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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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Results (42 matches)

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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
2002.2.a.a	$2002$	$2$	2002.a	1.a	$1$	$1$	$1$	$15.986$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-3q^{9}+\cdots$
2002.2.a.b	$2002$	$2$	2002.a	1.a	$1$	$1$	$1$	$15.986$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-3q^{9}+\cdots$
2002.2.a.c	$2002$	$2$	2002.a	1.a	$1$	$1$	$1$	$15.986$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{5}+q^{7}+q^{8}-3q^{9}+\cdots$
2002.2.a.d	$2002$	$2$	2002.a	1.a	$1$	$2$	$2$	$15.986$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$-1$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}+(-1+\beta )q^{5}+\beta q^{6}+\cdots$
2002.2.a.e	$2002$	$2$	2002.a	1.a	$1$	$2$	$2$	$15.986$	$\Q(\sqrt{13}) $	None	✓	$1$	$0$	$-2$	$1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots$
2002.2.a.f	$2002$	$2$	2002.a	1.a	$1$	$2$	$2$	$15.986$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-3$	$-5$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-2-\beta )q^{5}+\cdots$
2002.2.a.g	$2002$	$2$	2002.a	1.a	$1$	$2$	$2$	$15.986$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots$
2002.2.a.h	$2002$	$2$	2002.a	1.a	$1$	$2$	$2$	$15.986$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$2$	$-1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots$
2002.2.a.i	$2002$	$2$	2002.a	1.a	$1$	$3$	$3$	$15.986$	3.3.469.1	None	✓	$1$	$0$	$-3$	$1$	$5$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(2+\beta _{2})q^{5}-\beta _{1}q^{6}+\cdots$
2002.2.a.j	$2002$	$2$	2002.a	1.a	$1$	$3$	$3$	$15.986$	3.3.733.1	None	✓	$1$	$0$	$-3$	$3$	$-1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta _{2})q^{3}+q^{4}-\beta _{1}q^{5}+(-1+\cdots)q^{6}+\cdots$
2002.2.a.k	$2002$	$2$	2002.a	1.a	$1$	$3$	$3$	$15.986$	3.3.229.1	None	✓	$1$	$1$	$3$	$-3$	$-5$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-2-\beta _{2})q^{5}+\cdots$
2002.2.a.l	$2002$	$2$	2002.a	1.a	$1$	$4$	$4$	$15.986$	4.4.14272.1	None	✓	$1$	$1$	$-4$	$-2$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{3})q^{5}+\cdots$
2002.2.a.m	$2002$	$2$	2002.a	1.a	$1$	$4$	$4$	$15.986$	$\Q(\sqrt{2}, \sqrt{5})$	None	✓	$1$	$1$	$-4$	$-2$	$-2$	$4$	$+$	$3$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(-1+\beta _{3})q^{5}+\cdots$
2002.2.a.n	$2002$	$2$	2002.a	1.a	$1$	$5$	$5$	$15.986$	5.5.2055632.1	None	✓	$1$	$1$	$-5$	$-2$	$-6$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+(-2+\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
2002.2.a.o	$2002$	$2$	2002.a	1.a	$1$	$5$	$5$	$15.986$	5.5.4179152.1	None	✓	$1$	$1$	$-5$	$-2$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots$
2002.2.a.p	$2002$	$2$	2002.a	1.a	$1$	$5$	$5$	$15.986$	5.5.9353072.1	None	✓	$1$	$0$	$5$	$0$	$4$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{2})q^{5}+\beta _{1}q^{6}+\cdots$
2002.2.a.q	$2002$	$2$	2002.a	1.a	$1$	$5$	$5$	$15.986$	5.5.3430384.1	None	✓	$1$	$0$	$5$	$4$	$2$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{4})q^{3}+q^{4}+\beta _{1}q^{5}+(1+\cdots)q^{6}+\cdots$
2002.2.a.r	$2002$	$2$	2002.a	1.a	$1$	$5$	$5$	$15.986$	5.5.1590832.1	None	✓	$1$	$0$	$5$	$4$	$4$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1+\beta _{3})q^{5}+\cdots$
2002.2.a.s	$2002$	$2$	2002.a	1.a	$1$	$6$	$6$	$15.986$	6.6.1385718192.1	None	✓	$1$	$0$	$6$	$0$	$0$	$-6$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{4}q^{5}+\beta _{1}q^{6}+\cdots$
2002.2.c.a	$2002$	$2$	2002.c	77.b	$2$	$48$	$48$	$15.986$		None		$2$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{2}]$
2002.2.c.b	$2002$	$2$	2002.c	77.b	$2$	$48$	$48$	$15.986$		None		$2$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{2}]$
2002.2.g.a	$2002$	$2$	2002.g	13.b	$2$	$12$	$12$	$15.986$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$-2$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{2}+\beta _{10}q^{3}-q^{4}+(-\beta _{3}-\beta _{7}+\cdots)q^{5}+\cdots$
2002.2.g.b	$2002$	$2$	2002.g	13.b	$2$	$18$	$18$	$15.986$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		$2$	$0$	$0$	$-2$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}-\beta _{2}q^{3}-q^{4}-\beta _{9}q^{5}+\beta _{1}q^{6}+\cdots$
2002.2.g.c	$2002$	$2$	2002.g	13.b	$2$	$18$	$18$	$15.986$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		$2$	$0$	$0$	$2$	$0$	$0$		$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{2}-\beta _{3}q^{3}-q^{4}+(\beta _{6}+\beta _{8})q^{5}+\cdots$
2002.2.g.d	$2002$	$2$	2002.g	13.b	$2$	$20$	$20$	$15.986$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$0$	$2$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{11}q^{2}+\beta _{6}q^{3}-q^{4}+\beta _{14}q^{5}+\cdots$
2002.4.a.a	$2002$	$4$	2002.a	1.a	$1$	$1$	$1$	$118.122$	$\Q$	None	✓	$1$	$1$	$2$	$-2$	$-3$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-2q^{3}+4q^{4}-3q^{5}-4q^{6}+\cdots$
2002.4.a.b	$2002$	$4$	2002.a	1.a	$1$	$8$	$8$	$118.122$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$16$	$-5$	$-25$	$56$	$-$	$3^{3}$	$\mathrm{SU}(2)$	$q+2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(-3+\cdots)q^{5}+\cdots$
2002.4.a.c	$2002$	$4$	2002.a	1.a	$1$	$9$	$9$	$118.122$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$18$	$-6$	$-24$	$-63$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(-2+\cdots)q^{5}+\cdots$
2002.4.a.d	$2002$	$4$	2002.a	1.a	$1$	$10$	$10$	$118.122$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$-20$	$0$	$12$	$70$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-\beta _{1}q^{3}+4q^{4}+(1+\beta _{6})q^{5}+\cdots$
2002.4.a.e	$2002$	$4$	2002.a	1.a	$1$	$10$	$10$	$118.122$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$-20$	$11$	$22$	$-70$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(1+\beta _{1})q^{3}+4q^{4}+(2+\beta _{6}+\cdots)q^{5}+\cdots$
2002.4.a.f	$2002$	$4$	2002.a	1.a	$1$	$10$	$10$	$118.122$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$20$	$-18$	$-38$	$70$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-2+\beta _{1})q^{3}+4q^{4}+(-4+\cdots)q^{5}+\cdots$
2002.4.a.g	$2002$	$4$	2002.a	1.a	$1$	$10$	$10$	$118.122$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$20$	$5$	$2$	$-70$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}-\beta _{3}q^{5}+\cdots$
2002.4.a.h	$2002$	$4$	2002.a	1.a	$1$	$11$	$11$	$118.122$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$1$	$-22$	$-4$	$4$	$-77$	$-$	$2^{6}$	$\mathrm{SU}(2)$	$q-2q^{2}-\beta _{1}q^{3}+4q^{4}+\beta _{5}q^{5}+2\beta _{1}q^{6}+\cdots$
2002.4.a.i	$2002$	$4$	2002.a	1.a	$1$	$11$	$11$	$118.122$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$-22$	$0$	$-14$	$-77$	$+$	$2$	$\mathrm{SU}(2)$	$q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(-1+\beta _{5}+\cdots)q^{5}+\cdots$
2002.4.a.j	$2002$	$4$	2002.a	1.a	$1$	$11$	$11$	$118.122$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$-22$	$11$	$12$	$77$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	$q-2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(1+\beta _{5}+\cdots)q^{5}+\cdots$
2002.4.a.k	$2002$	$4$	2002.a	1.a	$1$	$12$	$12$	$118.122$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$-24$	$-9$	$-36$	$84$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(-3+\cdots)q^{5}+\cdots$
2002.4.a.l	$2002$	$4$	2002.a	1.a	$1$	$12$	$12$	$118.122$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$-24$	$2$	$-10$	$84$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(-1-\beta _{4}+\cdots)q^{5}+\cdots$
2002.4.a.m	$2002$	$4$	2002.a	1.a	$1$	$12$	$12$	$118.122$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$24$	$14$	$40$	$84$	$+$	$2^{5}$	$\mathrm{SU}(2)$	$q+2q^{2}+(1+\beta _{1})q^{3}+4q^{4}+(3-\beta _{5}+\cdots)q^{5}+\cdots$
2002.4.a.n	$2002$	$4$	2002.a	1.a	$1$	$13$	$13$	$118.122$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$1$	$-26$	$-3$	$-6$	$-91$	$-$	$2^{4}\cdot 5$	$\mathrm{SU}(2)$	$q-2q^{2}-\beta _{1}q^{3}+4q^{4}+\beta _{3}q^{5}+2\beta _{1}q^{6}+\cdots$
2002.4.a.o	$2002$	$4$	2002.a	1.a	$1$	$13$	$13$	$118.122$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$26$	$-3$	$-6$	$-91$	$+$	$2^{4}\cdot 7$	$\mathrm{SU}(2)$	$q+2q^{2}-\beta _{1}q^{3}+4q^{4}+\beta _{3}q^{5}-2\beta _{1}q^{6}+\cdots$
2002.4.a.p	$2002$	$4$	2002.a	1.a	$1$	$13$	$13$	$118.122$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$26$	$8$	$14$	$-91$	$+$	$2^{6}$	$\mathrm{SU}(2)$	$q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots$
2002.4.a.q	$2002$	$4$	2002.a	1.a	$1$	$14$	$14$	$118.122$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$28$	$15$	$24$	$98$	$+$	$2^{6}\cdot 3^{3}$	$\mathrm{SU}(2)$	$q+2q^{2}+(1+\beta _{1})q^{3}+4q^{4}+(2-\beta _{4}+\cdots)q^{5}+\cdots$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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.