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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 (37 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	23	29	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4002.2.a.a	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$2$	$-1$	$-1$	$-2$	$-2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-2q^{7}+\cdots$
4002.2.a.b	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$0$	$-4$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-4q^{7}-q^{8}+\cdots$
4002.2.a.c	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$1$	$4$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots$
4002.2.a.d	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$-3$	$-3$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-3q^{7}+\cdots$
4002.2.a.e	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$-1$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
4002.2.a.f	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$2$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots$
4002.2.a.g	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$4$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{8}+\cdots$
4002.2.a.h	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$-2$	$-2$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots$
4002.2.a.i	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$-2$	$2$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+2q^{7}+\cdots$
4002.2.a.j	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$1$	$-4$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots$
4002.2.a.k	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$1$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
4002.2.a.l	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$2$	$4$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+4q^{7}+\cdots$
4002.2.a.m	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-3$	$-4$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-4q^{7}+\cdots$
4002.2.a.n	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$-2$	$-4$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-4q^{7}+\cdots$
4002.2.a.o	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-1$	$-3$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-3q^{7}+\cdots$
4002.2.a.p	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-1$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
4002.2.a.q	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$4$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots$
4002.2.a.r	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$3$	$1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{7}+\cdots$
4002.2.a.s	$4002$	$2$	4002.a	1.a	$1$	$2$	$2$	$31.956$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$-2$	$-2$	$-3$	$3$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots$
4002.2.a.t	$4002$	$2$	4002.a	1.a	$1$	$2$	$2$	$31.956$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$-2$	$0$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2\beta q^{5}+q^{6}+\beta q^{7}+\cdots$
4002.2.a.u	$4002$	$2$	4002.a	1.a	$1$	$2$	$2$	$31.956$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$-2$	$2$	$1$	$1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+\beta q^{7}+\cdots$
4002.2.a.v	$4002$	$2$	4002.a	1.a	$1$	$2$	$2$	$31.956$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$2$	$-2$	$-3$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots$
4002.2.a.w	$4002$	$2$	4002.a	1.a	$1$	$2$	$2$	$31.956$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$2$	$6$	$6$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+3q^{7}+\cdots$
4002.2.a.x	$4002$	$2$	4002.a	1.a	$1$	$2$	$2$	$31.956$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$2$	$2$	$8$	$4$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+(2-\beta )q^{7}+\cdots$
4002.2.a.y	$4002$	$2$	4002.a	1.a	$1$	$3$	$3$	$31.956$	3.3.1772.1	None	✓	$1$	$0$	$-3$	$-3$	$-1$	$6$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+(2+\cdots)q^{7}+\cdots$
4002.2.a.z	$4002$	$2$	4002.a	1.a	$1$	$3$	$3$	$31.956$	3.3.316.1	None	✓	$1$	$1$	$3$	$-3$	$0$	$-2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots$
4002.2.a.ba	$4002$	$2$	4002.a	1.a	$1$	$4$	$4$	$31.956$	4.4.16448.2	None	✓	$1$	$0$	$-4$	$-4$	$2$	$6$	$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta _{3}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots$
4002.2.a.bb	$4002$	$2$	4002.a	1.a	$1$	$4$	$4$	$31.956$	4.4.23252.1	None	✓	$1$	$1$	$-4$	$4$	$-3$	$-2$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-1+\beta _{3})q^{5}-q^{6}+\cdots$
4002.2.a.bc	$4002$	$2$	4002.a	1.a	$1$	$4$	$4$	$31.956$	4.4.11324.1	None	✓	$1$	$1$	$4$	$4$	$-4$	$-4$	$-$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots$
4002.2.a.bd	$4002$	$2$	4002.a	1.a	$1$	$4$	$4$	$31.956$	4.4.19796.1	None	✓	$1$	$0$	$4$	$4$	$-1$	$2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-\beta _{3}q^{5}+q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots$
4002.2.a.be	$4002$	$2$	4002.a	1.a	$1$	$5$	$5$	$31.956$	5.5.2389280.1	None	✓	$1$	$1$	$-5$	$-5$	$1$	$-4$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta _{2}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
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	✓	$1$	$0$	$8$	$-8$	$2$	$5$	$-$	$+$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+(1+\cdots)q^{7}+\cdots$

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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.