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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (26 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	7	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8092.2.a.a	$8092$	$2$	8092.a	1.a	$1$	$1$	$1$	$64.615$	$\Q$	None	✓	✓			8092.2.a.a	$1$	$0$	$0$	$-3$	$-2$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-2q^{5}-q^{7}+6q^{9}+4q^{13}+\cdots$
8092.2.a.b	$8092$	$2$	8092.a	1.a	$1$	$1$	$1$	$64.615$	$\Q$	None	✓	✓			8092.2.a.b	$1$	$0$	$0$	$-2$	$2$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}+q^{7}+q^{9}+4q^{13}+\cdots$
8092.2.a.c	$8092$	$2$	8092.a	1.a	$1$	$1$	$1$	$64.615$	$\Q$	None	✓	✓			8092.2.a.c	$1$	$2$	$0$	$-1$	$-2$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{7}-2q^{9}-4q^{11}+\cdots$
8092.2.a.d	$8092$	$2$	8092.a	1.a	$1$	$1$	$1$	$64.615$	$\Q$	None	✓	✓			8092.2.a.d	$1$	$2$	$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}-2q^{9}-6q^{11}-4q^{13}+\cdots$
8092.2.a.e	$8092$	$2$	8092.a	1.a	$1$	$1$	$1$	$64.615$	$\Q$	None	✓	✓			8092.2.a.e	$1$	$1$	$0$	$0$	$-4$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+q^{7}-3q^{9}-4q^{11}-2q^{19}+\cdots$
8092.2.a.f	$8092$	$2$	8092.a	1.a	$1$	$1$	$1$	$64.615$	$\Q$	None	✓	✓			8092.2.a.e	$1$	$1$	$0$	$0$	$4$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-q^{7}-3q^{9}+4q^{11}-2q^{19}+\cdots$
8092.2.a.g	$8092$	$2$	8092.a	1.a	$1$	$1$	$1$	$64.615$	$\Q$	None	✓	✓			8092.2.a.d	$1$	$0$	$0$	$1$	$0$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}-2q^{9}+6q^{11}-4q^{13}+\cdots$
8092.2.a.h	$8092$	$2$	8092.a	1.a	$1$	$1$	$1$	$64.615$	$\Q$	None	✓	✓			8092.2.a.c	$1$	$0$	$0$	$1$	$2$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-q^{7}-2q^{9}+4q^{11}+\cdots$
8092.2.a.i	$8092$	$2$	8092.a	1.a	$1$	$1$	$1$	$64.615$	$\Q$	None	✓	✓			8092.2.a.b	$1$	$0$	$0$	$2$	$-2$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{5}-q^{7}+q^{9}+4q^{13}+\cdots$
8092.2.a.j	$8092$	$2$	8092.a	1.a	$1$	$1$	$1$	$64.615$	$\Q$	None	✓	✓			8092.2.a.a	$1$	$0$	$0$	$3$	$2$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+2q^{5}+q^{7}+6q^{9}+4q^{13}+\cdots$
8092.2.a.k	$8092$	$2$	8092.a	1.a	$1$	$2$	$2$	$64.615$	$\Q(\sqrt{13}) $	None	✓				476.2.a.d	$1$	$0$	$0$	$-1$	$1$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1-\beta )q^{5}-q^{7}+\beta q^{9}+(4+\cdots)q^{13}+\cdots$
8092.2.a.l	$8092$	$2$	8092.a	1.a	$1$	$2$	$2$	$64.615$	$\Q(\sqrt{13}) $	None	✓				476.2.a.c	$1$	$1$	$0$	$1$	$-1$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1+\beta )q^{5}+q^{7}+\beta q^{9}+\cdots$
8092.2.a.m	$8092$	$2$	8092.a	1.a	$1$	$2$	$2$	$64.615$	$\Q(\sqrt{5}) $	None	✓				476.2.a.b	$1$	$1$	$0$	$1$	$1$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1-\beta )q^{5}+q^{7}+(-2+\beta )q^{9}+\cdots$
8092.2.a.n	$8092$	$2$	8092.a	1.a	$1$	$2$	$2$	$64.615$	$\Q(\sqrt{13}) $	None	✓				476.2.a.a	$1$	$0$	$0$	$3$	$3$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(2-\beta )q^{5}-q^{7}+(1+3\beta )q^{9}+\cdots$
8092.2.a.o	$8092$	$2$	8092.a	1.a	$1$	$3$	$3$	$64.615$	3.3.788.1	None	✓	✓			8092.2.a.o	$1$	$1$	$0$	$-1$	$4$	$3$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(1+\beta _{2})q^{5}+q^{7}+(3-\beta _{1}+\cdots)q^{9}+\cdots$
8092.2.a.p	$8092$	$2$	8092.a	1.a	$1$	$3$	$3$	$64.615$	3.3.788.1	None	✓	✓			8092.2.a.o	$1$	$1$	$0$	$1$	$-4$	$-3$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(-1-\beta _{2})q^{5}-q^{7}+(3-\beta _{1}+\cdots)q^{9}+\cdots$
8092.2.a.q	$8092$	$2$	8092.a	1.a	$1$	$4$	$4$	$64.615$	4.4.1957.1	None	✓				476.2.b.a	$1$	$1$	$0$	$-4$	$-2$	$4$	$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{3}+(-1+\beta _{3})q^{5}+q^{7}+\cdots$
8092.2.a.r	$8092$	$2$	8092.a	1.a	$1$	$4$	$4$	$64.615$	4.4.1957.1	None	✓				476.2.b.a	$1$	$0$	$0$	$4$	$2$	$-4$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{2})q^{3}+(1-\beta _{3})q^{5}-q^{7}+(2+\cdots)q^{9}+\cdots$
8092.2.a.s	$8092$	$2$	8092.a	1.a	$1$	$8$	$8$	$64.615$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓				476.2.l.a	$1$	$1$	$0$	$-4$	$-4$	$8$	$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+(-1-\beta _{1})q^{5}+q^{7}+(-1+\cdots)q^{9}+\cdots$
8092.2.a.t	$8092$	$2$	8092.a	1.a	$1$	$8$	$8$	$64.615$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓				476.2.l.a	$1$	$0$	$0$	$4$	$4$	$-8$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+(1+\beta _{1})q^{5}-q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots$
8092.2.a.u	$8092$	$2$	8092.a	1.a	$1$	$12$	$12$	$64.615$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓		8092.2.a.u	$1$	$0$	$0$	$0$	$0$	$-12$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{7}q^{5}-q^{7}+(1+\beta _{6}+\beta _{8}+\cdots)q^{9}+\cdots$
8092.2.a.v	$8092$	$2$	8092.a	1.a	$1$	$12$	$12$	$64.615$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓			8092.2.a.v	$1$	$1$	$0$	$0$	$0$	$-12$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{10}q^{5}-q^{7}+(1-\beta _{3}+\beta _{8}+\cdots)q^{9}+\cdots$
8092.2.a.w	$8092$	$2$	8092.a	1.a	$1$	$12$	$12$	$64.615$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓		8092.2.a.v	$1$	$1$	$0$	$0$	$0$	$12$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{10}q^{5}+q^{7}+(1-\beta _{3}+\beta _{8}+\cdots)q^{9}+\cdots$
8092.2.a.x	$8092$	$2$	8092.a	1.a	$1$	$12$	$12$	$64.615$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓			8092.2.a.u	$1$	$0$	$0$	$0$	$0$	$12$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{7}q^{5}+q^{7}+(1+\beta _{6}+\beta _{8}+\cdots)q^{9}+\cdots$
8092.2.a.y	$8092$	$2$	8092.a	1.a	$1$	$20$	$20$	$64.615$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓		✓		476.2.u.a	$1$	$1$	$0$	$-8$	$-8$	$-20$	$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{12}q^{5}-q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
8092.2.a.z	$8092$	$2$	8092.a	1.a	$1$	$20$	$20$	$64.615$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓		✓		476.2.u.a	$1$	$0$	$0$	$8$	$8$	$20$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{12}q^{5}+q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$

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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.