$0$	$-1$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+\beta _{2}q^{5}-q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots$
1064.2.r.g	$1064$	$2$	1064.r	19.c	$3$	$8$	$4$	$8.496$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{6}q^{3}+(\beta _{1}-\beta _{4})q^{5}+q^{7}+(-2+\cdots)q^{9}+\cdots$
1064.2.r.h	$1064$	$2$	1064.r	19.c	$3$	$8$	$4$	$8.496$	8.0.3098592225.1	$_{}$	None	None		$2$	$0$	$0$	$2$	$1$	$-8$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{6}q^{3}+(-\beta _{4}-\beta _{7})q^{5}-q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots$
1064.2.r.i	$1064$	$2$	1064.r	19.c	$3$	$14$	$7$	$8.496$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$2$	$-3$	$-14$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{4})q^{3}+(-\beta _{7}+\beta _{9})q^{5}+\cdots$
1064.2.r.j	$1064$	$2$	1064.r	19.c	$3$	$16$	$8$	$8.496$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$3$	$-5$	$16$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2})q^{3}+(\beta _{7}-\beta _{13})q^{5}+q^{7}+\cdots$

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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.