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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 (33 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	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4352.2.a.a	$4352$	$2$	4352.a	1.a	$1$	$1$	$1$	$34.751$	$\Q$	None	✓				1088.2.c.a	$1$	$2$	$0$	$0$	$-2$	$-4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{7}-3q^{9}-4q^{11}-4q^{13}+\cdots$
4352.2.a.b	$4352$	$2$	4352.a	1.a	$1$	$1$	$1$	$34.751$	$\Q$	None	✓				1088.2.c.a	$1$	$1$	$0$	$0$	$-2$	$4$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+4q^{7}-3q^{9}+4q^{11}-4q^{13}+\cdots$
4352.2.a.c	$4352$	$2$	4352.a	1.a	$1$	$1$	$1$	$34.751$	$\Q$	None	✓				2176.2.c.a	$1$	$0$	$0$	$0$	$0$	$-4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}-3q^{9}-4q^{13}-q^{17}-8q^{19}+\cdots$
4352.2.a.d	$4352$	$2$	4352.a	1.a	$1$	$1$	$1$	$34.751$	$\Q$	None	✓				2176.2.c.a	$1$	$1$	$0$	$0$	$0$	$-4$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}-3q^{9}+4q^{13}-q^{17}+8q^{19}+\cdots$
4352.2.a.e	$4352$	$2$	4352.a	1.a	$1$	$1$	$1$	$34.751$	$\Q$	None	✓				2176.2.c.a	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}-3q^{9}-4q^{13}-q^{17}+8q^{19}+\cdots$
4352.2.a.f	$4352$	$2$	4352.a	1.a	$1$	$1$	$1$	$34.751$	$\Q$	None	✓				2176.2.c.a	$1$	$1$	$0$	$0$	$0$	$4$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}-3q^{9}+4q^{13}-q^{17}-8q^{19}+\cdots$
4352.2.a.g	$4352$	$2$	4352.a	1.a	$1$	$1$	$1$	$34.751$	$\Q$	None	✓				1088.2.c.a	$1$	$1$	$0$	$0$	$2$	$-4$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}-3q^{9}+4q^{11}+4q^{13}+\cdots$
4352.2.a.h	$4352$	$2$	4352.a	1.a	$1$	$1$	$1$	$34.751$	$\Q$	None	✓				1088.2.c.a	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+4q^{7}-3q^{9}-4q^{11}+4q^{13}+\cdots$
4352.2.a.i	$4352$	$2$	4352.a	1.a	$1$	$2$	$2$	$34.751$	$\Q(\sqrt{2}) $	None	✓				1088.2.c.c	$2$	$1$	$0$	$-4$	$0$	$0$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-2q^{3}-\beta q^{5}+\beta q^{7}+q^{9}+2q^{11}+\cdots$
4352.2.a.j	$4352$	$2$	4352.a	1.a	$1$	$2$	$2$	$34.751$	$\Q(\sqrt{2}) $	None	✓				2176.2.c.f	$2$	$1$	$0$	$0$	$-4$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2q^{5}+\beta q^{7}-q^{9}-\beta q^{11}+\cdots$
4352.2.a.k	$4352$	$2$	4352.a	1.a	$1$	$2$	$2$	$34.751$	$\Q(\sqrt{2}) $	None	✓				2176.2.c.b	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}-3q^{9}+2\beta q^{11}+2\beta q^{13}+\cdots$
4352.2.a.l	$4352$	$2$	4352.a	1.a	$1$	$2$	$2$	$34.751$	$\Q(\sqrt{2}) $	None	✓				2176.2.c.b	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{5}-3q^{9}+2\beta q^{11}-2\beta q^{13}+\cdots$
4352.2.a.m	$4352$	$2$	4352.a	1.a	$1$	$2$	$2$	$34.751$	$\Q(\sqrt{2}) $	None	✓				2176.2.c.e	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{7}+5q^{9}+\beta q^{11}-4q^{13}+\cdots$
4352.2.a.n	$4352$	$2$	4352.a	1.a	$1$	$2$	$2$	$34.751$	$\Q(\sqrt{2}) $	None	✓				2176.2.c.e	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{3}+\beta q^{7}+5q^{9}+\beta q^{11}+4q^{13}+\cdots$
4352.2.a.o	$4352$	$2$	4352.a	1.a	$1$	$2$	$2$	$34.751$	$\Q(\sqrt{2}) $	None	✓				2176.2.c.f	$2$	$1$	$0$	$0$	$4$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+2q^{5}-\beta q^{7}-q^{9}-\beta q^{11}+\cdots$
4352.2.a.p	$4352$	$2$	4352.a	1.a	$1$	$2$	$2$	$34.751$	$\Q(\sqrt{2}) $	None	✓				1088.2.c.c	$2$	$0$	$0$	$4$	$0$	$0$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+2q^{3}+\beta q^{5}+\beta q^{7}+q^{9}-2q^{11}+\cdots$
4352.2.a.q	$4352$	$2$	4352.a	1.a	$1$	$4$	$4$	$34.751$	$\Q(\sqrt{2}, \sqrt{5})$	None	✓				2176.2.c.k	$2$	$1$	$0$	$0$	$-4$	$0$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(2\beta _{1}+\beta _{3})q^{7}+\cdots$
4352.2.a.r	$4352$	$2$	4352.a	1.a	$1$	$4$	$4$	$34.751$	4.4.8000.1	None	✓				2176.2.c.i	$2$	$1$	$0$	$0$	$-4$	$0$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}-\beta _{1}q^{7}+(2+\cdots)q^{9}+\cdots$
4352.2.a.s	$4352$	$2$	4352.a	1.a	$1$	$4$	$4$	$34.751$	$\Q(\zeta_{24})^+$	None	✓				2176.2.c.g	$4$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{2}q^{7}-q^{9}-\beta _{1}q^{11}-\beta _{3}q^{13}+\cdots$
4352.2.a.t	$4352$	$2$	4352.a	1.a	$1$	$4$	$4$	$34.751$	$\Q(\zeta_{16})^+$	None	✓				2176.2.c.j	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{3}q^{5}-\beta _{2}q^{7}+(1+\beta _{3})q^{9}+\cdots$
4352.2.a.u	$4352$	$2$	4352.a	1.a	$1$	$4$	$4$	$34.751$	$\Q(\zeta_{16})^+$	None	✓				2176.2.c.j	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{3}q^{5}+\beta _{2}q^{7}+(1+\beta _{3})q^{9}+\cdots$
4352.2.a.v	$4352$	$2$	4352.a	1.a	$1$	$4$	$4$	$34.751$	$\Q(\sqrt{2}, \sqrt{5})$	None	✓				2176.2.c.k	$2$	$0$	$0$	$0$	$4$	$0$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1+\beta _{2})q^{5}+(-2\beta _{1}-\beta _{3})q^{7}+\cdots$
4352.2.a.w	$4352$	$2$	4352.a	1.a	$1$	$4$	$4$	$34.751$	4.4.8000.1	None	✓				2176.2.c.i	$2$	$0$	$0$	$0$	$4$	$0$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1-\beta _{2})q^{5}+\beta _{1}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
4352.2.a.x	$4352$	$2$	4352.a	1.a	$1$	$6$	$6$	$34.751$	6.6.15268608.1	None	✓				1088.2.c.e	$2$	$1$	$0$	$-4$	$0$	$0$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}-\beta _{4}q^{5}-\beta _{1}q^{7}+(2+\cdots)q^{9}+\cdots$
4352.2.a.y	$4352$	$2$	4352.a	1.a	$1$	$6$	$6$	$34.751$	6.6.111483648.1	None	✓				1088.2.c.d	$2$	$1$	$0$	$-4$	$0$	$0$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{3}+\beta _{4}q^{5}+\beta _{2}q^{7}+(3+\cdots)q^{9}+\cdots$
4352.2.a.z	$4352$	$2$	4352.a	1.a	$1$	$6$	$6$	$34.751$	6.6.15268608.1	None	✓				1088.2.c.e	$2$	$0$	$0$	$4$	$0$	$0$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}-\beta _{4}q^{5}+\beta _{1}q^{7}+(2+2\beta _{2}+\cdots)q^{9}+\cdots$
4352.2.a.ba	$4352$	$2$	4352.a	1.a	$1$	$6$	$6$	$34.751$	6.6.111483648.1	None	✓				1088.2.c.d	$2$	$0$	$0$	$4$	$0$	$0$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{3})q^{3}+\beta _{4}q^{5}-\beta _{2}q^{7}+(3-\beta _{3}+\cdots)q^{9}+\cdots$
4352.2.a.bb	$4352$	$2$	4352.a	1.a	$1$	$8$	$8$	$34.751$	8.8.$\cdots$.1	None	✓		✓		136.2.c.b	$2$	$1$	$0$	$0$	$0$	$-12$	$-$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}-\beta _{1}q^{5}+(-2-\beta _{4})q^{7}+(1+\cdots)q^{9}+\cdots$
4352.2.a.bc	$4352$	$2$	4352.a	1.a	$1$	$8$	$8$	$34.751$	8.8.$\cdots$.1	None	✓		✓		136.2.c.a	$2$	$1$	$0$	$0$	$0$	$-8$	$+$	$+$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{4}q^{5}+(-1+\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots$
4352.2.a.bd	$4352$	$2$	4352.a	1.a	$1$	$8$	$8$	$34.751$	8.8.$\cdots$.1	None	✓				2176.2.c.h	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$2^{8}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{2}q^{5}-\beta _{7}q^{7}+(4+\beta _{3}+\cdots)q^{9}+\cdots$
4352.2.a.be	$4352$	$2$	4352.a	1.a	$1$	$8$	$8$	$34.751$	8.8.$\cdots$.1	None	✓				136.2.c.a	$2$	$0$	$0$	$0$	$0$	$8$	$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{4}q^{5}+(1-\beta _{2})q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots$
4352.2.a.bf	$4352$	$2$	4352.a	1.a	$1$	$8$	$8$	$34.751$	8.8.$\cdots$.1	None	✓				136.2.c.b	$2$	$0$	$0$	$0$	$0$	$12$	$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+\beta _{1}q^{5}+(2+\beta _{4})q^{7}+(1+\beta _{4}+\cdots)q^{9}+\cdots$
4352.2.a.bg	$4352$	$2$	4352.a	1.a	$1$	$12$	$12$	$34.751$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓		✓		2176.2.c.l	$4$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$2^{15}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{3}q^{5}-\beta _{2}q^{7}+(2-\beta _{10}+\cdots)q^{9}+\cdots$

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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.