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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
6003.2.a.m	$6003$	$2$	6003.a	1.a	$1$	$11$	$11$	$47.934$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$1$	$-2$	$0$	$-2$	$3$	$+$	$3$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{4}q^{5}-\beta _{6}q^{7}+\cdots$
6003.2.a.n	$6003$	$2$	6003.a	1.a	$1$	$12$	$12$	$47.934$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$3$	$0$	$16$	$-7$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1-\beta _{4}-\beta _{6}+\beta _{8})q^{4}+(1+\cdots)q^{5}+\cdots$
6003.2.a.o	$6003$	$2$	6003.a	1.a	$1$	$13$	$13$	$47.934$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$1$	$-4$	$0$	$-16$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{8})q^{5}+\cdots$
6003.2.a.p	$6003$	$2$	6003.a	1.a	$1$	$14$	$14$	$47.934$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$2$	$0$	$3$	$-3$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{11}q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots$
6003.2.a.q	$6003$	$2$	6003.a	1.a	$1$	$16$	$16$	$47.934$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$1$	$-3$	$0$	$-16$	$1$	$+$	$2^{6}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots$
6003.2.a.r	$6003$	$2$	6003.a	1.a	$1$	$16$	$16$	$47.934$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$0$	$1$	$0$	$-3$	$13$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{8}q^{5}+(1-\beta _{10}+\cdots)q^{7}+\cdots$
6003.2.a.s	$6003$	$2$	6003.a	1.a	$1$	$20$	$20$	$47.934$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$1$	$0$	$-2$	$0$	$1$	$9$	$-$	$2^{7}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{6}q^{5}-\beta _{14}q^{7}+\cdots$
6010.2.a.c	$6010$	$2$	6010.a	1.a	$1$	$16$	$16$	$47.990$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$1$	$16$	$-8$	$16$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots$
6016.2.a.m	$6016$	$2$	6016.a	1.a	$1$	$13$	$13$	$48.038$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$1$	$0$	$-4$	$-6$	$2$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{8}q^{5}+\beta _{9}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
6016.2.a.n	$6016$	$2$	6016.a	1.a	$1$	$13$	$13$	$48.038$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$0$	$-4$	$6$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{8}q^{5}-\beta _{9}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
6016.2.a.o	$6016$	$2$	6016.a	1.a	$1$	$13$	$13$	$48.038$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$0$	$4$	$-6$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{8}q^{5}-\beta _{9}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
6016.2.a.p	$6016$	$2$	6016.a	1.a	$1$	$13$	$13$	$48.038$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$0$	$4$	$6$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{8}q^{5}+\beta _{9}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
6016.2.a.q	$6016$	$2$	6016.a	1.a	$1$	$14$	$14$	$48.038$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$1$	$0$	$-2$	$-6$	$-2$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{6}q^{5}-\beta _{12}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
6016.2.a.r	$6016$	$2$	6016.a	1.a	$1$	$14$	$14$	$48.038$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$0$	$-2$	$6$	$2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{6}q^{5}+\beta _{12}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
6016.2.a.s	$6016$	$2$	6016.a	1.a	$1$	$14$	$14$	$48.038$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$0$	$2$	$-6$	$2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{6}q^{5}+\beta _{12}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
6016.2.a.t	$6016$	$2$	6016.a	1.a	$1$	$14$	$14$	$48.038$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$0$	$2$	$6$	$-2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{6}q^{5}-\beta _{12}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
6018.2.a.z	$6018$	$2$	6018.a	1.a	$1$	$11$	$11$	$48.054$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$11$	$-11$	$4$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}-\beta _{2}q^{7}+\cdots$
6018.2.a.ba	$6018$	$2$	6018.a	1.a	$1$	$12$	$12$	$48.054$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$12$	$12$	$8$	$5$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1-\beta _{1})q^{5}+q^{6}+\cdots$
6018.2.a.bb	$6018$	$2$	6018.a	1.a	$1$	$13$	$13$	$48.054$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$13$	$13$	$4$	$11$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots$
6018.2.a.bc	$6018$	$2$	6018.a	1.a	$1$	$14$	$14$	$48.054$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$14$	$-14$	$2$	$1$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}-\beta _{6}q^{7}+\cdots$
6020.2.a.h	$6020$	$2$	6020.a	1.a	$1$	$12$	$12$	$48.070$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$0$	$3$	$-12$	$12$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+q^{7}+(2+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
6020.2.a.i	$6020$	$2$	6020.a	1.a	$1$	$12$	$12$	$48.070$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$0$	$3$	$12$	$12$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}+q^{7}+(2+\beta _{2})q^{9}+\beta _{6}q^{11}+\cdots$
6020.2.a.j	$6020$	$2$	6020.a	1.a	$1$	$13$	$13$	$48.070$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$0$	$-1$	$-13$	$-13$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}-q^{7}+(1+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots$
6020.2.a.k	$6020$	$2$	6020.a	1.a	$1$	$13$	$13$	$48.070$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$0$	$0$	$13$	$-13$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}-q^{7}+(1+\beta _{2})q^{9}+\beta _{8}q^{11}+\cdots$
6024.2.a.l	$6024$	$2$	6024.a	1.a	$1$	$11$	$11$	$48.102$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$0$	$-11$	$6$	$-5$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta _{3})q^{5}+(\beta _{3}-\beta _{10})q^{7}+\cdots$
6024.2.a.m	$6024$	$2$	6024.a	1.a	$1$	$11$	$11$	$48.102$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$1$	$0$	$11$	$-3$	$-10$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{5}q^{5}+(-1-\beta _{10})q^{7}+q^{9}+\cdots$
6024.2.a.n	$6024$	$2$	6024.a	1.a	$1$	$14$	$14$	$48.102$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$1$	$0$	$-14$	$-7$	$1$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta _{1})q^{5}-\beta _{3}q^{7}+q^{9}+\cdots$
6024.2.a.o	$6024$	$2$	6024.a	1.a	$1$	$14$	$14$	$48.102$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$1$	$0$	$-14$	$-3$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{1}q^{5}+(1-\beta _{7})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$
6024.2.a.p	$6024$	$2$	6024.a	1.a	$1$	$14$	$14$	$48.102$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$0$	$-14$	$6$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{1}q^{5}+\beta _{10}q^{7}+q^{9}-\beta _{8}q^{11}+\cdots$
6024.2.a.q	$6024$	$2$	6024.a	1.a	$1$	$18$	$18$	$48.102$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$0$	$0$	$18$	$1$	$7$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{1}q^{5}-\beta _{14}q^{7}+q^{9}-\beta _{15}q^{11}+\cdots$
6024.2.a.r	$6024$	$2$	6024.a	1.a	$1$	$20$	$20$	$48.102$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$1$	$0$	$0$	$20$	$9$	$9$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}+q^{9}-\beta _{13}q^{11}+\cdots$
6025.2.a.g	$6025$	$2$	6025.a	1.a	$1$	$11$	$11$	$48.110$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$4$	$8$	$0$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}+\beta _{2})q^{2}+(1+\beta _{2}+\beta _{3})q^{3}+\cdots$
6025.2.a.h	$6025$	$2$	6025.a	1.a	$1$	$12$	$12$	$48.110$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$-3$	$-1$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{3}+\cdots)q^{6}+\cdots$
6025.2.a.i	$6025$	$2$	6025.a	1.a	$1$	$15$	$15$	$48.110$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$1$	$-2$	$7$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{11}q^{3}+\beta _{2}q^{4}+(-\beta _{8}+\cdots)q^{6}+\cdots$
6026.2.a.f	$6026$	$2$	6026.a	1.a	$1$	$20$	$20$	$48.118$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$1$	$1$	$20$	$-5$	$-6$	$-12$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots$
6027.2.a.bf	$6027$	$2$	6027.a	1.a	$1$	$12$	$12$	$48.126$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$-2$	$-12$	$-12$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{4}+\cdots)q^{5}+\cdots$
6027.2.a.bg	$6027$	$2$	6027.a	1.a	$1$	$12$	$12$	$48.126$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$-2$	$12$	$12$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{4}+\cdots)q^{5}+\cdots$
6027.2.a.bh	$6027$	$2$	6027.a	1.a	$1$	$13$	$13$	$48.126$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$-4$	$-13$	$8$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{8}+\cdots)q^{5}+\cdots$
6027.2.a.bi	$6027$	$2$	6027.a	1.a	$1$	$13$	$13$	$48.126$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$1$	$-4$	$13$	$-8$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{8}+\cdots)q^{5}+\cdots$
6027.2.a.bj	$6027$	$2$	6027.a	1.a	$1$	$14$	$14$	$48.126$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$-2$	$-14$	$10$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots$
6027.2.a.bk	$6027$	$2$	6027.a	1.a	$1$	$14$	$14$	$48.126$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$1$	$-2$	$14$	$-10$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{3}+\cdots)q^{5}+\cdots$
6027.2.a.bl	$6027$	$2$	6027.a	1.a	$1$	$16$	$16$	$48.126$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$1$	$-4$	$-16$	$12$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{5}+\cdots)q^{5}+\cdots$
6027.2.a.bm	$6027$	$2$	6027.a	1.a	$1$	$16$	$16$	$48.126$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$1$	$-4$	$16$	$-12$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{5}+\cdots)q^{5}+\cdots$
6030.2.d.i	$6030$	$2$	6030.d	201.d	$2$	$16$	$16$	$48.150$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$-16$	$0$	$16$	$0$		$2^{9}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+q^{5}+\beta _{12}q^{7}-q^{8}-q^{10}+\cdots$
6030.2.d.j	$6030$	$2$	6030.d	201.d	$2$	$16$	$16$	$48.150$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$16$	$0$	$-16$	$0$		$2^{9}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}-q^{5}+\beta _{12}q^{7}+q^{8}-q^{10}+\cdots$
6032.2.a.bc	$6032$	$2$	6032.a	1.a	$1$	$11$	$11$	$48.166$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$0$	$6$	$-2$	$3$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+\beta _{5}q^{5}+\beta _{3}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
6032.2.a.bd	$6032$	$2$	6032.a	1.a	$1$	$12$	$12$	$48.166$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$0$	$-6$	$3$	$-6$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+\beta _{6}q^{5}+(-1-\beta _{5}+\cdots)q^{7}+\cdots$
6032.2.a.be	$6032$	$2$	6032.a	1.a	$1$	$13$	$13$	$48.166$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$0$	$4$	$5$	$-6$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{7}q^{5}-\beta _{5}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
6034.2.a.k	$6034$	$2$	6034.a	1.a	$1$	$20$	$20$	$48.182$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$1$	$1$	$-20$	$3$	$-3$	$20$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{15}q^{5}-\beta _{1}q^{6}+\cdots$
6034.2.a.l	$6034$	$2$	6034.a	1.a	$1$	$20$	$20$	$48.182$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$1$	$1$	$20$	$-3$	$-10$	$-20$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{7})q^{5}+\cdots$

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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.