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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 (42 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	5	11	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
7865.2.a.a	$7865$	$2$	7865.a	1.a	$1$	$1$	$1$	$62.802$	$\Q$	None	✓	✓			7865.2.a.a	$1$	$1$	$-1$	$3$	$-1$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}-q^{4}-q^{5}-3q^{6}-2q^{7}+\cdots$
7865.2.a.b	$7865$	$2$	7865.a	1.a	$1$	$1$	$1$	$62.802$	$\Q$	None	✓				715.2.a.b	$1$	$1$	$0$	$-2$	$1$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{4}+q^{5}-2q^{7}+q^{9}+4q^{12}+\cdots$
7865.2.a.c	$7865$	$2$	7865.a	1.a	$1$	$1$	$1$	$62.802$	$\Q$	None	✓				65.2.a.a	$1$	$1$	$1$	$-2$	$-1$	$4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}-q^{4}-q^{5}-2q^{6}+4q^{7}+\cdots$
7865.2.a.d	$7865$	$2$	7865.a	1.a	$1$	$1$	$1$	$62.802$	$\Q$	None	✓	✓			7865.2.a.a	$1$	$0$	$1$	$3$	$-1$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}-q^{4}-q^{5}+3q^{6}+2q^{7}+\cdots$
7865.2.a.e	$7865$	$2$	7865.a	1.a	$1$	$1$	$1$	$62.802$	$\Q$	None	✓				715.2.a.a	$1$	$1$	$2$	$0$	$1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{5}-3q^{9}+2q^{10}+\cdots$
7865.2.a.f	$7865$	$2$	7865.a	1.a	$1$	$2$	$2$	$62.802$	$\Q(\sqrt{5}) $	None	✓				715.2.v.a	$1$	$1$	$-1$	$0$	$2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
7865.2.a.g	$7865$	$2$	7865.a	1.a	$1$	$2$	$2$	$62.802$	$\Q(\sqrt{2}) $	None	✓				715.2.a.c	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+\beta q^{3}+q^{5}+2q^{6}+(2+\beta )q^{7}+\cdots$
7865.2.a.h	$7865$	$2$	7865.a	1.a	$1$	$2$	$2$	$62.802$	$\Q(\sqrt{3}) $	None	✓				65.2.a.c	$1$	$0$	$0$	$2$	$-2$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{3}+q^{4}-q^{5}+(3+\beta )q^{6}+\cdots$
7865.2.a.i	$7865$	$2$	7865.a	1.a	$1$	$2$	$2$	$62.802$	$\Q(\sqrt{5}) $	None	✓				715.2.v.a	$1$	$1$	$1$	$0$	$2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
7865.2.a.j	$7865$	$2$	7865.a	1.a	$1$	$2$	$2$	$62.802$	$\Q(\sqrt{2}) $	None	✓				65.2.a.b	$1$	$0$	$2$	$0$	$2$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-\beta q^{3}+(1+2\beta )q^{4}+q^{5}+\cdots$
7865.2.a.k	$7865$	$2$	7865.a	1.a	$1$	$3$	$3$	$62.802$	3.3.148.1	None	✓				715.2.a.e	$1$	$0$	$-2$	$0$	$-3$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
7865.2.a.l	$7865$	$2$	7865.a	1.a	$1$	$3$	$3$	$62.802$	3.3.148.1	None	✓				715.2.a.d	$1$	$1$	$0$	$2$	$-3$	$-6$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\cdots$
7865.2.a.m	$7865$	$2$	7865.a	1.a	$1$	$4$	$4$	$62.802$	4.4.6224.1	None	✓	✓			7865.2.a.m	$1$	$1$	$-2$	$2$	$4$	$-8$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
7865.2.a.n	$7865$	$2$	7865.a	1.a	$1$	$4$	$4$	$62.802$	4.4.6224.1	None	✓	✓			7865.2.a.m	$1$	$0$	$2$	$2$	$4$	$8$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{3})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
7865.2.a.o	$7865$	$2$	7865.a	1.a	$1$	$6$	$6$	$62.802$	6.6.37261816.1	None	✓				715.2.a.g	$1$	$1$	$1$	$-4$	$-6$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
7865.2.a.p	$7865$	$2$	7865.a	1.a	$1$	$6$	$6$	$62.802$	6.6.3486377.1	None	✓				715.2.a.f	$1$	$0$	$5$	$-2$	$-6$	$8$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{4})q^{2}-\beta _{5}q^{3}+(1+\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots$
7865.2.a.q	$7865$	$2$	7865.a	1.a	$1$	$7$	$7$	$62.802$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓			7865.2.a.q	$1$	$1$	$0$	$0$	$7$	$-3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
7865.2.a.r	$7865$	$2$	7865.a	1.a	$1$	$7$	$7$	$62.802$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓			7865.2.a.q	$1$	$0$	$0$	$0$	$7$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
7865.2.a.s	$7865$	$2$	7865.a	1.a	$1$	$8$	$8$	$62.802$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓				715.2.a.h	$1$	$1$	$-2$	$0$	$8$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
7865.2.a.t	$7865$	$2$	7865.a	1.a	$1$	$8$	$8$	$62.802$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓			7865.2.a.t	$1$	$1$	$-1$	$-5$	$-8$	$-9$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
7865.2.a.u	$7865$	$2$	7865.a	1.a	$1$	$8$	$8$	$62.802$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓			7865.2.a.t	$1$	$0$	$1$	$-5$	$-8$	$9$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
7865.2.a.v	$7865$	$2$	7865.a	1.a	$1$	$9$	$9$	$62.802$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓			7865.2.a.v	$1$	$1$	$-1$	$-2$	$9$	$-10$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
7865.2.a.w	$7865$	$2$	7865.a	1.a	$1$	$9$	$9$	$62.802$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓				715.2.a.i	$1$	$0$	$-1$	$2$	$9$	$4$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(2+\beta _{2})q^{4}+q^{5}+\cdots$
7865.2.a.x	$7865$	$2$	7865.a	1.a	$1$	$9$	$9$	$62.802$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓			7865.2.a.x	$1$	$0$	$0$	$-2$	$-9$	$9$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
7865.2.a.y	$7865$	$2$	7865.a	1.a	$1$	$9$	$9$	$62.802$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓			7865.2.a.x	$1$	$1$	$0$	$-2$	$-9$	$-9$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
7865.2.a.z	$7865$	$2$	7865.a	1.a	$1$	$9$	$9$	$62.802$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓			7865.2.a.v	$1$	$0$	$1$	$-2$	$9$	$10$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
7865.2.a.ba	$7865$	$2$	7865.a	1.a	$1$	$11$	$11$	$62.802$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓			7865.2.a.ba	$1$	$1$	$-1$	$2$	$-11$	$-10$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
7865.2.a.bb	$7865$	$2$	7865.a	1.a	$1$	$11$	$11$	$62.802$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓			7865.2.a.bb	$1$	$1$	$0$	$2$	$11$	$-9$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
7865.2.a.bc	$7865$	$2$	7865.a	1.a	$1$	$11$	$11$	$62.802$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓			7865.2.a.bb	$1$	$0$	$0$	$2$	$11$	$9$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
7865.2.a.bd	$7865$	$2$	7865.a	1.a	$1$	$11$	$11$	$62.802$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓			7865.2.a.ba	$1$	$0$	$1$	$2$	$-11$	$10$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
7865.2.a.be	$7865$	$2$	7865.a	1.a	$1$	$16$	$16$	$62.802$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓				715.2.v.b	$1$	$1$	$-2$	$-7$	$16$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{14}q^{3}+(1+\beta _{8}-\beta _{9})q^{4}+\cdots$
7865.2.a.bf	$7865$	$2$	7865.a	1.a	$1$	$16$	$16$	$62.802$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓		✓		715.2.v.b	$1$	$1$	$2$	$-7$	$16$	$3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{14}q^{3}+(1+\beta _{8}-\beta _{9})q^{4}+\cdots$
7865.2.a.bg	$7865$	$2$	7865.a	1.a	$1$	$18$	$18$	$62.802$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	✓	✓		7865.2.a.bg	$1$	$1$	$-2$	$-4$	$18$	$-20$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{10}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
7865.2.a.bh	$7865$	$2$	7865.a	1.a	$1$	$18$	$18$	$62.802$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	✓			7865.2.a.bg	$1$	$0$	$2$	$-4$	$18$	$20$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{10}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
7865.2.a.bi	$7865$	$2$	7865.a	1.a	$1$	$22$	$22$	$62.802$		None	✓	✓			7865.2.a.bi	$1$	$1$	$-2$	$4$	$-22$	$-20$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
7865.2.a.bj	$7865$	$2$	7865.a	1.a	$1$	$22$	$22$	$62.802$		None	✓				715.2.v.c	$1$	$1$	$-1$	$-7$	$-22$	$-5$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
7865.2.a.bk	$7865$	$2$	7865.a	1.a	$1$	$22$	$22$	$62.802$		None	✓		✓		715.2.v.c	$1$	$1$	$1$	$-7$	$-22$	$5$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
7865.2.a.bl	$7865$	$2$	7865.a	1.a	$1$	$22$	$22$	$62.802$		None	✓	✓			7865.2.a.bi	$1$	$0$	$2$	$4$	$-22$	$20$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
7865.2.a.bm	$7865$	$2$	7865.a	1.a	$1$	$26$	$26$	$62.802$		None	✓		✓		715.2.v.d	$1$	$0$	$-1$	$9$	$-26$	$-3$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
7865.2.a.bn	$7865$	$2$	7865.a	1.a	$1$	$26$	$26$	$62.802$		None	✓		✓		715.2.v.d	$1$	$0$	$1$	$9$	$-26$	$3$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
7865.2.a.bo	$7865$	$2$	7865.a	1.a	$1$	$30$	$30$	$62.802$		None	✓		✓		715.2.v.e	$1$	$0$	$-1$	$9$	$30$	$-5$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
7865.2.a.bp	$7865$	$2$	7865.a	1.a	$1$	$30$	$30$	$62.802$		None	✓		✓		715.2.v.e	$1$	$0$	$1$	$9$	$30$	$5$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

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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.