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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 (29 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				A-L signs				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	5	167	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5010.2.a.a	$5010$	$2$	5010.a	1.a	$1$	$1$	$1$	$40.005$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$1$	$2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+2q^{7}+\cdots$
5010.2.a.b	$5010$	$2$	5010.a	1.a	$1$	$1$	$1$	$40.005$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$1$	$5$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+5q^{7}+\cdots$
5010.2.a.c	$5010$	$2$	5010.a	1.a	$1$	$1$	$1$	$40.005$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$-1$	$-4$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots$
5010.2.a.d	$5010$	$2$	5010.a	1.a	$1$	$1$	$1$	$40.005$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$-1$	$2$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots$
5010.2.a.e	$5010$	$2$	5010.a	1.a	$1$	$1$	$1$	$40.005$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$-1$	$-4$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots$
5010.2.a.f	$5010$	$2$	5010.a	1.a	$1$	$1$	$1$	$40.005$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$-1$	$2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots$
5010.2.a.g	$5010$	$2$	5010.a	1.a	$1$	$1$	$1$	$40.005$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-1$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
5010.2.a.h	$5010$	$2$	5010.a	1.a	$1$	$1$	$1$	$40.005$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$1$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
5010.2.a.i	$5010$	$2$	5010.a	1.a	$1$	$2$	$2$	$40.005$	$\Q(\sqrt{33}) $	None	✓	$1$	$0$	$-2$	$-2$	$-2$	$3$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(1+\beta )q^{7}+\cdots$
5010.2.a.j	$5010$	$2$	5010.a	1.a	$1$	$2$	$2$	$40.005$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$-2$	$2$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+\beta q^{7}+\cdots$
5010.2.a.k	$5010$	$2$	5010.a	1.a	$1$	$2$	$2$	$40.005$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$2$	$-2$	$3$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+3\beta q^{7}+\cdots$
5010.2.a.l	$5010$	$2$	5010.a	1.a	$1$	$2$	$2$	$40.005$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$2$	$2$	$6$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(3+\beta )q^{7}+\cdots$
5010.2.a.m	$5010$	$2$	5010.a	1.a	$1$	$3$	$3$	$40.005$	3.3.785.1	None	✓	$1$	$1$	$-3$	$-3$	$3$	$-5$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots$
5010.2.a.n	$5010$	$2$	5010.a	1.a	$1$	$3$	$3$	$40.005$	3.3.316.1	None	✓	$1$	$0$	$-3$	$-3$	$3$	$1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(1-2\beta _{1}+\cdots)q^{7}+\cdots$
5010.2.a.o	$5010$	$2$	5010.a	1.a	$1$	$3$	$3$	$40.005$	3.3.321.1	None	✓	$1$	$1$	$3$	$3$	$-3$	$-3$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
5010.2.a.p	$5010$	$2$	5010.a	1.a	$1$	$3$	$3$	$40.005$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$3$	$3$	$3$	$-7$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots$
5010.2.a.q	$5010$	$2$	5010.a	1.a	$1$	$4$	$4$	$40.005$	4.4.314425.1	None	✓	$1$	$0$	$-4$	$-4$	$4$	$-7$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots$
5010.2.a.r	$5010$	$2$	5010.a	1.a	$1$	$4$	$4$	$40.005$	4.4.27329.1	None	✓	$1$	$1$	$-4$	$4$	$-4$	$1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+\beta _{1}q^{7}+\cdots$
5010.2.a.s	$5010$	$2$	5010.a	1.a	$1$	$4$	$4$	$40.005$	4.4.2777.1	None	✓	$1$	$1$	$4$	$-4$	$4$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
5010.2.a.t	$5010$	$2$	5010.a	1.a	$1$	$5$	$5$	$40.005$	5.5.2931521.1	None	✓	$1$	$0$	$-5$	$-5$	$-5$	$6$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(1+\beta _{4})q^{7}+\cdots$
5010.2.a.u	$5010$	$2$	5010.a	1.a	$1$	$5$	$5$	$40.005$	5.5.138136.1	None	✓	$1$	$0$	$-5$	$5$	$-5$	$3$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(1+\beta _{2}+\cdots)q^{7}+\cdots$
5010.2.a.v	$5010$	$2$	5010.a	1.a	$1$	$5$	$5$	$40.005$	5.5.1686952.1	None	✓	$1$	$0$	$-5$	$5$	$5$	$-3$	$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
5010.2.a.w	$5010$	$2$	5010.a	1.a	$1$	$5$	$5$	$40.005$	5.5.1387436.1	None	✓	$1$	$1$	$5$	$-5$	$-5$	$-5$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
5010.2.a.x	$5010$	$2$	5010.a	1.a	$1$	$6$	$6$	$40.005$	6.6.50061269.1	None	✓	$1$	$1$	$-6$	$6$	$6$	$-6$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
5010.2.a.y	$5010$	$2$	5010.a	1.a	$1$	$7$	$7$	$40.005$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$-7$	$-7$	$-7$	$-12$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots$
5010.2.a.z	$5010$	$2$	5010.a	1.a	$1$	$7$	$7$	$40.005$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$7$	$-7$	$-7$	$10$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
5010.2.a.ba	$5010$	$2$	5010.a	1.a	$1$	$9$	$9$	$40.005$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$9$	$9$	$-9$	$2$	$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+\beta _{6}q^{7}+\cdots$
5010.2.a.bb	$5010$	$2$	5010.a	1.a	$1$	$10$	$10$	$40.005$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$10$	$-10$	$10$	$2$	$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+\beta _{1}q^{7}+\cdots$
5010.2.a.bc	$5010$	$2$	5010.a	1.a	$1$	$10$	$10$	$40.005$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$10$	$10$	$10$	$5$	$-$	$-$	$-$	$+$	$-$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(1-\beta _{2}+\cdots)q^{7}+\cdots$

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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.