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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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
207.1.f.a	$207$	$1$	207.f	207.f	$6$	$6$	$3$	$0.103$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{2}+\zeta_{18}^{2}q^{3}+(-\zeta_{18}^{3}+\cdots)q^{4}+\cdots$
217.1.n.a	$217$	$1$	217.n	217.n	$6$	$6$	$3$	$0.108$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{5})q^{2}+(-\zeta_{18}+\zeta_{18}^{2}+\cdots)q^{4}+\cdots$
299.1.h.a	$299$	$1$	299.h	299.h	$6$	$6$	$3$	$0.149$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{5})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{4}+\cdots)q^{3}+\cdots$
299.1.j.a	$299$	$1$	299.j	299.j	$6$	$6$	$3$	$0.149$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}-\zeta_{18}^{8})q^{2}+(\zeta_{18}^{5}+\zeta_{18}^{7}+\cdots)q^{3}+\cdots$
343.1.d.a	$343$	$1$	343.d	7.d	$6$	$6$	$3$	$0.171$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{2}+(-1+\cdots)q^{4}+\cdots$
531.1.g.a	$531$	$1$	531.g	531.g	$6$	$6$	$3$	$0.265$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{8}q^{3}+\zeta_{18}^{6}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{8}+\cdots)q^{5}+\cdots$
581.1.g.b	$581$	$1$	581.g	581.g	$6$	$6$	$3$	$0.290$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{5})q^{3}-\zeta_{18}^{3}q^{4}+\zeta_{18}^{8}q^{7}+\cdots$
589.1.m.a	$589$	$1$	589.m	589.m	$6$	$6$	$3$	$0.294$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{5})q^{2}+(-\zeta_{18}+\zeta_{18}^{2}+\cdots)q^{4}+\cdots$
609.1.p.a	$609$	$1$	609.p	609.p	$6$	$6$	$3$	$0.304$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$0$	$-3$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{5})q^{2}+\zeta_{18}^{6}q^{3}+(-\zeta_{18}+\cdots)q^{4}+\cdots$
609.1.p.b	$609$	$1$	609.p	609.p	$6$	$6$	$3$	$0.304$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$0$	$3$	$0$	$0$	$1$		$q+(-\zeta_{18}^{2}-\zeta_{18}^{4})q^{2}-\zeta_{18}^{6}q^{3}+\cdots$
621.1.f.a	$621$	$1$	621.f	207.f	$6$	$6$	$3$	$0.310$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$3$		$q+(\zeta_{18}-\zeta_{18}^{2})q^{2}+(\zeta_{18}^{2}-\zeta_{18}^{3}+\cdots)q^{4}+\cdots$
713.1.g.b	$713$	$1$	713.g	713.g	$6$	$6$	$3$	$0.356$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+(-\zeta_{18}^{5}-\zeta_{18}^{7}+\cdots)q^{3}+\cdots$
728.1.bs.a	$728$	$1$	728.bs	728.as	$6$	$6$	$3$	$0.363$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-26}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{3}q^{2}+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{3}+\zeta_{18}^{6}q^{4}+\cdots$
728.1.bs.b	$728$	$1$	728.bs	728.as	$6$	$6$	$3$	$0.363$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-26}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{3}q^{2}+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{3}+\zeta_{18}^{6}q^{4}+\cdots$
747.1.g.a	$747$	$1$	747.g	747.g	$6$	$6$	$3$	$0.373$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{8}q^{3}-\zeta_{18}^{3}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{8}+\cdots)q^{7}+\cdots$
828.1.j.a	$828$	$1$	828.j	828.j	$6$	$6$	$3$	$0.413$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{4}q^{2}+\zeta_{18}q^{3}+\zeta_{18}^{8}q^{4}+\zeta_{18}^{5}q^{6}+\cdots$
828.1.j.b	$828$	$1$	828.j	828.j	$6$	$6$	$3$	$0.413$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{2}q^{2}-\zeta_{18}q^{3}+\zeta_{18}^{4}q^{4}+\zeta_{18}^{3}q^{6}+\cdots$
868.1.bj.a	$868$	$1$	868.bj	868.aj	$6$	$6$	$3$	$0.433$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{7}q^{2}-\zeta_{18}^{5}q^{4}+(\zeta_{18}^{2}-\zeta_{18}^{4}+\cdots)q^{5}+\cdots$
868.1.bj.b	$868$	$1$	868.bj	868.aj	$6$	$6$	$3$	$0.433$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}+(\zeta_{18}-\zeta_{18}^{5}+\cdots)q^{5}+\cdots$
936.1.bs.a	$936$	$1$	936.bs	936.as	$6$	$6$	$3$	$0.467$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-26}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{3}q^{2}+\zeta_{18}^{8}q^{3}+\zeta_{18}^{6}q^{4}+\cdots$
936.1.bs.b	$936$	$1$	936.bs	936.as	$6$	$6$	$3$	$0.467$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-26}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{3}q^{2}+\zeta_{18}^{8}q^{3}+\zeta_{18}^{6}q^{4}+\cdots$
973.1.r.b	$973$	$1$	973.r	973.r	$6$	$6$	$3$	$0.486$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-139}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{3}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{5}-\zeta_{18}^{5}q^{7}+\cdots$
19.3.d.a	$19$	$3$	19.d	19.d	$6$	$6$	$3$	$0.518$	6.0.6967728.1	$_{}$	None	None		$2$	$0$	$-3$	$-9$	$-2$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\beta _{5})q^{2}+(\beta _{1}+2\beta _{2}+\beta _{3}+\beta _{5})q^{3}+\cdots$
1044.1.o.a	$1044$	$1$	1044.o	1044.o	$6$	$6$	$3$	$0.521$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{6}q^{2}+\zeta_{18}^{4}q^{3}-\zeta_{18}^{3}q^{4}+\cdots$
1044.1.o.b	$1044$	$1$	1044.o	1044.o	$6$	$6$	$3$	$0.521$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{6}q^{2}+\zeta_{18}^{7}q^{3}-\zeta_{18}^{3}q^{4}+\cdots$
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		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{6}q^{2}+(-\zeta_{18}^{2}-\zeta_{18}^{4})q^{3}+\cdots$
1085.1.bh.a	$1085$	$1$	1085.bh	1085.ah	$6$	$6$	$3$	$0.541$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}+\zeta_{18}^{2})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{4}+\cdots$
1085.1.bh.b	$1085$	$1$	1085.bh	1085.ah	$6$	$6$	$3$	$0.541$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}-\zeta_{18}^{8})q^{2}+(\zeta_{18}^{3}-\zeta_{18}^{7}+\cdots)q^{4}+\cdots$
1121.1.g.a	$1121$	$1$	1121.g	1121.g	$6$	$6$	$3$	$0.559$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{3}-\zeta_{18}^{3}q^{4}+(-\zeta_{18}+\cdots)q^{5}+\cdots$
1183.1.n.a	$1183$	$1$	1183.n	91.n	$6$	$6$	$3$	$0.590$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$3$	$1$		$q+(-1+\beta _{1}+\beta _{4}+\beta _{5})q^{2}+(-\beta _{3}+\cdots)q^{4}+\cdots$
1183.1.n.b	$1183$	$1$	1183.n	91.n	$6$	$6$	$3$	$0.590$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$-3$	$1$		$q+(1-\beta _{1}-\beta _{4}-\beta _{5})q^{2}+(-\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
1215.1.h.a	$1215$	$1$	1215.h	45.h	$6$	$6$	$3$	$0.606$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$-3$	$0$	$3$		$q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{2}+(-\zeta_{18}^{3}-\zeta_{18}^{7}+\cdots)q^{4}+\cdots$
1215.1.h.b	$1215$	$1$	1215.h	45.h	$6$	$6$	$3$	$0.606$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$3$	$0$	$3$		$q+(\zeta_{18}-\zeta_{18}^{2})q^{2}+(\zeta_{18}^{2}-\zeta_{18}^{3}+\cdots)q^{4}+\cdots$
1352.1.n.b	$1352$	$1$	1352.n	104.n	$6$	$6$	$3$	$0.675$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-3$	$1$	$0$	$0$	$1$		$q-\beta _{5}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots$
1352.1.n.c	$1352$	$1$	1352.n	104.n	$6$	$6$	$3$	$0.675$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$3$	$1$	$0$	$0$	$1$		$q+\beta _{5}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots$
1368.1.ce.a	$1368$	$1$	1368.ce	1368.be	$6$	$6$	$3$	$0.683$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{6}q^{2}+\zeta_{18}^{4}q^{3}-\zeta_{18}^{3}q^{4}+\cdots$
1368.1.ce.b	$1368$	$1$	1368.ce	1368.be	$6$	$6$	$3$	$0.683$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{6}q^{2}+\zeta_{18}^{7}q^{3}-\zeta_{18}^{3}q^{4}+\cdots$
86.2.e.b	$86$	$2$	86.e	43.e	$7$	$18$	$3$	$0.687$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		$2$	$0$	$-3$	$2$	$-3$	$-8$	$1$	$\mathrm{SU}(2)[C_{7}]$	$q+\beta _{8}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3}-\beta _{5}+\beta _{6}+\cdots)q^{3}+\cdots$
1391.1.h.a	$1391$	$1$	1391.h	1391.h	$6$	$6$	$3$	$0.694$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{3}+\zeta_{18}^{3}q^{4}+(-\zeta_{18}^{3}+\cdots)q^{9}+\cdots$
1391.1.i.a	$1391$	$1$	1391.i	1391.i	$6$	$6$	$3$	$0.694$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{3}-\zeta_{18}^{3}q^{4}+(-\zeta_{18}^{3}+\cdots)q^{9}+\cdots$
87.2.g.a	$87$	$2$	87.g	29.d	$7$	$18$	$3$	$0.695$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		$2$	$0$	$-4$	$-3$	$-1$	$-4$	$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-\beta _{3}+\beta _{9})q^{2}-\beta _{10}q^{3}+(2\beta _{1}+\beta _{5}+\cdots)q^{4}+\cdots$
87.2.g.b	$87$	$2$	87.g	29.d	$7$	$18$	$3$	$0.695$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		$2$	$0$	$-2$	$3$	$-7$	$-4$	$1$	$\mathrm{SU}(2)[C_{7}]$	$q-\beta _{3}q^{2}+\beta _{14}q^{3}+(-\beta _{10}-\beta _{16}+\cdots)q^{4}+\cdots$
1508.1.x.a	$1508$	$1$	1508.x	1508.x	$6$	$6$	$3$	$0.753$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{3}q^{2}+(-\zeta_{18}-\zeta_{18}^{5})q^{3}+\zeta_{18}^{6}q^{4}+\cdots$
1508.1.x.b	$1508$	$1$	1508.x	1508.x	$6$	$6$	$3$	$0.753$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{3}q^{2}+(-\zeta_{18}^{2}-\zeta_{18}^{4})q^{3}+\cdots$
1519.1.n.c	$1519$	$1$	1519.n	217.n	$6$	$6$	$3$	$0.758$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$3$		$q+(-\zeta_{18}^{7}+\zeta_{18}^{8})q^{2}+(-\zeta_{18}^{5}+\zeta_{18}^{6}+\cdots)q^{4}+\cdots$
95.2.k.a	$95$	$2$	95.k	19.e	$9$	$18$	$3$	$0.759$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		$2$	$0$	$-3$	$-3$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\beta _{4}+\beta _{15})q^{2}+(\beta _{5}+\beta _{6}+\beta _{8}+\cdots)q^{3}+\cdots$
95.2.k.b	$95$	$2$	95.k	19.e	$9$	$18$	$3$	$0.759$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		$2$	$0$	$3$	$-3$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q-\beta _{14}q^{2}+(-\beta _{4}+\beta _{6}-\beta _{7}-\beta _{15}+\cdots)q^{3}+\cdots$
98.2.e.a	$98$	$2$	98.e	49.e	$7$	$18$	$3$	$0.783$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		$2$	$0$	$-3$	$3$	$-6$	$-7$	$7$	$\mathrm{SU}(2)[C_{7}]$	$q-\beta _{13}q^{2}+(\beta _{1}-\beta _{14})q^{3}+(-1+\beta _{8}+\cdots)q^{4}+\cdots$
98.2.e.b	$98$	$2$	98.e	49.e	$7$	$18$	$3$	$0.783$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		$2$	$0$	$3$	$-5$	$0$	$-1$	$1$	$\mathrm{SU}(2)[C_{7}]$	$q-\beta _{9}q^{2}+\beta _{4}q^{3}+(-1-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$

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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.