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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 94 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
345.1.p.a	$345$	$1$	345.p	345.p	$22$	$10$	$1$	$0.172$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$-1$	$0$		$1$		$q+(-\zeta_{22}^{3}-\zeta_{22}^{5})q^{2}+\zeta_{22}^{10}q^{3}+\cdots$
345.1.p.b	$345$	$1$	345.p	345.p	$22$	$10$	$1$	$0.172$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$1$	$0$		$1$		$q+(\zeta_{22}^{3}+\zeta_{22}^{5})q^{2}-\zeta_{22}^{10}q^{3}+(\zeta_{22}^{6}+\cdots)q^{4}+\cdots$
345.2.a.a	$345$	$2$	345.a	1.a	$1$	$1$	$1$	$2.755$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$1$	$1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}-5q^{7}+\cdots$
345.2.a.b	$345$	$2$	345.a	1.a	$1$	$1$	$1$	$2.755$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+4q^{7}+\cdots$
345.2.a.c	$345$	$2$	345.a	1.a	$1$	$1$	$1$	$2.755$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}+4q^{11}+\cdots$
345.2.a.d	$345$	$2$	345.a	1.a	$1$	$1$	$1$	$2.755$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{5}-3q^{7}+q^{9}-4q^{11}+\cdots$
345.2.a.e	$345$	$2$	345.a	1.a	$1$	$1$	$1$	$2.755$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}+4q^{7}+\cdots$
345.2.a.f	$345$	$2$	345.a	1.a	$1$	$1$	$1$	$2.755$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$-1$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+3q^{7}+\cdots$
345.2.a.g	$345$	$2$	345.a	1.a	$1$	$2$	$2$	$2.755$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$-2$	$2$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-q^{3}+(2-2\beta )q^{4}+q^{5}+\cdots$
345.2.a.h	$345$	$2$	345.a	1.a	$1$	$2$	$2$	$2.755$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}-q^{5}-\beta q^{6}+(-1-2\beta )q^{7}+\cdots$
345.2.a.i	$345$	$2$	345.a	1.a	$1$	$2$	$2$	$2.755$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+4q^{4}-q^{5}+\beta q^{6}-q^{7}+\cdots$
345.2.a.j	$345$	$2$	345.a	1.a	$1$	$3$	$3$	$2.755$	3.3.316.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$3$	$3$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
345.2.b.a	$345$	$2$	345.b	5.b	$2$	$2$	$2$	$2.755$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+iq^{3}+q^{4}+(1+2i)q^{5}-q^{6}+\cdots$
345.2.b.b	$345$	$2$	345.b	5.b	$2$	$2$	$2$	$2.755$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-iq^{3}+q^{4}+(2-i)q^{5}+q^{6}+\cdots$
345.2.b.c	$345$	$2$	345.b	5.b	$2$	$6$	$6$	$2.755$	6.0.350464.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}-\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
345.2.b.d	$345$	$2$	345.b	5.b	$2$	$14$	$14$	$2.755$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}-\beta _{2}q^{3}+(-2-\beta _{8}+\beta _{9}+\cdots)q^{4}+\cdots$
345.2.c.a	$345$	$2$	345.c	69.c	$2$	$16$	$16$	$2.755$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-16$	$0$		$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{6}q^{3}+(-1+\beta _{2})q^{4}-q^{5}+\cdots$
345.2.c.b	$345$	$2$	345.c	69.c	$2$	$16$	$16$	$2.755$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$16$	$0$		$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{6}q^{3}+(-1+\beta _{2})q^{4}+q^{5}+\cdots$
345.2.h.a	$345$	$2$	345.h	345.h	$2$	$4$	$4$	$2.755$	$\Q(\sqrt{3}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{3}q^{2}-\beta _{3}q^{3}+q^{4}-\beta _{1}q^{5}+3q^{6}+\cdots$
345.2.h.b	$345$	$2$	345.h	345.h	$2$	$8$	$8$	$2.755$	8.0.3057647616.5	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-24$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+\beta _{2}q^{3}+(1-\beta _{6})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
345.2.h.c	$345$	$2$	345.h	345.h	$2$	$8$	$8$	$2.755$	8.0.3057647616.5	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$24$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+\beta _{2}q^{3}+(1-\beta _{6})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
345.2.h.d	$345$	$2$	345.h	345.h	$2$	$24$	$24$	$2.755$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
345.2.i.a	$345$	$2$	345.i	15.e	$4$	$4$	$2$	$2.755$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$1$	$-4$	$-4$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\zeta_{8}^{2})q^{2}+(-1+\zeta_{8}+\zeta_{8}^{3})q^{3}+\cdots$
345.2.i.b	$345$	$2$	345.i	15.e	$4$	$4$	$2$	$2.755$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$4$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\zeta_{8}^{2})q^{2}+(-\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots$
345.2.i.c	$345$	$2$	345.i	15.e	$4$	$80$	$40$	$2.755$		$_{}$	None	None		$4$	$0$	$0$	$4$	$0$	$8$			$\mathrm{SU}(2)[C_{4}]$
345.2.j.a	$345$	$2$	345.j	115.e	$4$	$48$	$24$	$2.755$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
345.2.m.a	$345$	$2$	345.m	23.c	$11$	$30$	$3$	$2.755$		$_{}$	None	None		$2$	$0$	$0$	$3$	$3$	$1$			$\mathrm{SU}(2)[C_{11}]$
345.2.m.b	$345$	$2$	345.m	23.c	$11$	$30$	$3$	$2.755$		$_{}$	None	None		$2$	$0$	$6$	$-3$	$-3$	$7$			$\mathrm{SU}(2)[C_{11}]$
345.2.m.c	$345$	$2$	345.m	23.c	$11$	$50$	$5$	$2.755$		$_{}$	None	None		$2$	$0$	$0$	$-5$	$5$	$-3$			$\mathrm{SU}(2)[C_{11}]$
345.2.m.d	$345$	$2$	345.m	23.c	$11$	$50$	$5$	$2.755$		$_{}$	None	None		$2$	$0$	$2$	$5$	$-5$	$3$			$\mathrm{SU}(2)[C_{11}]$
345.2.n.a	$345$	$2$	345.n	345.n	$22$	$40$	$4$	$2.755$		$_{}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{U}(1)[D_{22}]$
345.2.n.b	$345$	$2$	345.n	345.n	$22$	$400$	$40$	$2.755$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
345.2.s.a	$345$	$2$	345.s	69.g	$22$	$160$	$16$	$2.755$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-16$	$0$			$\mathrm{SU}(2)[C_{22}]$
345.2.s.b	$345$	$2$	345.s	69.g	$22$	$160$	$16$	$2.755$		$_{}$	None	None		$2$	$0$	$0$	$0$	$16$	$0$			$\mathrm{SU}(2)[C_{22}]$
345.2.t.a	$345$	$2$	345.t	115.j	$22$	$240$	$24$	$2.755$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{22}]$
345.2.w.a	$345$	$2$	345.w	115.l	$44$	$480$	$24$	$2.755$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{44}]$
345.2.x.a	$345$	$2$	345.x	345.x	$44$	$880$	$44$	$2.755$		$_{}$	None	None		$8$	$0$	$0$	$-22$	$0$	$-36$			$\mathrm{SU}(2)[C_{44}]$
345.3.d.a	$345$	$3$	345.d	115.c	$2$	$48$	$48$	$9.401$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
345.3.e.a	$345$	$3$	345.e	3.b	$2$	$60$	$60$	$9.401$		$_{}$	None	None		$2$	$0$	$0$	$8$	$0$	$24$			$\mathrm{SU}(2)[C_{2}]$
345.3.f.a	$345$	$3$	345.f	15.d	$2$	$88$	$88$	$9.401$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
345.3.g.a	$345$	$3$	345.g	23.b	$2$	$32$	$32$	$9.401$		$_{}$	None	None		$2$	$0$	$8$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
345.3.k.a	$345$	$3$	345.k	5.c	$4$	$88$	$44$	$9.401$		$_{}$	None	None		$2$	$0$	$8$	$0$	$16$	$16$			$\mathrm{SU}(2)[C_{4}]$
345.3.l.a	$345$	$3$	345.l	345.l	$4$	$184$	$92$	$9.401$		$_{}$	None	None		$8$	$0$	$0$	$-8$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
345.3.o.a	$345$	$3$	345.o	23.d	$22$	$320$	$32$	$9.401$		$_{}$	None	None		$2$	$0$	$-8$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
345.3.p.a	$345$	$3$	345.p	345.p	$22$	$20$	$2$	$9.401$	20.0.$\cdots$.3	$_{}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$6$	$-10$	$0$		$1$	$\mathrm{U}(1)[D_{22}]$	$q+(\beta _{5}-\beta _{6}+\beta _{8}+\beta _{14})q^{2}-3\beta _{16}q^{3}+\cdots$
345.3.p.b	$345$	$3$	345.p	345.p	$22$	$20$	$2$	$9.401$	20.0.$\cdots$.3	$_{}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$-6$	$10$	$0$		$1$	$\mathrm{U}(1)[D_{22}]$	$q+(-\beta _{1}-\beta _{3}-\beta _{8}-\beta _{14})q^{2}+3\beta _{2}q^{3}+\cdots$
345.3.p.c	$345$	$3$	345.p	345.p	$22$	$880$	$88$	$9.401$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
345.3.q.a	$345$	$3$	345.q	69.h	$22$	$640$	$64$	$9.401$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
345.3.r.a	$345$	$3$	345.r	115.i	$22$	$480$	$48$	$9.401$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
345.3.u.a	$345$	$3$	345.u	345.u	$44$	$1840$	$92$	$9.401$		$_{}$	None	None		$8$	$0$	$0$	$-14$	$0$	$-44$			$\mathrm{SU}(2)[C_{44}]$

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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.