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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

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4.9.b.a	$4$	$9$	4.b	4.b	$2$	$1$	$1$	$1.630$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$16$	$0$	$-1054$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{2}+2^{8}q^{4}-1054q^{5}+2^{12}q^{8}+\cdots$
3.13.b.a	$3$	$13$	3.b	3.b	$2$	$1$	$1$	$2.742$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$729$	$0$	$-153502$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3^{6}q^{3}+2^{12}q^{4}-153502q^{7}+3^{12}q^{9}+\cdots$
7.9.b.a	$7$	$9$	7.b	7.b	$2$	$1$	$1$	$2.852$	$\Q$	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$-31$	$0$	$0$	$2401$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-31q^{2}+705q^{4}+7^{4}q^{7}-13919q^{8}+\cdots$
8.9.d.a	$8$	$9$	8.d	8.d	$2$	$1$	$1$	$3.259$	$\Q$	$\Q(\sqrt{-2}) $	✓	$2$	$0$	$16$	$34$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{2}+34q^{3}+2^{8}q^{4}+544q^{6}+\cdots$
4.13.b.a	$4$	$13$	4.b	4.b	$2$	$1$	$1$	$3.656$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$-64$	$0$	$23506$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2^{6}q^{2}+2^{12}q^{4}+23506q^{5}-2^{18}q^{8}+\cdots$
7.11.b.a	$7$	$11$	7.b	7.b	$2$	$1$	$1$	$4.448$	$\Q$	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$57$	$0$	$0$	$-16807$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+57q^{2}+2225q^{4}-7^{5}q^{7}+68457q^{8}+\cdots$
11.9.b.a	$11$	$9$	11.b	11.b	$2$	$1$	$1$	$4.481$	$\Q$	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$-113$	$1151$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-113q^{3}+2^{8}q^{4}+1151q^{5}+6208q^{9}+\cdots$
9.10.a.b	$9$	$10$	9.a	1.a	$1$	$1$	$1$	$4.635$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$1$	$0$	$0$	$0$	$-12580$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2^{9}q^{4}-12580q^{7}+118370q^{13}+\cdots$
12.9.c.a	$12$	$9$	12.c	3.b	$2$	$1$	$1$	$4.889$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$81$	$0$	$4034$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3^{4}q^{3}+4034q^{7}+3^{8}q^{9}-35806q^{13}+\cdots$
8.11.d.a	$8$	$11$	8.d	8.d	$2$	$1$	$1$	$5.083$	$\Q$	$\Q(\sqrt{-2}) $	✓	$2$	$0$	$-32$	$-482$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2^{5}q^{2}-482q^{3}+2^{10}q^{4}+15424q^{6}+\cdots$
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}) $	✓	$2$	$0$	$17$	$81$	$625$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+17q^{2}+3^{4}q^{3}+33q^{4}+5^{4}q^{5}+\cdots$
7.13.b.a	$7$	$13$	7.b	7.b	$2$	$1$	$1$	$6.398$	$\Q$	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$-47$	$0$	$0$	$117649$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-47q^{2}-1887q^{4}+7^{6}q^{7}+281201q^{8}+\cdots$
11.11.b.a	$11$	$11$	11.b	11.b	$2$	$1$	$1$	$6.989$	$\Q$	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$475$	$-3001$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+475q^{3}+2^{10}q^{4}-3001q^{5}+166576q^{9}+\cdots$
8.13.d.a	$8$	$13$	8.d	8.d	$2$	$1$	$1$	$7.312$	$\Q$	$\Q(\sqrt{-2}) $	✓	$2$	$0$	$64$	$658$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{6}q^{2}+658q^{3}+2^{12}q^{4}+42112q^{6}+\cdots$
12.11.c.a	$12$	$11$	12.c	3.b	$2$	$1$	$1$	$7.624$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$-243$	$0$	$22082$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-3^{5}q^{3}+22082q^{7}+3^{10}q^{9}+702218q^{13}+\cdots$
19.9.b.a	$19$	$9$	19.b	19.b	$2$	$1$	$1$	$7.740$	$\Q$	$\Q(\sqrt{-19}) $	✓	$2$	$0$	$0$	$0$	$-289$	$527$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{8}q^{4}-17^{2}q^{5}+527q^{7}+3^{8}q^{9}+\cdots$
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}) $	✓	$2$	$0$	$16$	$-158$	$625$	$1922$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{2}-158q^{3}+2^{8}q^{4}+5^{4}q^{5}+\cdots$
21.9.h.a	$21$	$9$	21.h	21.h	$6$	$2$	$1$	$8.555$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$-81$	$0$	$239$		$1$	$\mathrm{U}(1)[D_{6}]$	$q-3^{4}\zeta_{6}q^{3}-2^{8}\zeta_{6}q^{4}+(-1265+2769\zeta_{6})q^{7}+\cdots$
7.15.b.a	$7$	$15$	7.b	7.b	$2$	$1$	$1$	$8.703$	$\Q$	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$-87$	$0$	$0$	$-823543$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-87q^{2}-8815q^{4}-7^{7}q^{7}+2192313q^{8}+\cdots$
23.9.b.a	$23$	$9$	23.b	23.b	$2$	$3$	$3$	$9.370$	3.3.621.1	$\Q(\sqrt{-23}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$		$7$	$\mathrm{U}(1)[D_{2}]$	$q+(-3\beta _{1}-2\beta _{2})q^{2}+(13\beta _{1}-17\beta _{2})q^{3}+\cdots$
15.11.d.a	$15$	$11$	15.d	15.d	$2$	$1$	$1$	$9.530$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$-61$	$243$	$-3125$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-61q^{2}+3^{5}q^{3}+2697q^{4}-5^{5}q^{5}+\cdots$
15.11.d.b	$15$	$11$	15.d	15.d	$2$	$1$	$1$	$9.530$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$61$	$-243$	$3125$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+61q^{2}-3^{5}q^{3}+2697q^{4}+5^{5}q^{5}+\cdots$
24.9.h.a	$24$	$9$	24.h	24.h	$2$	$1$	$1$	$9.777$	$\Q$	$\Q(\sqrt{-6}) $	✓	$2$	$0$	$-16$	$-81$	$-866$	$-4798$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2^{4}q^{2}-3^{4}q^{3}+2^{8}q^{4}-866q^{5}+\cdots$
24.9.h.b	$24$	$9$	24.h	24.h	$2$	$1$	$1$	$9.777$	$\Q$	$\Q(\sqrt{-6}) $	✓	$2$	$0$	$16$	$81$	$866$	$-4798$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{2}+3^{4}q^{3}+2^{8}q^{4}+866q^{5}+\cdots$
8.15.d.a	$8$	$15$	8.d	8.d	$2$	$1$	$1$	$9.946$	$\Q$	$\Q(\sqrt{-2}) $	✓	$2$	$0$	$-128$	$3022$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2^{7}q^{2}+3022q^{3}+2^{14}q^{4}-386816q^{6}+\cdots$
11.13.b.a	$11$	$13$	11.b	11.b	$2$	$1$	$1$	$10.054$	$\Q$	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$-1358$	$-25774$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-1358q^{3}+2^{12}q^{4}-25774q^{5}+\cdots$
16.11.c.a	$16$	$11$	16.c	4.b	$2$	$1$	$1$	$10.166$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$0$	$0$	$474$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+474q^{5}+3^{10}q^{9}+683050q^{13}+\cdots$
20.10.e.a	$20$	$10$	20.e	20.e	$4$	$2$	$1$	$10.301$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $		$4$	$0$	$-32$	$0$	$1436$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-2^{4}-2^{4}i)q^{2}+2^{9}iq^{4}+(718+\cdots)q^{5}+\cdots$
21.10.c.a	$21$	$10$	21.c	21.c	$2$	$2$	$2$	$10.816$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$0$	$0$	$12580$		$2\cdot 3^{3}$	$\mathrm{U}(1)[D_{2}]$	$q-3\zeta_{6}q^{3}+2^{9}q^{4}+(6290-19\zeta_{6})q^{7}+\cdots$
27.9.b.a	$27$	$9$	27.b	3.b	$2$	$1$	$1$	$10.999$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$0$	$0$	$239$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{8}q^{4}+239q^{7}+56447q^{13}+2^{16}q^{16}+\cdots$
19.11.b.a	$19$	$11$	19.b	19.b	$2$	$1$	$1$	$12.072$	$\Q$	$\Q(\sqrt{-19}) $	✓	$2$	$0$	$0$	$0$	$3951$	$-32525$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{10}q^{4}+3951q^{5}-32525q^{7}+\cdots$
24.10.f.a	$24$	$10$	24.f	24.f	$2$	$2$	$2$	$12.361$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-2}) $		$4$	$0$	$0$	$190$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}\beta q^{2}+(95-73\beta )q^{3}-2^{9}q^{4}+\cdots$
31.9.b.a	$31$	$9$	31.b	31.b	$2$	$3$	$3$	$12.629$	3.3.837.1	$\Q(\sqrt{-31}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+(-6\beta _{1}+\beta _{2})q^{2}+(2^{8}-\beta _{1}+3^{4}\beta _{2})q^{4}+\cdots$
20.11.d.a	$20$	$11$	20.d	20.d	$2$	$1$	$1$	$12.707$	$\Q$	$\Q(\sqrt{-5}) $	✓	$2$	$0$	$-32$	$-236$	$-3125$	$-33364$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2^{5}q^{2}-236q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots$
20.11.d.b	$20$	$11$	20.d	20.d	$2$	$1$	$1$	$12.707$	$\Q$	$\Q(\sqrt{-5}) $	✓	$2$	$0$	$32$	$236$	$-3125$	$33364$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{5}q^{2}+236q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots$
20.11.d.c	$20$	$11$	20.d	20.d	$2$	$2$	$2$	$12.707$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $		$4$	$0$	$0$	$0$	$-474$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+8iq^{2}-2^{10}q^{4}+(-237+779i)q^{5}+\cdots$
9.16.a.b	$9$	$16$	9.a	1.a	$1$	$1$	$1$	$12.842$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$0$	$0$	$1244900$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2^{15}q^{4}+1244900q^{7}+397771850q^{13}+\cdots$
32.9.d.a	$32$	$9$	32.d	8.d	$2$	$1$	$1$	$13.036$	$\Q$	$\Q(\sqrt{-2}) $	✓	$2$	$0$	$0$	$-34$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-34q^{3}-5405q^{9}+27166q^{11}+\cdots$
21.11.h.a	$21$	$11$	21.h	21.h	$6$	$2$	$1$	$13.343$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$243$	$0$	$10907$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+3^{5}\zeta_{6}q^{3}-2^{10}\zeta_{6}q^{4}+(-3725+\cdots)q^{7}+\cdots$
11.15.b.a	$11$	$15$	11.b	11.b	$2$	$1$	$1$	$13.676$	$\Q$	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$2515$	$100799$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2515q^{3}+2^{14}q^{4}+100799q^{5}+\cdots$
15.13.d.a	$15$	$13$	15.d	15.d	$2$	$1$	$1$	$13.710$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$-7$	$729$	$15625$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-7q^{2}+3^{6}q^{3}-4047q^{4}+5^{6}q^{5}+\cdots$
15.13.d.b	$15$	$13$	15.d	15.d	$2$	$1$	$1$	$13.710$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$7$	$-729$	$-15625$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+7q^{2}-3^{6}q^{3}-4047q^{4}-5^{6}q^{5}+\cdots$
35.9.c.a	$35$	$9$	35.c	35.c	$2$	$1$	$1$	$14.258$	$\Q$	$\Q(\sqrt{-35}) $	✓	$2$	$0$	$0$	$-127$	$-625$	$-2401$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-127q^{3}+2^{8}q^{4}-5^{4}q^{5}-7^{4}q^{7}+\cdots$
35.9.c.b	$35$	$9$	35.c	35.c	$2$	$1$	$1$	$14.258$	$\Q$	$\Q(\sqrt{-35}) $	✓	$2$	$0$	$0$	$127$	$625$	$2401$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+127q^{3}+2^{8}q^{4}+5^{4}q^{5}+7^{4}q^{7}+\cdots$
28.10.d.a	$28$	$10$	28.d	28.d	$2$	$2$	$2$	$14.421$	$\Q(\sqrt{-7}) $	$\Q(\sqrt{-7}) $		$4$	$0$	$5$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-6+17\beta )q^{2}+(-542+85\beta )q^{4}+\cdots$
23.11.b.a	$23$	$11$	23.b	23.b	$2$	$3$	$3$	$14.613$	3.3.621.1	$\Q(\sqrt{-23}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-23\beta _{1}-2\beta _{2})q^{2}+(-66\beta _{1}+119\beta _{2})q^{3}+\cdots$
36.9.d.a	$36$	$9$	36.d	4.b	$2$	$1$	$1$	$14.666$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$-16$	$0$	$1054$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2^{4}q^{2}+2^{8}q^{4}+1054q^{5}-2^{12}q^{8}+\cdots$
12.15.c.a	$12$	$15$	12.c	3.b	$2$	$1$	$1$	$14.919$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$-2187$	$0$	$-1389022$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-3^{7}q^{3}-1389022q^{7}+3^{14}q^{9}+\cdots$

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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.