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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 (34 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	5	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4840.2.a.a	$4840$	$2$	4840.a	1.a	$1$	$1$	$1$	$38.648$	$\Q$	None	✓	✓			4840.2.a.a	$1$	$0$	$0$	$-2$	$-1$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots$
4840.2.a.b	$4840$	$2$	4840.a	1.a	$1$	$1$	$1$	$38.648$	$\Q$	None	✓	✓			4840.2.a.a	$1$	$1$	$0$	$-2$	$-1$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+q^{9}+2q^{13}+2q^{15}+\cdots$
4840.2.a.c	$4840$	$2$	4840.a	1.a	$1$	$1$	$1$	$38.648$	$\Q$	None	✓				440.2.a.a	$1$	$1$	$0$	$0$	$-1$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-3q^{9}+8q^{19}-8q^{23}+\cdots$
4840.2.a.d	$4840$	$2$	4840.a	1.a	$1$	$1$	$1$	$38.648$	$\Q$	None	✓				440.2.a.b	$1$	$0$	$0$	$0$	$-1$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-3q^{9}+4q^{13}+4q^{17}+\cdots$
4840.2.a.e	$4840$	$2$	4840.a	1.a	$1$	$1$	$1$	$38.648$	$\Q$	None	✓				440.2.a.c	$1$	$0$	$0$	$0$	$1$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{7}-3q^{9}-6q^{13}+6q^{17}+\cdots$
4840.2.a.f	$4840$	$2$	4840.a	1.a	$1$	$1$	$1$	$38.648$	$\Q$	None	✓				40.2.a.a	$1$	$0$	$0$	$0$	$1$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+4q^{7}-3q^{9}+2q^{13}-2q^{17}+\cdots$
4840.2.a.g	$4840$	$2$	4840.a	1.a	$1$	$1$	$1$	$38.648$	$\Q$	None	✓	✓			4840.2.a.g	$1$	$0$	$0$	$1$	$-1$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-3q^{7}-2q^{9}+4q^{13}+\cdots$
4840.2.a.h	$4840$	$2$	4840.a	1.a	$1$	$1$	$1$	$38.648$	$\Q$	None	✓	✓			4840.2.a.g	$1$	$1$	$0$	$1$	$-1$	$3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+3q^{7}-2q^{9}-4q^{13}+\cdots$
4840.2.a.i	$4840$	$2$	4840.a	1.a	$1$	$1$	$1$	$38.648$	$\Q$	None	✓				440.2.a.d	$1$	$0$	$0$	$3$	$1$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{5}-q^{7}+6q^{9}+6q^{13}+\cdots$
4840.2.a.j	$4840$	$2$	4840.a	1.a	$1$	$2$	$2$	$38.648$	$\Q(\sqrt{17}) $	None	✓				440.2.a.e	$1$	$1$	$0$	$-1$	$2$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+q^{5}+\beta q^{7}+(1+\beta )q^{9}-2q^{13}+\cdots$
4840.2.a.k	$4840$	$2$	4840.a	1.a	$1$	$2$	$2$	$38.648$	$\Q(\sqrt{3}) $	None	✓	✓			4840.2.a.k	$1$	$1$	$0$	$0$	$2$	$-4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}+(-2-\beta )q^{7}+2\beta q^{13}+\cdots$
4840.2.a.l	$4840$	$2$	4840.a	1.a	$1$	$2$	$2$	$38.648$	$\Q(\sqrt{3}) $	None	✓	✓			4840.2.a.k	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}+(2+\beta )q^{7}-2\beta q^{13}+\cdots$
4840.2.a.m	$4840$	$2$	4840.a	1.a	$1$	$2$	$2$	$38.648$	$\Q(\sqrt{17}) $	None	✓				440.2.a.g	$1$	$0$	$0$	$1$	$-2$	$-5$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+(-2-\beta )q^{7}+(1+\beta )q^{9}+\cdots$
4840.2.a.n	$4840$	$2$	4840.a	1.a	$1$	$2$	$2$	$38.648$	$\Q(\sqrt{17}) $	None	✓				440.2.a.f	$1$	$1$	$0$	$1$	$-2$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+(-2+\beta )q^{7}+(1+\beta )q^{9}+\cdots$
4840.2.a.o	$4840$	$2$	4840.a	1.a	$1$	$2$	$2$	$38.648$	$\Q(\sqrt{2}) $	None	✓	✓			4840.2.a.o	$1$	$1$	$0$	$2$	$2$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}+(-1-\beta )q^{7}+2\beta q^{9}+\cdots$
4840.2.a.p	$4840$	$2$	4840.a	1.a	$1$	$2$	$2$	$38.648$	$\Q(\sqrt{2}) $	None	✓	✓			4840.2.a.o	$1$	$0$	$0$	$2$	$2$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}+(1+\beta )q^{7}+2\beta q^{9}+\cdots$
4840.2.a.q	$4840$	$2$	4840.a	1.a	$1$	$3$	$3$	$38.648$	3.3.568.1	None	✓	✓			4840.2.a.q	$1$	$0$	$0$	$-1$	$3$	$-1$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+q^{5}+\beta _{2}q^{7}+(3-\beta _{1})q^{9}+\cdots$
4840.2.a.r	$4840$	$2$	4840.a	1.a	$1$	$3$	$3$	$38.648$	3.3.568.1	None	✓	✓			4840.2.a.q	$1$	$1$	$0$	$-1$	$3$	$1$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+q^{5}-\beta _{2}q^{7}+(3-\beta _{1})q^{9}+\cdots$
4840.2.a.s	$4840$	$2$	4840.a	1.a	$1$	$3$	$3$	$38.648$	3.3.788.1	None	✓	✓			4840.2.a.s	$1$	$1$	$0$	$1$	$-3$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+(-1-\beta _{1}+\beta _{2})q^{7}+\cdots$
4840.2.a.t	$4840$	$2$	4840.a	1.a	$1$	$3$	$3$	$38.648$	3.3.404.1	None	✓	✓			4840.2.a.t	$1$	$1$	$0$	$1$	$-3$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}-q^{5}-\beta _{1}q^{7}+(2+\beta _{1}-\beta _{2})q^{9}+\cdots$
4840.2.a.u	$4840$	$2$	4840.a	1.a	$1$	$3$	$3$	$38.648$	3.3.404.1	None	✓	✓			4840.2.a.t	$1$	$0$	$0$	$1$	$-3$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}-q^{5}+\beta _{1}q^{7}+(2+\beta _{1}-\beta _{2})q^{9}+\cdots$
4840.2.a.v	$4840$	$2$	4840.a	1.a	$1$	$3$	$3$	$38.648$	3.3.788.1	None	✓	✓			4840.2.a.s	$1$	$0$	$0$	$1$	$-3$	$3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots$
4840.2.a.w	$4840$	$2$	4840.a	1.a	$1$	$4$	$4$	$38.648$	4.4.4752.1	None	✓	✓			4840.2.a.w	$1$	$1$	$0$	$-2$	$-4$	$-6$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}-q^{5}+(-2-\beta _{2}+\beta _{3})q^{7}+\cdots$
4840.2.a.x	$4840$	$2$	4840.a	1.a	$1$	$4$	$4$	$38.648$	4.4.4752.1	None	✓	✓			4840.2.a.w	$1$	$0$	$0$	$-2$	$-4$	$6$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}-q^{5}+(2+\beta _{2}-\beta _{3})q^{7}+\cdots$
4840.2.a.y	$4840$	$2$	4840.a	1.a	$1$	$4$	$4$	$38.648$	4.4.725.1	None	✓				440.2.y.a	$1$	$1$	$0$	$-2$	$4$	$-7$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+q^{5}+(-2+\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots$
4840.2.a.z	$4840$	$2$	4840.a	1.a	$1$	$4$	$4$	$38.648$	4.4.725.1	None	✓		✓		440.2.y.a	$1$	$1$	$0$	$-2$	$4$	$7$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+q^{5}+(2-\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots$
4840.2.a.ba	$4840$	$2$	4840.a	1.a	$1$	$6$	$6$	$38.648$	6.6.25903625.1	None	✓		✓		440.2.y.c	$1$	$1$	$0$	$-3$	$-6$	$-7$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+(-1+\beta _{2}-\beta _{3}+\beta _{5})q^{7}+\cdots$
4840.2.a.bb	$4840$	$2$	4840.a	1.a	$1$	$6$	$6$	$38.648$	6.6.25903625.1	None	✓		✓		440.2.y.c	$1$	$1$	$0$	$-3$	$-6$	$7$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+(1-\beta _{2}+\beta _{3}-\beta _{5})q^{7}+\cdots$
4840.2.a.bc	$4840$	$2$	4840.a	1.a	$1$	$6$	$6$	$38.648$	6.6.22733568.1	None	✓	✓	✓		4840.2.a.bc	$1$	$1$	$0$	$-2$	$6$	$-4$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}+(-\beta _{3}-\beta _{4})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots$
4840.2.a.bd	$4840$	$2$	4840.a	1.a	$1$	$6$	$6$	$38.648$	6.6.22733568.1	None	✓	✓			4840.2.a.bc	$1$	$0$	$0$	$-2$	$6$	$4$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}+(\beta _{3}+\beta _{4})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots$
4840.2.a.be	$4840$	$2$	4840.a	1.a	$1$	$6$	$6$	$38.648$	6.6.45753625.1	None	✓		✓		440.2.y.b	$1$	$0$	$0$	$2$	$-6$	$-6$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}-q^{5}+(-1+\beta _{2}+\beta _{5})q^{7}+\cdots$
4840.2.a.bf	$4840$	$2$	4840.a	1.a	$1$	$6$	$6$	$38.648$	6.6.45753625.1	None	✓		✓		440.2.y.b	$1$	$0$	$0$	$2$	$-6$	$6$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}-q^{5}+(1-\beta _{2}-\beta _{5})q^{7}+(-2\beta _{2}+\cdots)q^{9}+\cdots$
4840.2.a.bg	$4840$	$2$	4840.a	1.a	$1$	$8$	$8$	$38.648$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓		✓		440.2.y.d	$1$	$0$	$0$	$1$	$8$	$-6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}+(-1-\beta _{4})q^{7}+(3+\beta _{4}+\cdots)q^{9}+\cdots$
4840.2.a.bh	$4840$	$2$	4840.a	1.a	$1$	$8$	$8$	$38.648$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓		✓		440.2.y.d	$1$	$0$	$0$	$1$	$8$	$6$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}+(1+\beta _{4})q^{7}+(3+\beta _{4}+\cdots)q^{9}+\cdots$

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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.