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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
52.1.j.a	$52$	$1$	52.j	52.j	$6$	$2$	$1$	$0.026$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
57.1.h.a	$57$	$1$	57.h	57.h	$6$	$2$	$1$	$0.028$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{7}-\zeta_{6}q^{9}+q^{12}+\cdots$
72.1.p.a	$72$	$1$	72.p	72.p	$6$	$2$	$1$	$0.036$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots$
77.1.j.a	$77$	$1$	77.j	77.j	$10$	$4$	$1$	$0.038$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
84.1.p.a	$84$	$1$	84.p	21.h	$6$	$2$	$1$	$0.042$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}-q^{13}+\cdots$
88.1.l.a	$88$	$1$	88.l	88.l	$10$	$4$	$1$	$0.044$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q-\zeta_{10}q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}+\zeta_{10}^{2}q^{4}+\cdots$
93.1.l.a	$93$	$1$	93.l	93.l	$10$	$4$	$1$	$0.046$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{10}q^{3}-\zeta_{10}^{3}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots$
99.1.h.a	$99$	$1$	99.h	99.h	$6$	$2$	$1$	$0.049$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-1$	$1$	$0$	$1$		$q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+\cdots$
100.1.j.a	$100$	$1$	100.j	100.j	$10$	$4$	$1$	$0.050$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{5}+\zeta_{10}^{4}q^{8}+\cdots$
111.1.h.a	$111$	$1$	111.h	111.h	$6$	$2$	$1$	$0.055$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q-\zeta_{6}q^{3}+\zeta_{6}q^{4}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
111.1.i.a	$111$	$1$	111.i	111.i	$6$	$2$	$1$	$0.055$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$1$	$1$		$q-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
124.1.i.a	$124$	$1$	124.i	124.i	$6$	$4$	$2$	$0.062$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-\zeta_{12}^{3}q^{2}-\zeta_{12}q^{3}-q^{4}-\zeta_{12}^{2}q^{5}+\cdots$
133.1.m.a	$133$	$1$	133.m	133.m	$6$	$4$	$2$	$0.066$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{5}q^{5}+\cdots$
133.1.r.a	$133$	$1$	133.r	133.r	$6$	$2$	$1$	$0.066$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$1$	$-1$	$1$		$q-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
136.1.p.a	$136$	$1$	136.p	136.p	$8$	$4$	$1$	$0.068$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{3}q^{2}+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$
140.1.p.a	$140$	$1$	140.p	140.p	$6$	$2$	$1$	$0.070$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$1$	$-1$	$-1$	$1$		$q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots$
140.1.p.b	$140$	$1$	140.p	140.p	$6$	$2$	$1$	$0.070$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$-1$	$-1$	$1$	$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots$
148.1.i.a	$148$	$1$	148.i	148.i	$6$	$2$	$1$	$0.074$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
152.1.k.a	$152$	$1$	152.k	152.k	$6$	$2$	$1$	$0.076$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots$
156.1.o.a	$156$	$1$	156.o	39.i	$6$	$2$	$1$	$0.078$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$1$	$1$		$q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{13}+\cdots$
156.1.s.a	$156$	$1$	156.s	39.h	$6$	$2$	$1$	$0.078$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-3$	$1$		$q+\zeta_{6}q^{3}+(-1-\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
164.1.j.a	$164$	$1$	164.j	164.j	$10$	$4$	$1$	$0.082$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{5}+\cdots$
164.1.l.a	$164$	$1$	164.l	164.l	$10$	$4$	$1$	$0.082$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$2$	$0$	$1$		$q+\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
168.1.s.a	$168$	$1$	168.s	168.s	$6$	$2$	$1$	$0.084$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$-1$	$-1$	$1$	$-1$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$
168.1.s.b	$168$	$1$	168.s	168.s	$6$	$2$	$1$	$0.084$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$1$	$1$	$-1$	$-1$	$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\cdots$
171.1.o.a	$171$	$1$	171.o	171.o	$6$	$4$	$2$	$0.085$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$-2$	$1$		$q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{5}+\cdots$
171.1.p.a	$171$	$1$	171.p	19.d	$6$	$2$	$1$	$0.085$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q-\zeta_{6}q^{4}+q^{7}+(-1+\zeta_{6}^{2})q^{13}+\zeta_{6}^{2}q^{16}+\cdots$
180.1.p.a	$180$	$1$	180.p	180.p	$6$	$2$	$1$	$0.090$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$-1$	$-1$	$1$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$
180.1.p.b	$180$	$1$	180.p	180.p	$6$	$2$	$1$	$0.090$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$1$	$-1$	$-1$	$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$
183.1.l.a	$183$	$1$	183.l	183.l	$10$	$4$	$1$	$0.091$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-5$	$1$		$q-\zeta_{10}q^{3}-\zeta_{10}^{2}q^{4}+(-1-\zeta_{10}^{3}+\cdots)q^{7}+\cdots$
183.1.n.a	$183$	$1$	183.n	183.n	$10$	$4$	$1$	$0.091$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$3$	$1$		$q+\zeta_{10}^{4}q^{3}-\zeta_{10}^{3}q^{4}+(1+\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
189.1.m.a	$189$	$1$	189.m	7.d	$6$	$2$	$1$	$0.094$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+\zeta_{6}q^{4}-q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+\cdots$
189.1.q.a	$189$	$1$	189.q	21.h	$6$	$2$	$1$	$0.094$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+\zeta_{6}^{2}q^{4}+q^{7}-q^{13}-\zeta_{6}q^{16}-\zeta_{6}q^{19}+\cdots$
196.1.g.a	$196$	$1$	196.g	28.g	$6$	$2$	$1$	$0.098$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{7}) $		$8$	$0$	$1$	$0$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
201.1.g.a	$201$	$1$	201.g	201.g	$6$	$4$	$2$	$0.100$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{3}q^{3}-\zeta_{12}^{2}q^{6}+\cdots$
207.1.f.a	$207$	$1$	207.f	207.f	$6$	$6$	$3$	$0.103$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{2}+\zeta_{18}^{2}q^{3}+(-\zeta_{18}^{3}+\cdots)q^{4}+\cdots$
13.2.e.a	$13$	$2$	13.e	13.e	$6$	$2$	$1$	$0.104$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-3$	$-2$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
208.1.y.a	$208$	$1$	208.y	52.i	$6$	$2$	$1$	$0.104$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{13}+\cdots$
209.1.h.a	$209$	$1$	209.h	209.h	$6$	$4$	$2$	$0.104$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{2}q^{3}-\zeta_{12}^{2}q^{5}+\cdots$
209.1.m.a	$209$	$1$	209.m	209.m	$10$	$4$	$1$	$0.104$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$3$	$1$		$q+\zeta_{10}^{4}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{5}+(1+\cdots)q^{7}+\cdots$
216.1.p.a	$216$	$1$	216.p	72.p	$6$	$2$	$1$	$0.108$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}+\zeta_{6}^{2}q^{11}+\cdots$
217.1.n.a	$217$	$1$	217.n	217.n	$6$	$6$	$3$	$0.108$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{5})q^{2}+(-\zeta_{18}+\zeta_{18}^{2}+\cdots)q^{4}+\cdots$
219.1.i.a	$219$	$1$	219.i	219.i	$6$	$2$	$1$	$0.109$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-q^{3}+\zeta_{6}^{2}q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{7}+q^{9}+\cdots$
219.1.j.a	$219$	$1$	219.j	219.j	$6$	$2$	$1$	$0.109$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$2$	$0$	$-2$	$1$		$q+q^{3}+\zeta_{6}^{2}q^{4}-q^{7}+q^{9}+\zeta_{6}^{2}q^{12}+\cdots$
219.1.j.b	$219$	$1$	219.j	219.j	$6$	$4$	$2$	$0.109$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{4}q^{6}+\cdots$
224.1.r.a	$224$	$1$	224.r	28.g	$6$	$4$	$2$	$0.112$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+\zeta_{12}^{5}q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{3}q^{7}+\cdots$
224.1.v.a	$224$	$1$	224.v	224.v	$8$	$4$	$1$	$0.112$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{7}+\zeta_{8}^{3}q^{8}+\cdots$
243.1.d.a	$243$	$1$	243.d	9.d	$6$	$2$	$1$	$0.121$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$1$	$1$		$q+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{7}-\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}+\cdots$
244.1.j.a	$244$	$1$	244.j	244.j	$6$	$2$	$1$	$0.122$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+q^{8}+q^{9}+\cdots$
244.1.n.a	$244$	$1$	244.n	244.n	$10$	$4$	$1$	$0.122$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$3$	$0$	$1$		$q+\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}+(1-\zeta_{10})q^{5}+\cdots$

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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.