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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				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
8001.2.a.l	$8001$	$2$	8001.a	1.a	$1$	$7$	$7$	$63.888$	7.7.118870813.1	None	✓	$1$	$1$	$2$	$0$	$8$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$
8004.2.a.d	$8004$	$2$	8004.a	1.a	$1$	$8$	$8$	$63.912$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$0$	$8$	$-5$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta _{7})q^{5}+(\beta _{6}+\beta _{7})q^{7}+\cdots$
8004.2.a.e	$8004$	$2$	8004.a	1.a	$1$	$9$	$9$	$63.912$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$0$	$-9$	$-3$	$7$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{1}q^{5}+(1-\beta _{3})q^{7}+q^{9}+(\beta _{3}+\cdots)q^{11}+\cdots$
8004.2.a.f	$8004$	$2$	8004.a	1.a	$1$	$9$	$9$	$63.912$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$0$	$9$	$-1$	$-5$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{1}q^{5}+(-1-\beta _{6})q^{7}+q^{9}+\cdots$
8008.2.a.k	$8008$	$2$	8008.a	1.a	$1$	$6$	$6$	$63.944$	6.6.244558277.1	None	✓	$1$	$0$	$0$	$-1$	$1$	$6$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{5}q^{5}+q^{7}+(2+\beta _{2})q^{9}+\cdots$
8008.2.a.l	$8008$	$2$	8008.a	1.a	$1$	$8$	$8$	$63.944$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$0$	$-5$	$-7$	$8$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{3}+(-1+\beta _{5})q^{5}+q^{7}+\cdots$
8008.2.a.m	$8008$	$2$	8008.a	1.a	$1$	$9$	$9$	$63.944$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$0$	$-5$	$-5$	$-9$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1+\beta _{6})q^{5}-q^{7}+\cdots$
8008.2.a.n	$8008$	$2$	8008.a	1.a	$1$	$9$	$9$	$63.944$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$0$	$-3$	$1$	$-9$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{6}q^{5}-q^{7}+(1+\beta _{4}-\beta _{5}+\cdots)q^{9}+\cdots$
8008.2.a.o	$8008$	$2$	8008.a	1.a	$1$	$9$	$9$	$63.944$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$0$	$-2$	$-4$	$9$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{4}q^{5}+q^{7}+\beta _{2}q^{9}-q^{11}+\cdots$
8008.2.a.p	$8008$	$2$	8008.a	1.a	$1$	$9$	$9$	$63.944$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$0$	$1$	$-4$	$-9$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{3}q^{5}-q^{7}+(-\beta _{3}+\beta _{5}+\cdots)q^{9}+\cdots$
8008.2.a.q	$8008$	$2$	8008.a	1.a	$1$	$9$	$9$	$63.944$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$0$	$3$	$8$	$9$	$-$	$5$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1-\beta _{7})q^{5}+q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$
8008.2.a.r	$8008$	$2$	8008.a	1.a	$1$	$9$	$9$	$63.944$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$0$	$5$	$3$	$-9$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+\beta _{6}q^{5}-q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots$
8008.2.a.s	$8008$	$2$	8008.a	1.a	$1$	$10$	$10$	$63.944$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$0$	$-3$	$-4$	$10$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{9}q^{5}+q^{7}+(1+\beta _{5}-\beta _{6}+\cdots)q^{9}+\cdots$
8008.2.a.t	$8008$	$2$	8008.a	1.a	$1$	$10$	$10$	$63.944$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$0$	$1$	$3$	$10$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{6}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots$
8008.2.a.u	$8008$	$2$	8008.a	1.a	$1$	$10$	$10$	$63.944$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$0$	$2$	$-4$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{6}q^{5}-q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots$
8010.2.a.bk	$8010$	$2$	8010.a	1.a	$1$	$6$	$6$	$63.960$	6.6.63199488.1	None	✓	$1$	$1$	$-6$	$0$	$6$	$1$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-\beta _{1}q^{7}-q^{8}-q^{10}+\cdots$
8010.2.a.bl	$8010$	$2$	8010.a	1.a	$1$	$6$	$6$	$63.960$	6.6.63199488.1	None	✓	$1$	$0$	$6$	$0$	$-6$	$1$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-\beta _{1}q^{7}+q^{8}-q^{10}+\cdots$
8010.2.a.bm	$8010$	$2$	8010.a	1.a	$1$	$6$	$6$	$63.960$	6.6.387230992.1	None	✓	$1$	$0$	$6$	$0$	$-6$	$6$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+(1+\beta _{3}+\beta _{5})q^{7}+\cdots$
8010.2.a.bn	$8010$	$2$	8010.a	1.a	$1$	$7$	$7$	$63.960$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$7$	$0$	$7$	$1$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-\beta _{2}q^{7}+q^{8}+q^{10}+\cdots$
8010.2.a.bo	$8010$	$2$	8010.a	1.a	$1$	$8$	$8$	$63.960$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$-8$	$0$	$8$	$-5$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+(-1-\beta _{5})q^{7}-q^{8}+\cdots$
8010.2.a.bp	$8010$	$2$	8010.a	1.a	$1$	$8$	$8$	$63.960$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$8$	$0$	$-8$	$-5$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+(-1-\beta _{5})q^{7}+q^{8}+\cdots$
8010.2.a.bq	$8010$	$2$	8010.a	1.a	$1$	$10$	$10$	$63.960$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-10$	$0$	$-10$	$3$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-\beta _{5}q^{7}-q^{8}+q^{10}+\cdots$
8010.2.a.br	$8010$	$2$	8010.a	1.a	$1$	$10$	$10$	$63.960$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$10$	$0$	$10$	$3$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-\beta _{5}q^{7}+q^{8}+q^{10}+\cdots$
8016.2.a.v	$8016$	$2$	8016.a	1.a	$1$	$7$	$7$	$64.008$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$-7$	$5$	$-7$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(1-\beta _{1})q^{5}+(-1+\beta _{3})q^{7}+\cdots$
8016.2.a.w	$8016$	$2$	8016.a	1.a	$1$	$7$	$7$	$64.008$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$0$	$7$	$-3$	$-8$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{1}q^{5}+(-1-\beta _{2})q^{7}+q^{9}+\cdots$
8016.2.a.x	$8016$	$2$	8016.a	1.a	$1$	$8$	$8$	$64.008$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$0$	$-8$	$7$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta _{2})q^{5}+(1-\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots$
8016.2.a.y	$8016$	$2$	8016.a	1.a	$1$	$8$	$8$	$64.008$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$0$	$8$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots$
8016.2.a.z	$8016$	$2$	8016.a	1.a	$1$	$8$	$8$	$64.008$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$0$	$8$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(\beta _{1}+\beta _{2}-\beta _{5})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
8016.2.a.ba	$8016$	$2$	8016.a	1.a	$1$	$9$	$9$	$64.008$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$0$	$-9$	$-6$	$11$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta _{1})q^{5}+(2-\beta _{5}-\beta _{7}+\cdots)q^{7}+\cdots$
8016.2.a.bb	$8016$	$2$	8016.a	1.a	$1$	$9$	$9$	$64.008$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$0$	$-9$	$9$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-\beta _{1})q^{5}+\beta _{6}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
8016.2.a.bc	$8016$	$2$	8016.a	1.a	$1$	$9$	$9$	$64.008$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$0$	$9$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{1}q^{5}+(\beta _{3}+\beta _{6})q^{7}+q^{9}+\cdots$
8016.2.a.bd	$8016$	$2$	8016.a	1.a	$1$	$10$	$10$	$64.008$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$0$	$10$	$-10$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta _{1})q^{5}+(-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots$
8022.2.a.l	$8022$	$2$	8022.a	1.a	$1$	$7$	$7$	$64.056$	7.7.118870813.1	None	✓	$1$	$1$	$7$	$7$	$-8$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1+\beta _{1}-\beta _{5}+\cdots)q^{5}+\cdots$
8022.2.a.m	$8022$	$2$	8022.a	1.a	$1$	$7$	$7$	$64.056$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$7$	$7$	$-3$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1-\beta _{2}+\beta _{6})q^{5}+\cdots$
8022.2.a.n	$8022$	$2$	8022.a	1.a	$1$	$8$	$8$	$64.056$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$-8$	$-8$	$9$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1+\beta _{4})q^{5}+q^{6}+\cdots$
8022.2.a.o	$8022$	$2$	8022.a	1.a	$1$	$8$	$8$	$64.056$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-8$	$8$	$2$	$8$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots$
8022.2.a.p	$8022$	$2$	8022.a	1.a	$1$	$9$	$9$	$64.056$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$9$	$-9$	$-4$	$9$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-\beta _{6}q^{5}-q^{6}+q^{7}+\cdots$
8022.2.a.q	$8022$	$2$	8022.a	1.a	$1$	$9$	$9$	$64.056$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$9$	$-9$	$6$	$-9$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1+\beta _{2})q^{5}-q^{6}+\cdots$
8022.2.a.r	$8022$	$2$	8022.a	1.a	$1$	$10$	$10$	$64.056$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$10$	$-10$	$8$	$10$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}-q^{6}+\cdots$
8025.2.a.ba	$8025$	$2$	8025.a	1.a	$1$	$6$	$6$	$64.080$	6.6.13231312.1	None	✓	$1$	$0$	$-3$	$-6$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-q^{3}+(1-\beta _{4})q^{4}+\beta _{2}q^{6}+\cdots$
8025.2.a.bb	$8025$	$2$	8025.a	1.a	$1$	$7$	$7$	$64.080$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$7$	$0$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{5}q^{2}+q^{3}+(2-\beta _{1}-\beta _{4})q^{4}-\beta _{5}q^{6}+\cdots$
8025.2.a.bc	$8025$	$2$	8025.a	1.a	$1$	$10$	$10$	$64.080$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-2$	$10$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
8028.2.a.j	$8028$	$2$	8028.a	1.a	$1$	$7$	$7$	$64.104$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$0$	$7$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1}+\beta _{6})q^{5}+(\beta _{3}+\beta _{6})q^{7}+(1+\cdots)q^{11}+\cdots$
8028.2.a.k	$8028$	$2$	8028.a	1.a	$1$	$8$	$8$	$64.104$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$0$	$0$	$-5$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{2}+\beta _{3}+\beta _{6}+\beta _{7})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots$
8028.2.a.l	$8028$	$2$	8028.a	1.a	$1$	$8$	$8$	$64.104$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$0$	$0$	$5$	$-13$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{4}-\beta _{5})q^{5}+(-2+\beta _{2})q^{7}+(\beta _{2}+\cdots)q^{11}+\cdots$
8030.2.a.w	$8030$	$2$	8030.a	1.a	$1$	$6$	$6$	$64.120$	6.6.47685496.1	None	✓	$1$	$1$	$-6$	$-1$	$-6$	$6$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
8030.2.a.x	$8030$	$2$	8030.a	1.a	$1$	$6$	$6$	$64.120$	6.6.32730625.1	None	✓	$1$	$1$	$-6$	$2$	$-6$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}-q^{5}+\cdots$
8030.2.a.y	$8030$	$2$	8030.a	1.a	$1$	$6$	$6$	$64.120$	6.6.80296592.1	None	✓	$1$	$1$	$6$	$-3$	$6$	$3$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots$
8030.2.a.z	$8030$	$2$	8030.a	1.a	$1$	$7$	$7$	$64.120$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$-7$	$-2$	$7$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
8030.2.a.ba	$8030$	$2$	8030.a	1.a	$1$	$7$	$7$	$64.120$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$-7$	$2$	$7$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{2}q^{3}+q^{4}+q^{5}+\beta _{2}q^{6}+\cdots$

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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.