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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
3.9.b.a	$3$	$9$	3.b	3.b	$2$	$2$	$2$	$1.222$	$\Q(\sqrt{-14}) $	None		$2$	$0$	$0$	$90$	$0$	$-3500$	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+(45-3\beta )q^{3}-248q^{4}-10\beta q^{5}+\cdots$
4.9.b.a	$4$	$9$	4.b	4.b	$2$	$1$	$1$	$1.630$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$16$	$0$	$-1054$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{2}+2^{8}q^{4}-1054q^{5}+2^{12}q^{8}+\cdots$
4.9.b.b	$4$	$9$	4.b	4.b	$2$	$2$	$2$	$1.630$	$\Q(\sqrt{-39}) $	None		$2$	$0$	$-20$	$0$	$1220$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-10-\beta )q^{2}-8\beta q^{3}+(-56+20\beta )q^{4}+\cdots$
5.9.c.a	$5$	$9$	5.c	5.c	$4$	$6$	$3$	$2.037$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None		$2$	$0$	$-2$	$-72$	$220$	$-2352$	$2^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{3}q^{2}+(-12-12\beta _{1}-\beta _{2}-\beta _{5})q^{3}+\cdots$
6.9.b.a	$6$	$9$	6.b	3.b	$2$	$2$	$2$	$2.444$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$-126$	$0$	$5572$	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{2}+(-63+9\beta )q^{3}-2^{7}q^{4}+\cdots$
7.9.b.a	$7$	$9$	7.b	7.b	$2$	$1$	$1$	$2.852$	$\Q$	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$-31$	$0$	$0$	$2401$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-31q^{2}+705q^{4}+7^{4}q^{7}-13919q^{8}+\cdots$
7.9.b.b	$7$	$9$	7.b	7.b	$2$	$4$	$4$	$2.852$	$\mathbb{Q}[x]/(x^{4} + \cdots)$	None		$2$	$0$	$32$	$0$	$0$	$1428$	$2^{4}\cdot 3\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	$q+(8+\beta _{3})q^{2}-\beta _{1}q^{3}+(-8+2^{4}\beta _{3})q^{4}+\cdots$
7.9.d.a	$7$	$9$	7.d	7.d	$6$	$8$	$4$	$2.852$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$-4$	$-84$	$-840$	$-140$	$2^{4}\cdot 3\cdot 7^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(-7+7\beta _{2}+\cdots)q^{3}+\cdots$
8.9.d.a	$8$	$9$	8.d	8.d	$2$	$1$	$1$	$3.259$	$\Q$	$\Q(\sqrt{-2}) $	✓	$2$	$0$	$16$	$34$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{2}+34q^{3}+2^{8}q^{4}+544q^{6}+\cdots$
8.9.d.b	$8$	$9$	8.d	8.d	$2$	$6$	$6$	$3.259$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None		$2$	$0$	$-14$	$-36$	$0$	$0$	$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2+\beta _{1})q^{2}+(-6-\beta _{1}-\beta _{2})q^{3}+\cdots$
9.9.b.a	$9$	$9$	9.b	3.b	$2$	$2$	$2$	$3.666$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$0$	$3304$	$3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+238q^{4}+233\beta q^{5}+1652q^{7}+\cdots$
9.9.d.a	$9$	$9$	9.d	9.d	$6$	$14$	$7$	$3.666$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		$2$	$0$	$-3$	$-93$	$438$	$922$	$2^{6}\cdot 3^{21}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{1}q^{2}+(-5-3\beta _{3}+\beta _{4}+\beta _{6})q^{3}+\cdots$
10.9.c.a	$10$	$9$	10.c	5.c	$4$	$4$	$2$	$4.074$	$\Q(i, \sqrt{249})$	None		$2$	$0$	$-32$	$54$	$90$	$-1186$	$2\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-8+8\beta _{1})q^{2}+(13+13\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
10.9.c.b	$10$	$9$	10.c	5.c	$4$	$4$	$2$	$4.074$	$\Q(i, \sqrt{601})$	None		$2$	$0$	$32$	$86$	$-870$	$5726$	$2\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(8+8\beta _{1})q^{2}+(22-21\beta _{1}+\beta _{3})q^{3}+\cdots$
11.9.b.a	$11$	$9$	11.b	11.b	$2$	$1$	$1$	$4.481$	$\Q$	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$-113$	$1151$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-113q^{3}+2^{8}q^{4}+1151q^{5}+6208q^{9}+\cdots$
11.9.b.b	$11$	$9$	11.b	11.b	$2$	$6$	$6$	$4.481$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		$2$	$0$	$0$	$-36$	$-448$	$0$	$2^{7}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-6-\beta _{4})q^{3}+(-203+3\beta _{3}+\cdots)q^{4}+\cdots$
11.9.d.a	$11$	$9$	11.d	11.d	$10$	$28$	$7$	$4.481$		None		$2$	$0$	$-5$	$144$	$-708$	$5470$		$\mathrm{SU}(2)[C_{10}]$
12.9.c.a	$12$	$9$	12.c	3.b	$2$	$1$	$1$	$4.889$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$81$	$0$	$4034$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+3^{4}q^{3}+4034q^{7}+3^{8}q^{9}-35806q^{13}+\cdots$
12.9.c.b	$12$	$9$	12.c	3.b	$2$	$2$	$2$	$4.889$	$\Q(\sqrt{-110}) $	None		$2$	$0$	$0$	$-102$	$0$	$-6188$	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+(-51+\beta )q^{3}-18\beta q^{5}-3094q^{7}+\cdots$
12.9.d.a	$12$	$9$	12.d	4.b	$2$	$8$	$8$	$4.889$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$6$	$0$	$-336$	$0$	$2^{22}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-6+\cdots)q^{4}+\cdots$
13.9.d.a	$13$	$9$	13.d	13.d	$4$	$18$	$9$	$5.296$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		$2$	$0$	$-2$	$-4$	$166$	$5308$	$2^{16}\cdot 3^{2}\cdot 13^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{3}q^{2}+\beta _{6}q^{3}+(-\beta _{1}-142\beta _{2}+\cdots)q^{4}+\cdots$
13.9.f.a	$13$	$9$	13.f	13.f	$12$	$32$	$8$	$5.296$		None		$2$	$0$	$-4$	$-2$	$-172$	$-2784$		$\mathrm{SU}(2)[C_{12}]$
14.9.b.a	$14$	$9$	14.b	7.b	$2$	$4$	$4$	$5.703$	4.0.3520512.3	None		$2$	$0$	$0$	$0$	$0$	$-6076$	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta _{3}q^{2}+(2\beta _{1}-\beta _{2})q^{3}+2^{7}q^{4}+\cdots$
14.9.d.a	$14$	$9$	14.d	7.d	$6$	$12$	$6$	$5.703$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$162$	$1674$	$-1308$	$2^{24}\cdot 3^{4}\cdot 7^{3}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{2}+\beta _{3})q^{2}+(18-9\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
15.9.c.a	$15$	$9$	15.c	3.b	$2$	$10$	$10$	$6.111$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$0$	$-112$	$0$	$7156$	$2^{4}\cdot 3^{10}\cdot 5^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-11-2\beta _{1}-\beta _{2})q^{3}+(-79+\cdots)q^{4}+\cdots$
15.9.d.a	$15$	$9$	15.d	15.d	$2$	$1$	$1$	$6.111$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$-17$	$-81$	$-625$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-17q^{2}-3^{4}q^{3}+33q^{4}-5^{4}q^{5}+\cdots$
15.9.d.b	$15$	$9$	15.d	15.d	$2$	$1$	$1$	$6.111$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$17$	$81$	$625$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+17q^{2}+3^{4}q^{3}+33q^{4}+5^{4}q^{5}+\cdots$
15.9.d.c	$15$	$9$	15.d	15.d	$2$	$12$	$12$	$6.111$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{13}\cdot 3^{18}\cdot 5^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(\beta _{2}-\beta _{3})q^{3}+(142-\beta _{1}+\cdots)q^{4}+\cdots$
15.9.f.a	$15$	$9$	15.f	5.c	$4$	$16$	$8$	$6.111$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$0$	$-444$	$4540$	$2^{11}\cdot 3^{20}\cdot 5^{7}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{2}-\beta _{6}q^{3}+(158\beta _{1}-3\beta _{2}+3\beta _{3}+\cdots)q^{4}+\cdots$
16.9.c.a	$16$	$9$	16.c	4.b	$2$	$2$	$2$	$6.518$	$\Q(\sqrt{-35}) $	None		$2$	$0$	$0$	$0$	$-1020$	$0$	$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}-510q^{5}+18\beta q^{7}-13599q^{9}+\cdots$
16.9.c.b	$16$	$9$	16.c	4.b	$2$	$2$	$2$	$6.518$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$0$	$516$	$0$	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{6}q^{3}+258q^{5}-238\zeta_{6}q^{7}+6369q^{9}+\cdots$
16.9.f.a	$16$	$9$	16.f	16.f	$4$	$30$	$15$	$6.518$		None		$2$	$0$	$-2$	$-2$	$-2$	$-4$		$\mathrm{SU}(2)[C_{4}]$
17.9.e.a	$17$	$9$	17.e	17.e	$16$	$88$	$11$	$6.925$		None		$2$	$0$	$-8$	$-8$	$-8$	$-8$		$\mathrm{SU}(2)[C_{16}]$
18.9.b.a	$18$	$9$	18.b	3.b	$2$	$2$	$2$	$7.333$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$0$	$-7064$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+8\beta q^{2}-2^{7}q^{4}+165\beta q^{5}-3532q^{7}+\cdots$
18.9.b.b	$18$	$9$	18.b	3.b	$2$	$2$	$2$	$7.333$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$0$	$3304$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+8\beta q^{2}-2^{7}q^{4}-645\beta q^{5}+1652q^{7}+\cdots$
18.9.d.a	$18$	$9$	18.d	9.d	$6$	$16$	$8$	$7.333$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$126$	$-882$	$-1846$	$2^{28}\cdot 3^{22}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{4}q^{2}+(7+2\beta _{1}+\beta _{3}+\beta _{4})q^{3}+\cdots$
19.9.b.a	$19$	$9$	19.b	19.b	$2$	$1$	$1$	$7.740$	$\Q$	$\Q(\sqrt{-19}) $	✓	$2$	$0$	$0$	$0$	$-289$	$527$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{8}q^{4}-17^{2}q^{5}+527q^{7}+3^{8}q^{9}+\cdots$
19.9.b.b	$19$	$9$	19.b	19.b	$2$	$12$	$12$	$7.740$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$8$	$3686$	$2^{8}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-131+\beta _{2})q^{4}+\cdots$
19.9.d.a	$19$	$9$	19.d	19.d	$6$	$26$	$13$	$7.740$		None		$2$	$0$	$-3$	$-171$	$278$	$-7504$		$\mathrm{SU}(2)[C_{6}]$
19.9.f.a	$19$	$9$	19.f	19.f	$18$	$72$	$12$	$7.740$		None		$2$	$0$	$-6$	$162$	$-6$	$3282$		$\mathrm{SU}(2)[C_{18}]$
20.9.b.a	$20$	$9$	20.b	4.b	$2$	$16$	$16$	$8.148$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$6$	$0$	$0$	$0$	$2^{58}\cdot 5^{16}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-3+\beta _{2}+\cdots)q^{4}+\cdots$
20.9.d.a	$20$	$9$	20.d	20.d	$2$	$1$	$1$	$8.148$	$\Q$	$\Q(\sqrt{-5}) $	✓	$2$	$0$	$-16$	$158$	$625$	$-1922$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-2^{4}q^{2}+158q^{3}+2^{8}q^{4}+5^{4}q^{5}+\cdots$
20.9.d.b	$20$	$9$	20.d	20.d	$2$	$1$	$1$	$8.148$	$\Q$	$\Q(\sqrt{-5}) $	✓	$2$	$0$	$16$	$-158$	$625$	$1922$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{2}-158q^{3}+2^{8}q^{4}+5^{4}q^{5}+\cdots$
20.9.d.c	$20$	$9$	20.d	20.d	$2$	$20$	$20$	$8.148$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$4$	$0$	$0$	$0$	$-1420$	$0$	$2^{74}\cdot 3^{4}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{6})q^{3}+(-38+\beta _{2}+\cdots)q^{4}+\cdots$
20.9.f.a	$20$	$9$	20.f	5.c	$4$	$8$	$4$	$8.148$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$-70$	$894$	$-2030$	$2^{13}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-9-9\beta _{1}+\beta _{2})q^{3}+(112-58\beta _{1}+\cdots)q^{5}+\cdots$
21.9.b.a	$21$	$9$	21.b	3.b	$2$	$16$	$16$	$8.555$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$-182$	$0$	$0$	$2^{9}\cdot 3^{20}\cdot 7^{13}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-11+\beta _{1}-\beta _{3})q^{3}+(-98+\cdots)q^{4}+\cdots$
21.9.d.a	$21$	$9$	21.d	7.b	$2$	$10$	$10$	$8.555$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$-6$	$0$	$0$	$-4002$	$2^{8}\cdot 3^{12}\cdot 7^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{1})q^{2}-\beta _{4}q^{3}+(119-5\beta _{1}+\cdots)q^{4}+\cdots$
21.9.f.a	$21$	$9$	21.f	7.d	$6$	$10$	$5$	$8.555$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$3$	$-405$	$285$	$4305$	$2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(-54-3^{3}\beta _{3}+\cdots)q^{3}+\cdots$
21.9.f.b	$21$	$9$	21.f	7.d	$6$	$12$	$6$	$8.555$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$3$	$486$	$1389$	$-1226$	$2^{8}\cdot 3^{5}\cdot 7^{5}$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\beta _{2}-\beta _{3})q^{2}+(54+3^{3}\beta _{2})q^{3}+\cdots$
21.9.h.a	$21$	$9$	21.h	21.h	$6$	$2$	$1$	$8.555$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$-81$	$0$	$239$	$1$	$\mathrm{U}(1)[D_{6}]$	$q-3^{4}\zeta_{6}q^{3}-2^{8}\zeta_{6}q^{4}+(-1265+2769\zeta_{6})q^{7}+\cdots$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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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.