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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 (40 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	7	37	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5439.2.a.a	$5439$	$2$	5439.a	1.a	$1$	$1$	$1$	$43.431$	$\Q$	None	✓				777.2.a.b	$1$	$1$	$-2$	$-1$	$-1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}+q^{9}+\cdots$
5439.2.a.b	$5439$	$2$	5439.a	1.a	$1$	$1$	$1$	$43.431$	$\Q$	None	✓				777.2.a.a	$1$	$0$	$-2$	$1$	$-1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}+q^{9}+\cdots$
5439.2.a.c	$5439$	$2$	5439.a	1.a	$1$	$1$	$1$	$43.431$	$\Q$	None	✓				777.2.a.c	$1$	$0$	$-1$	$1$	$2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}+2q^{5}-q^{6}+3q^{8}+\cdots$
5439.2.a.d	$5439$	$2$	5439.a	1.a	$1$	$1$	$1$	$43.431$	$\Q$	None	✓				777.2.a.e	$1$	$0$	$0$	$-1$	$1$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{5}+q^{9}-q^{11}+2q^{12}+\cdots$
5439.2.a.e	$5439$	$2$	5439.a	1.a	$1$	$1$	$1$	$43.431$	$\Q$	None	✓				777.2.a.d	$1$	$1$	$0$	$1$	$-3$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-3q^{5}+q^{9}-q^{11}-2q^{12}+\cdots$
5439.2.a.f	$5439$	$2$	5439.a	1.a	$1$	$1$	$1$	$43.431$	$\Q$	None	✓	✓			5439.2.a.f	$1$	$1$	$1$	$-1$	$-4$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-4q^{5}-q^{6}-3q^{8}+\cdots$
5439.2.a.g	$5439$	$2$	5439.a	1.a	$1$	$1$	$1$	$43.431$	$\Q$	None	✓				777.2.a.g	$1$	$1$	$1$	$-1$	$2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+2q^{5}-q^{6}-3q^{8}+\cdots$
5439.2.a.h	$5439$	$2$	5439.a	1.a	$1$	$1$	$1$	$43.431$	$\Q$	None	✓				777.2.a.f	$1$	$0$	$1$	$1$	$2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+2q^{5}+q^{6}-3q^{8}+\cdots$
5439.2.a.i	$5439$	$2$	5439.a	1.a	$1$	$1$	$1$	$43.431$	$\Q$	None	✓	✓			5439.2.a.f	$1$	$0$	$1$	$1$	$4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+4q^{5}+q^{6}-3q^{8}+\cdots$
5439.2.a.j	$5439$	$2$	5439.a	1.a	$1$	$2$	$2$	$43.431$	$\Q(\sqrt{2}) $	None	✓	✓			5439.2.a.j	$1$	$0$	$-2$	$-2$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+(1+\cdots)q^{6}+\cdots$
5439.2.a.k	$5439$	$2$	5439.a	1.a	$1$	$2$	$2$	$43.431$	$\Q(\sqrt{2}) $	None	✓	✓			5439.2.a.j	$1$	$1$	$-2$	$2$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots$
5439.2.a.l	$5439$	$2$	5439.a	1.a	$1$	$2$	$2$	$43.431$	$\Q(\sqrt{3}) $	None	✓				777.2.a.h	$1$	$1$	$0$	$2$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+q^{4}+\beta q^{6}-\beta q^{8}+q^{9}+\cdots$
5439.2.a.m	$5439$	$2$	5439.a	1.a	$1$	$2$	$2$	$43.431$	$\Q(\sqrt{2}) $	None	✓	✓			5439.2.a.m	$1$	$1$	$2$	$-2$	$-4$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots$
5439.2.a.n	$5439$	$2$	5439.a	1.a	$1$	$2$	$2$	$43.431$	$\Q(\sqrt{2}) $	None	✓	✓			5439.2.a.n	$1$	$0$	$2$	$-2$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}+2\beta q^{5}+\cdots$
5439.2.a.o	$5439$	$2$	5439.a	1.a	$1$	$2$	$2$	$43.431$	$\Q(\sqrt{2}) $	None	✓				777.2.a.j	$1$	$0$	$2$	$-2$	$4$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}+2q^{5}+\cdots$
5439.2.a.p	$5439$	$2$	5439.a	1.a	$1$	$2$	$2$	$43.431$	$\Q(\sqrt{2}) $	None	✓	✓			5439.2.a.n	$1$	$1$	$2$	$2$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}-2\beta q^{5}+\cdots$
5439.2.a.q	$5439$	$2$	5439.a	1.a	$1$	$2$	$2$	$43.431$	$\Q(\sqrt{2}) $	None	✓				777.2.a.i	$1$	$0$	$2$	$2$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}-2\beta q^{5}+\cdots$
5439.2.a.r	$5439$	$2$	5439.a	1.a	$1$	$2$	$2$	$43.431$	$\Q(\sqrt{2}) $	None	✓	✓			5439.2.a.m	$1$	$0$	$2$	$2$	$4$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+(2+\beta )q^{5}+\cdots$
5439.2.a.s	$5439$	$2$	5439.a	1.a	$1$	$3$	$3$	$43.431$	3.3.148.1	None	✓				111.2.a.a	$1$	$0$	$3$	$3$	$-4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
5439.2.a.t	$5439$	$2$	5439.a	1.a	$1$	$4$	$4$	$43.431$	$\Q(\sqrt{6 +3 \sqrt{2}})$	None	✓	✓			5439.2.a.t	$1$	$0$	$0$	$-4$	$4$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-q^{3}+(1-\beta _{3})q^{5}+\beta _{2}q^{6}+\cdots$
5439.2.a.u	$5439$	$2$	5439.a	1.a	$1$	$4$	$4$	$43.431$	4.4.6224.1	None	✓				111.2.a.b	$1$	$0$	$0$	$-4$	$2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
5439.2.a.v	$5439$	$2$	5439.a	1.a	$1$	$4$	$4$	$43.431$	$\Q(\sqrt{6 +3 \sqrt{2}})$	None	✓	✓			5439.2.a.t	$1$	$1$	$0$	$4$	$-4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+q^{3}+(-1+\beta _{3})q^{5}-\beta _{2}q^{6}+\cdots$
5439.2.a.w	$5439$	$2$	5439.a	1.a	$1$	$5$	$5$	$43.431$	5.5.265504.1	None	✓				777.2.a.k	$1$	$1$	$-2$	$5$	$3$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+q^{3}+(1-\beta _{1}-\beta _{4})q^{4}+(1+\cdots)q^{5}+\cdots$
5439.2.a.x	$5439$	$2$	5439.a	1.a	$1$	$5$	$5$	$43.431$	5.5.643312.1	None	✓				777.2.a.l	$1$	$0$	$-2$	$5$	$5$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
5439.2.a.y	$5439$	$2$	5439.a	1.a	$1$	$5$	$5$	$43.431$	5.5.2911216.1	None	✓				777.2.a.m	$1$	$0$	$0$	$-5$	$-5$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots$
5439.2.a.z	$5439$	$2$	5439.a	1.a	$1$	$7$	$7$	$43.431$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓				777.2.a.n	$1$	$1$	$0$	$-7$	$-3$	$0$	$+$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{2}-q^{3}+(1-\beta _{3})q^{4}+\beta _{2}q^{5}+\cdots$
5439.2.a.ba	$5439$	$2$	5439.a	1.a	$1$	$8$	$8$	$43.431$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓				777.2.i.b	$1$	$1$	$-4$	$-8$	$-2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-q^{3}+(1+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
5439.2.a.bb	$5439$	$2$	5439.a	1.a	$1$	$8$	$8$	$43.431$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓				777.2.i.b	$1$	$1$	$-4$	$8$	$2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(1+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
5439.2.a.bc	$5439$	$2$	5439.a	1.a	$1$	$8$	$8$	$43.431$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓				777.2.i.a	$1$	$1$	$-2$	$-8$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{6}q^{2}-q^{3}-\beta _{5}q^{4}+(-\beta _{1}+\beta _{7})q^{5}+\cdots$
5439.2.a.bd	$5439$	$2$	5439.a	1.a	$1$	$8$	$8$	$43.431$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓		✓		777.2.i.a	$1$	$1$	$-2$	$8$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{6}q^{2}+q^{3}-\beta _{5}q^{4}+(\beta _{1}-\beta _{7})q^{5}+\cdots$
5439.2.a.be	$5439$	$2$	5439.a	1.a	$1$	$9$	$9$	$43.431$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓		5439.2.a.be	$1$	$1$	$-1$	$-9$	$0$	$0$	$+$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots$
5439.2.a.bf	$5439$	$2$	5439.a	1.a	$1$	$9$	$9$	$43.431$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓			5439.2.a.be	$1$	$0$	$-1$	$9$	$0$	$0$	$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots$
5439.2.a.bg	$5439$	$2$	5439.a	1.a	$1$	$16$	$16$	$43.431$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	✓			5439.2.a.bg	$1$	$0$	$0$	$-16$	$12$	$0$	$+$	$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{5}+\cdots)q^{5}+\cdots$
5439.2.a.bh	$5439$	$2$	5439.a	1.a	$1$	$16$	$16$	$43.431$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	✓	✓		5439.2.a.bg	$1$	$1$	$0$	$16$	$-12$	$0$	$-$	$+$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{5}+\cdots)q^{5}+\cdots$
5439.2.a.bi	$5439$	$2$	5439.a	1.a	$1$	$16$	$16$	$43.431$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓		✓		777.2.i.d	$1$	$0$	$2$	$-16$	$-2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots$
5439.2.a.bj	$5439$	$2$	5439.a	1.a	$1$	$16$	$16$	$43.431$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓				777.2.i.d	$1$	$0$	$2$	$16$	$2$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots$
5439.2.a.bk	$5439$	$2$	5439.a	1.a	$1$	$16$	$16$	$43.431$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓				777.2.i.c	$1$	$0$	$4$	$-16$	$0$	$0$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{8}q^{5}+\cdots$
5439.2.a.bl	$5439$	$2$	5439.a	1.a	$1$	$16$	$16$	$43.431$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓		✓		777.2.i.c	$1$	$0$	$4$	$16$	$0$	$0$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots$
5439.2.a.bm	$5439$	$2$	5439.a	1.a	$1$	$18$	$18$	$43.431$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	✓	✓		5439.2.a.bm	$1$	$1$	$-2$	$-18$	$0$	$0$	$+$	$+$	$+$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots$
5439.2.a.bn	$5439$	$2$	5439.a	1.a	$1$	$18$	$18$	$43.431$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	✓	✓		5439.2.a.bm	$1$	$0$	$-2$	$18$	$0$	$0$	$-$	$+$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
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.