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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
4002.2.a.bf	$4002$	$2$	4002.a	1.a	$1$	$6$	$6$	$31.956$	6.6.61157024.1	None	✓	$1$	$0$	$-6$	$6$	$3$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+\beta _{4}q^{5}-q^{6}+(\beta _{4}+\cdots)q^{7}+\cdots$
4002.2.a.bg	$4002$	$2$	4002.a	1.a	$1$	$7$	$7$	$31.956$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$-7$	$-7$	$2$	$-5$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-\beta _{5}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
4002.2.a.bh	$4002$	$2$	4002.a	1.a	$1$	$7$	$7$	$31.956$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$7$	$7$	$1$	$-2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+\beta _{3}q^{5}+q^{6}-\beta _{6}q^{7}+\cdots$
4002.2.a.bi	$4002$	$2$	4002.a	1.a	$1$	$8$	$8$	$31.956$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-8$	$8$	$-3$	$-6$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-\beta _{4}q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
4002.2.a.bj	$4002$	$2$	4002.a	1.a	$1$	$8$	$8$	$31.956$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$8$	$-8$	$1$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}-\beta _{4}q^{7}+\cdots$
4002.2.a.bk	$4002$	$2$	4002.a	1.a	$1$	$8$	$8$	$31.956$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$8$	$-8$	$2$	$5$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+(1+\cdots)q^{7}+\cdots$
4004.2.a.g	$4004$	$2$	4004.a	1.a	$1$	$6$	$6$	$31.972$	6.6.246302029.1	None	✓	$1$	$1$	$0$	$-2$	$-3$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1-\beta _{4})q^{5}+q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots$
4004.2.a.h	$4004$	$2$	4004.a	1.a	$1$	$9$	$9$	$31.972$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$0$	$3$	$0$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{4}q^{5}+q^{7}+(2+\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots$
4004.2.a.i	$4004$	$2$	4004.a	1.a	$1$	$9$	$9$	$31.972$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$0$	$4$	$4$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{7}q^{5}+q^{7}+(1+\beta _{3}+\beta _{4}+\cdots)q^{9}+\cdots$
4004.2.a.j	$4004$	$2$	4004.a	1.a	$1$	$10$	$10$	$31.972$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$0$	$-2$	$-2$	$-10$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{3}q^{5}-q^{7}+(1+\beta _{2})q^{9}+\cdots$
4004.2.a.k	$4004$	$2$	4004.a	1.a	$1$	$10$	$10$	$31.972$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$0$	$1$	$4$	$-10$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{4}q^{5}-q^{7}+(2+\beta _{2})q^{9}+\cdots$
4005.2.a.n	$4005$	$2$	4005.a	1.a	$1$	$6$	$6$	$31.980$	6.6.10407557.1	None	✓	$1$	$0$	$4$	$0$	$6$	$1$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+(2+\beta _{2}+\beta _{3})q^{4}+q^{5}+\cdots$
4005.2.a.o	$4005$	$2$	4005.a	1.a	$1$	$7$	$7$	$31.980$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$4$	$0$	$-7$	$-16$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{3})q^{4}-q^{5}+\cdots$
4005.2.a.p	$4005$	$2$	4005.a	1.a	$1$	$8$	$8$	$31.980$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-1$	$0$	$8$	$-6$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
4005.2.a.q	$4005$	$2$	4005.a	1.a	$1$	$9$	$9$	$31.980$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$-5$	$0$	$9$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
4005.2.a.r	$4005$	$2$	4005.a	1.a	$1$	$10$	$10$	$31.980$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$-6$	$0$	$-10$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
4005.2.a.s	$4005$	$2$	4005.a	1.a	$1$	$10$	$10$	$31.980$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-1$	$0$	$-10$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{6}q^{7}+\cdots$
4005.2.a.t	$4005$	$2$	4005.a	1.a	$1$	$10$	$10$	$31.980$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$0$	$0$	$10$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots$
4008.2.a.g	$4008$	$2$	4008.a	1.a	$1$	$7$	$7$	$32.004$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$-7$	$-3$	$8$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{1}q^{5}+(1+\beta _{2})q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$
4008.2.a.h	$4008$	$2$	4008.a	1.a	$1$	$8$	$8$	$32.004$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$0$	$-8$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{1}q^{5}+\beta _{3}q^{7}+q^{9}+(\beta _{2}+\beta _{4}+\cdots)q^{11}+\cdots$
4008.2.a.i	$4008$	$2$	4008.a	1.a	$1$	$9$	$9$	$32.004$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$0$	$9$	$-6$	$-11$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta _{1})q^{5}+(-2+\beta _{5}+\beta _{7}+\cdots)q^{7}+\cdots$
4008.2.a.j	$4008$	$2$	4008.a	1.a	$1$	$10$	$10$	$32.004$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$0$	$-10$	$-10$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{1})q^{5}+(\beta _{2}+\beta _{4}+\beta _{7}+\cdots)q^{7}+\cdots$
4010.2.a.h	$4010$	$2$	4010.a	1.a	$1$	$9$	$9$	$32.020$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$9$	$-4$	$9$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{7}q^{3}+q^{4}+q^{5}-\beta _{7}q^{6}+\cdots$
4010.2.a.i	$4010$	$2$	4010.a	1.a	$1$	$10$	$10$	$32.020$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-10$	$-4$	$10$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{7}q^{3}+q^{4}+q^{5}+\beta _{7}q^{6}+\cdots$
4014.2.a.s	$4014$	$2$	4014.a	1.a	$1$	$6$	$6$	$32.052$	6.6.232773917.1	None	✓	$1$	$1$	$-6$	$0$	$-6$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1+\beta _{1})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots$
4014.2.a.t	$4014$	$2$	4014.a	1.a	$1$	$6$	$6$	$32.052$	6.6.103354048.1	None	✓	$1$	$1$	$-6$	$0$	$-2$	$8$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(\beta _{4}-\beta _{5})q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots$
4014.2.a.u	$4014$	$2$	4014.a	1.a	$1$	$6$	$6$	$32.052$	6.6.103354048.1	None	✓	$1$	$0$	$6$	$0$	$2$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-\beta _{4}+\beta _{5})q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots$
4014.2.a.v	$4014$	$2$	4014.a	1.a	$1$	$7$	$7$	$32.052$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$-7$	$0$	$-6$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta _{4})q^{5}-\beta _{3}q^{7}+\cdots$
4014.2.a.w	$4014$	$2$	4014.a	1.a	$1$	$7$	$7$	$32.052$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$-7$	$0$	$-2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta _{3}q^{5}+(1-\beta _{2}+\beta _{6})q^{7}+\cdots$
4014.2.a.x	$4014$	$2$	4014.a	1.a	$1$	$8$	$8$	$32.052$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$-8$	$0$	$6$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta _{5}-\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots$
4014.2.a.y	$4014$	$2$	4014.a	1.a	$1$	$8$	$8$	$32.052$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$8$	$0$	$-6$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{5}+\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots$
4014.2.a.z	$4014$	$2$	4014.a	1.a	$1$	$8$	$8$	$32.052$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$8$	$0$	$-4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{3})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
4016.2.a.f	$4016$	$2$	4016.a	1.a	$1$	$6$	$6$	$32.068$	6.6.60853001.1	None	✓	$1$	$1$	$0$	$-1$	$-1$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{3}+(-1+\beta _{1}-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots$
4016.2.a.g	$4016$	$2$	4016.a	1.a	$1$	$7$	$7$	$32.068$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$3$	$-2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{5}q^{5}+(1+\beta _{6})q^{7}+(-1+\cdots)q^{9}+\cdots$
4016.2.a.h	$4016$	$2$	4016.a	1.a	$1$	$9$	$9$	$32.068$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$0$	$1$	$-5$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1-\beta _{5})q^{5}+(-\beta _{6}+\beta _{7}+\cdots)q^{7}+\cdots$
4018.2.a.bn	$4018$	$2$	4018.a	1.a	$1$	$6$	$6$	$32.084$	6.6.52046292.1	None	✓	$1$	$0$	$-6$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{3}q^{3}+q^{4}+\beta _{4}q^{5}-\beta _{3}q^{6}+\cdots$
4018.2.a.bo	$4018$	$2$	4018.a	1.a	$1$	$6$	$6$	$32.084$	6.6.52046292.1	None	✓	$1$	$0$	$-6$	$1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{3}q^{3}+q^{4}-\beta _{4}q^{5}+\beta _{3}q^{6}+\cdots$
4018.2.a.bp	$4018$	$2$	4018.a	1.a	$1$	$6$	$6$	$32.084$	6.6.5163008.1	None	✓	$1$	$1$	$6$	$-4$	$-12$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta _{2}-\beta _{3}+\beta _{4})q^{3}+q^{4}+\cdots$
4018.2.a.bq	$4018$	$2$	4018.a	1.a	$1$	$6$	$6$	$32.084$	6.6.5163008.1	None	✓	$1$	$0$	$6$	$4$	$12$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta _{2}+\beta _{3}-\beta _{4})q^{3}+q^{4}+\cdots$
4018.2.a.br	$4018$	$2$	4018.a	1.a	$1$	$10$	$10$	$32.084$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-10$	$-4$	$-4$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{3}q^{3}+q^{4}-\beta _{2}q^{5}-\beta _{3}q^{6}+\cdots$
4018.2.a.bs	$4018$	$2$	4018.a	1.a	$1$	$10$	$10$	$32.084$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$-10$	$4$	$4$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{3}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{3}q^{6}+\cdots$
4018.2.a.bt	$4018$	$2$	4018.a	1.a	$1$	$10$	$10$	$32.084$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$10$	$-1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots$
4018.2.a.bu	$4018$	$2$	4018.a	1.a	$1$	$10$	$10$	$32.084$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$10$	$1$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{4}q^{5}+\beta _{1}q^{6}+\cdots$
4020.2.a.f	$4020$	$2$	4020.a	1.a	$1$	$6$	$6$	$32.100$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$0$	$0$	$-6$	$6$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+\beta _{1}q^{7}+q^{9}+(-1-\beta _{5})q^{11}+\cdots$
4020.2.a.g	$4020$	$2$	4020.a	1.a	$1$	$6$	$6$	$32.100$	6.6.195727752.1	None	✓	$1$	$0$	$0$	$6$	$-6$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+(\beta _{1}+\beta _{4})q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots$
4020.2.a.h	$4020$	$2$	4020.a	1.a	$1$	$7$	$7$	$32.100$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$-7$	$-7$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+\beta _{1}q^{7}+q^{9}+(-1+\beta _{2}+\cdots)q^{11}+\cdots$
4020.2.a.i	$4020$	$2$	4020.a	1.a	$1$	$7$	$7$	$32.100$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$7$	$7$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-\beta _{4}q^{7}+q^{9}+(\beta _{3}+\beta _{6})q^{11}+\cdots$
4025.2.a.s	$4025$	$2$	4025.a	1.a	$1$	$8$	$8$	$32.140$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-3$	$-2$	$0$	$8$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{6}+\cdots)q^{6}+\cdots$
4025.2.a.t	$4025$	$2$	4025.a	1.a	$1$	$8$	$8$	$32.140$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-1$	$-7$	$0$	$-8$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(1+\beta _{2})q^{4}+\cdots$
4025.2.a.u	$4025$	$2$	4025.a	1.a	$1$	$8$	$8$	$32.140$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-1$	$-4$	$0$	$8$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$

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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.