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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	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
4.5.b.a	$4$	$5$	4.b	4.b	$2$	$1$	$1$	$0.413$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$-4$	$0$	$-14$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-4q^{2}+2^{4}q^{4}-14q^{5}-2^{6}q^{8}+3^{4}q^{9}+\cdots$
5.5.c.a	$5$	$5$	5.c	5.c	$4$	$2$	$1$	$0.517$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-2$	$-12$	$40$	$-52$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-i)q^{2}+(-6+6i)q^{3}-14iq^{4}+\cdots$
6.5.b.a	$6$	$5$	6.b	3.b	$2$	$2$	$2$	$0.620$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$-6$	$0$	$52$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+(-3-3\beta )q^{3}-8q^{4}+6\beta q^{5}+\cdots$
7.5.b.a	$7$	$5$	7.b	7.b	$2$	$1$	$1$	$0.724$	$\Q$	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$1$	$0$	$0$	$49$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+q^{2}-15q^{4}+7^{2}q^{7}-31q^{8}+3^{4}q^{9}+\cdots$
7.5.d.a	$7$	$5$	7.d	7.d	$6$	$4$	$2$	$0.724$	$\Q(\sqrt{-3}, \sqrt{22})$	None		$2$	$0$	$-4$	$6$	$-30$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2+\beta _{1}-2\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
8.5.d.a	$8$	$5$	8.d	8.d	$2$	$1$	$1$	$0.827$	$\Q$	$\Q(\sqrt{-2}) $	✓	$2$	$0$	$4$	$-14$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{2}-14q^{3}+2^{4}q^{4}-56q^{6}+2^{6}q^{8}+\cdots$
8.5.d.b	$8$	$5$	8.d	8.d	$2$	$2$	$2$	$0.827$	$\Q(\sqrt{-15}) $	None		$2$	$0$	$-2$	$12$	$0$	$0$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta )q^{2}+6q^{3}+(-14+2\beta )q^{4}+\cdots$
9.5.b.a	$9$	$5$	9.b	3.b	$2$	$2$	$2$	$0.930$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$0$	$-56$	$3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-2q^{4}-7\beta q^{5}-28q^{7}+14\beta q^{8}+\cdots$
9.5.d.a	$9$	$5$	9.d	9.d	$6$	$6$	$3$	$0.930$	6.0.39400128.1	None		$2$	$0$	$-3$	$-3$	$-12$	$12$	$3^{3}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{2}q^{2}+(-3+\beta _{1}-3\beta _{3}+\beta _{4})q^{3}+\cdots$
10.5.c.a	$10$	$5$	10.c	5.c	$4$	$2$	$1$	$1.034$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-4$	$18$	$-30$	$58$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2-2i)q^{2}+(9-9i)q^{3}+8iq^{4}+\cdots$
10.5.c.b	$10$	$5$	10.c	5.c	$4$	$2$	$1$	$1.034$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$4$	$2$	$-30$	$-38$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(2+2i)q^{2}+(1-i)q^{3}+8iq^{4}+(-15+\cdots)q^{5}+\cdots$
11.5.b.a	$11$	$5$	11.b	11.b	$2$	$1$	$1$	$1.137$	$\Q$	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$7$	$-49$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+7q^{3}+2^{4}q^{4}-7^{2}q^{5}-2^{5}q^{9}+11^{2}q^{11}+\cdots$
11.5.b.b	$11$	$5$	11.b	11.b	$2$	$2$	$2$	$1.137$	$\Q(\sqrt{-30}) $	None		$2$	$0$	$0$	$-6$	$62$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-3q^{3}-14q^{4}+31q^{5}-3\beta q^{6}+\cdots$
11.5.d.a	$11$	$5$	11.d	11.d	$10$	$12$	$3$	$1.137$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$-5$	$-6$	$-18$	$-80$	$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-1-\beta _{2}-2\beta _{3}-\beta _{4}+\beta _{7})q^{2}+\cdots$
12.5.c.a	$12$	$5$	12.c	3.b	$2$	$1$	$1$	$1.240$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$9$	$0$	$-94$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+9q^{3}-94q^{7}+3^{4}q^{9}+146q^{13}+\cdots$
12.5.d.a	$12$	$5$	12.d	4.b	$2$	$4$	$4$	$1.240$	$\Q(\sqrt{-3}, \sqrt{13})$	None		$2$	$0$	$6$	$0$	$24$	$0$	$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+(2-\beta _{1})q^{2}-\beta _{2}q^{3}+(-4-3\beta _{1}+\cdots)q^{4}+\cdots$
13.5.d.a	$13$	$5$	13.d	13.d	$4$	$6$	$3$	$1.344$	6.0.$\cdots$.1	None		$2$	$0$	$-2$	$-4$	$-14$	$48$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
13.5.f.a	$13$	$5$	13.f	13.f	$12$	$16$	$4$	$1.344$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$-4$	$-2$	$8$	$56$	$2^{4}\cdot 3^{2}\cdot 13^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q-\beta _{12}q^{2}+(-1-\beta _{8}+\beta _{9}+\beta _{12}+\cdots)q^{3}+\cdots$
14.5.b.a	$14$	$5$	14.b	7.b	$2$	$4$	$4$	$1.447$	4.0.1308672.3	None		$2$	$0$	$0$	$0$	$0$	$-76$	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-\beta _{1}q^{3}+8q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots$
14.5.d.a	$14$	$5$	14.d	7.d	$6$	$4$	$2$	$1.447$	$\Q(\sqrt{2}, \sqrt{-3})$	None		$2$	$0$	$0$	$-18$	$54$	$-28$	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-6+2\beta _{1}-3\beta _{2}-2\beta _{3})q^{3}+\cdots$
15.5.c.a	$15$	$5$	15.c	3.b	$2$	$6$	$6$	$1.551$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		$2$	$0$	$0$	$8$	$0$	$76$	$3\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(-8+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
15.5.d.a	$15$	$5$	15.d	15.d	$2$	$1$	$1$	$1.551$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$-7$	$9$	$25$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-7q^{2}+9q^{3}+33q^{4}+5^{2}q^{5}-63q^{6}+\cdots$
15.5.d.b	$15$	$5$	15.d	15.d	$2$	$1$	$1$	$1.551$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$7$	$-9$	$-25$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+7q^{2}-9q^{3}+33q^{4}-5^{2}q^{5}-63q^{6}+\cdots$
15.5.d.c	$15$	$5$	15.d	15.d	$2$	$4$	$4$	$1.551$	$\Q(\sqrt{10}, \sqrt{-26})$	None		$4$	$0$	$0$	$0$	$0$	$0$	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-6q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots$
15.5.f.a	$15$	$5$	15.f	5.c	$4$	$8$	$4$	$1.551$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$0$	$-84$	$20$	$3^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-\beta _{1}-12\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots$
16.5.c.a	$16$	$5$	16.c	4.b	$2$	$2$	$2$	$1.654$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$0$	$36$	$0$	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{6}q^{3}+18q^{5}+2\zeta_{6}q^{7}-111q^{9}+\cdots$
16.5.f.a	$16$	$5$	16.f	16.f	$4$	$14$	$7$	$1.654$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		$2$	$0$	$-2$	$-2$	$-2$	$-4$	$2^{21}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{4}q^{2}-\beta _{6}q^{3}+(-1+2\beta _{3}-\beta _{11}+\cdots)q^{4}+\cdots$
17.5.e.a	$17$	$5$	17.e	17.e	$16$	$40$	$5$	$1.757$		None		$2$	$0$	$-8$	$-8$	$-8$	$-8$		$\mathrm{SU}(2)[C_{16}]$
18.5.d.a	$18$	$5$	18.d	9.d	$6$	$8$	$4$	$1.861$	8.0.$\cdots$.4	None		$2$	$0$	$0$	$6$	$18$	$-26$	$2^{4}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{3}q^{2}+(2+\beta _{1}-3\beta _{2}-\beta _{5})q^{3}+\cdots$
19.5.b.a	$19$	$5$	19.b	19.b	$2$	$1$	$1$	$1.964$	$\Q$	$\Q(\sqrt{-19}) $	✓	$2$	$0$	$0$	$0$	$31$	$-73$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{4}+31q^{5}-73q^{7}+3^{4}q^{9}+\cdots$
19.5.b.b	$19$	$5$	19.b	19.b	$2$	$4$	$4$	$1.964$	4.0.12107488.1	None		$2$	$0$	$0$	$0$	$-42$	$136$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-3+3\beta _{2})q^{4}+\cdots$
19.5.d.a	$19$	$5$	19.d	19.d	$6$	$10$	$5$	$1.964$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$-3$	$9$	$8$	$-24$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{1}q^{2}+(\beta _{3}+\beta _{5})q^{3}+(6\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
19.5.f.a	$19$	$5$	19.f	19.f	$18$	$36$	$6$	$1.964$		None		$2$	$0$	$-6$	$-18$	$-6$	$-48$		$\mathrm{SU}(2)[C_{18}]$
20.5.b.a	$20$	$5$	20.b	4.b	$2$	$8$	$8$	$2.067$	8.0.$\cdots$.1	None		$2$	$0$	$6$	$0$	$0$	$0$	$2^{14}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{1})q^{2}+\beta _{3}q^{3}+(-2+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
20.5.d.a	$20$	$5$	20.d	20.d	$2$	$1$	$1$	$2.067$	$\Q$	$\Q(\sqrt{-5}) $	✓	$2$	$0$	$-4$	$2$	$25$	$82$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-4q^{2}+2q^{3}+2^{4}q^{4}+5^{2}q^{5}-8q^{6}+\cdots$
20.5.d.b	$20$	$5$	20.d	20.d	$2$	$1$	$1$	$2.067$	$\Q$	$\Q(\sqrt{-5}) $	✓	$2$	$0$	$4$	$-2$	$25$	$-82$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{2}-2q^{3}+2^{4}q^{4}+5^{2}q^{5}-8q^{6}+\cdots$
20.5.d.c	$20$	$5$	20.d	20.d	$2$	$8$	$8$	$2.067$	8.0.$\cdots$.2	None		$4$	$0$	$0$	$0$	$-40$	$0$	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-6+\beta _{3})q^{4}+(-5+\cdots)q^{5}+\cdots$
20.5.f.a	$20$	$5$	20.f	5.c	$4$	$4$	$2$	$2.067$	$\Q(i, \sqrt{241})$	None		$2$	$0$	$0$	$-10$	$-6$	$110$	$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2+2\beta _{1}+\beta _{3})q^{3}+(-6\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
21.5.b.a	$21$	$5$	21.b	3.b	$2$	$8$	$8$	$2.171$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$0$	$-2$	$0$	$0$	$2\cdot 3^{3}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-5+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots$
21.5.d.a	$21$	$5$	21.d	7.b	$2$	$6$	$6$	$2.171$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		$2$	$0$	$-6$	$0$	$0$	$-22$	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(10-\beta _{4}+\cdots)q^{4}+\cdots$
21.5.f.a	$21$	$5$	21.f	7.d	$6$	$2$	$1$	$2.171$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-2$	$9$	$18$	$77$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q-2\zeta_{6}q^{2}+(3+3\zeta_{6})q^{3}+(12-12\zeta_{6})q^{4}+\cdots$
21.5.f.b	$21$	$5$	21.f	7.d	$6$	$2$	$1$	$2.171$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$5$	$9$	$-3$	$-91$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+5\zeta_{6}q^{2}+(3+3\zeta_{6})q^{3}+(-9+9\zeta_{6})q^{4}+\cdots$
21.5.f.c	$21$	$5$	21.f	7.d	$6$	$6$	$3$	$2.171$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		$2$	$0$	$3$	$-27$	$39$	$23$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}+\beta _{2})q^{2}+(-3-3\beta _{2})q^{3}+\cdots$
21.5.h.a	$21$	$5$	21.h	21.h	$6$	$2$	$1$	$2.171$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$-9$	$0$	$71$	$1$	$\mathrm{U}(1)[D_{6}]$	$q-9\zeta_{6}q^{3}-2^{4}\zeta_{6}q^{4}+(55-39\zeta_{6})q^{7}+\cdots$
21.5.h.b	$21$	$5$	21.h	21.h	$6$	$16$	$8$	$2.171$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$4$	$0$	$0$	$8$	$0$	$-168$	$3^{7}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{7})q^{3}+(-10\beta _{2}+\cdots)q^{4}+\cdots$
22.5.b.a	$22$	$5$	22.b	11.b	$2$	$4$	$4$	$2.274$	$\Q(\sqrt{-2}, \sqrt{553})$	None		$2$	$0$	$0$	$2$	$-30$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-\beta _{1}q^{3}-8q^{4}+(-8-\beta _{1}+\cdots)q^{5}+\cdots$
22.5.d.a	$22$	$5$	22.d	11.d	$10$	$16$	$4$	$2.274$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$-2$	$30$	$150$	$2^{8}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{10}]$	$q-\beta _{4}q^{2}+(1+\beta _{2}+3\beta _{3}-\beta _{10}-\beta _{13}+\cdots)q^{3}+\cdots$
23.5.b.a	$23$	$5$	23.b	23.b	$2$	$3$	$3$	$2.378$	3.3.621.1	$\Q(\sqrt{-23}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{1}-2\beta _{2})q^{2}+(6\beta _{1}-\beta _{2})q^{3}+(2^{4}+\cdots)q^{4}+\cdots$
23.5.b.b	$23$	$5$	23.b	23.b	$2$	$4$	$4$	$2.378$	$\mathbb{Q}[x]/(x^{4} + \cdots)$	None		$2$	$0$	$-8$	$-12$	$0$	$0$	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2-\beta _{3})q^{2}+(-3+3\beta _{3})q^{3}+(-6+\cdots)q^{4}+\cdots$
23.5.d.a	$23$	$5$	23.d	23.d	$22$	$70$	$7$	$2.378$		None		$2$	$0$	$-3$	$1$	$-11$	$-11$		$\mathrm{SU}(2)[C_{22}]$

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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.