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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 147 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
104.1.h.a	$104$	$1$	104.h	104.h	$2$	$1$	$1$	$0.052$	$\Q$	$D_{3}$	$\Q(\sqrt{-26}) $	None	✓	$2$	$0$	$-1$	$-1$	$1$	$1$		$1$		$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
104.1.h.b	$104$	$1$	104.h	104.h	$2$	$1$	$1$	$0.052$	$\Q$	$D_{3}$	$\Q(\sqrt{-26}) $	None	✓	$2$	$0$	$1$	$-1$	$-1$	$-1$		$1$		$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
104.2.a.a	$104$	$2$	104.a	1.a	$1$	$1$	$1$	$0.830$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+5q^{7}-2q^{9}-2q^{11}+\cdots$
104.2.a.b	$104$	$2$	104.a	1.a	$1$	$2$	$2$	$0.830$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(2-\beta )q^{5}-\beta q^{7}+(1+\beta )q^{9}+\cdots$
104.2.b.a	$104$	$2$	104.b	8.b	$2$	$2$	$2$	$0.830$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+i)q^{2}-iq^{3}-2iq^{4}+3iq^{5}+\cdots$
104.2.b.b	$104$	$2$	104.b	8.b	$2$	$4$	$4$	$0.830$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$-12$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+2\zeta_{12}^{2}q^{3}+(\zeta_{12}+\cdots)q^{4}+\cdots$
104.2.b.c	$104$	$2$	104.b	8.b	$2$	$6$	$6$	$0.830$	6.0.399424.1	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{5})q^{3}+(\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
104.2.e.a	$104$	$2$	104.e	104.e	$2$	$2$	$2$	$0.830$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$-2$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+i)q^{2}-iq^{3}-2iq^{4}+q^{5}+\cdots$
104.2.e.b	$104$	$2$	104.e	104.e	$2$	$2$	$2$	$0.830$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+i)q^{2}+iq^{3}+2iq^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots$
104.2.e.c	$104$	$2$	104.e	104.e	$2$	$8$	$8$	$0.830$	8.0.4521217600.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{3}-\beta _{5}q^{4}-\beta _{6}q^{5}+\cdots$
104.2.f.a	$104$	$2$	104.f	13.b	$2$	$4$	$4$	$0.830$	$\Q(i, \sqrt{17})$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{3})q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
104.2.i.a	$104$	$2$	104.i	13.c	$3$	$2$	$1$	$0.830$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$4$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+2q^{5}+\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots$
104.2.i.b	$104$	$2$	104.i	13.c	$3$	$4$	$2$	$0.830$	$\Q(\sqrt{-3}, \sqrt{17})$	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-6$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots$
104.2.m.a	$104$	$2$	104.m	104.m	$4$	$4$	$2$	$0.830$	$\Q(i, \sqrt{26})$	$_{}$	None	None		$4$	$0$	$-4$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{2})q^{2}-q^{3}+2\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots$
104.2.m.b	$104$	$2$	104.m	104.m	$4$	$20$	$10$	$0.830$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$4$	$0$	$2$	$-4$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{14}q^{2}-\beta _{5}q^{3}-\beta _{2}q^{4}+\beta _{10}q^{5}+\cdots$
104.2.o.a	$104$	$2$	104.o	13.e	$6$	$8$	$4$	$0.830$	8.0.195105024.2	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$-6$		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{2}+\beta _{4}-\beta _{5})q^{3}+(\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{5}+\cdots$
104.2.r.a	$104$	$2$	104.r	104.r	$6$	$24$	$12$	$0.830$		$_{}$	None	None		$4$	$0$	$-1$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{6}]$
104.2.s.a	$104$	$2$	104.s	104.s	$6$	$4$	$2$	$0.830$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$1$	$-4$	$-6$	$-8$	$-12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots$
104.2.s.b	$104$	$2$	104.s	104.s	$6$	$4$	$2$	$0.830$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$-2$	$6$	$8$	$-12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(1+\zeta_{12}+\cdots)q^{3}+\cdots$
104.2.s.c	$104$	$2$	104.s	104.s	$6$	$16$	$8$	$0.830$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$3$	$0$	$0$	$18$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}-\beta _{14})q^{2}+(\beta _{3}-\beta _{11})q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots$
104.2.u.a	$104$	$2$	104.u	104.u	$12$	$48$	$12$	$0.830$		$_{}$	None	None		$4$	$0$	$-4$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$
104.3.g.a	$104$	$3$	104.g	8.d	$2$	$24$	$24$	$2.834$		$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
104.3.h.a	$104$	$3$	104.h	104.h	$2$	$3$	$3$	$2.834$	3.3.2808.1	$_{}$	$\Q(\sqrt{-26}) $	None	✓	$2$	$0$	$-6$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+\beta _{2}q^{3}+4q^{4}+(\beta _{1}+\beta _{2})q^{5}+\cdots$
104.3.h.b	$104$	$3$	104.h	104.h	$2$	$3$	$3$	$2.834$	3.3.2808.1	$_{}$	$\Q(\sqrt{-26}) $	None	✓	$2$	$0$	$6$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+\beta _{2}q^{3}+4q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots$
104.3.h.c	$104$	$3$	104.h	104.h	$2$	$20$	$20$	$2.834$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$0$		$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-1+\beta _{4})q^{4}+\beta _{11}q^{5}+\cdots$
104.3.j.a	$104$	$3$	104.j	104.j	$4$	$52$	$26$	$2.834$		$_{}$	None	None		$4$	$0$	$-2$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
104.3.l.a	$104$	$3$	104.l	13.d	$4$	$2$	$1$	$2.834$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$4$	$10$	$-6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+2q^{3}+(5+5i)q^{5}+(-3+3i)q^{7}+\cdots$
104.3.l.b	$104$	$3$	104.l	13.d	$4$	$6$	$3$	$2.834$	6.0.891380736.2	$_{}$	None	None		$2$	$0$	$0$	$-4$	$-14$	$16$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{1}+\beta _{2})q^{3}+(-2+\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
104.3.l.c	$104$	$3$	104.l	13.d	$4$	$6$	$3$	$2.834$	6.0.195552256.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{3}-\beta _{4}q^{5}+(2+\beta _{1}-2\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
104.3.n.a	$104$	$3$	104.n	104.n	$6$	$4$	$2$	$2.834$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		$4$	$0$	$4$	$-8$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(2-2\beta _{1})q^{2}+(-4+4\beta _{1})q^{3}-4\beta _{1}q^{4}+\cdots$
104.3.n.b	$104$	$3$	104.n	104.n	$6$	$48$	$24$	$2.834$		$_{}$	None	None		$4$	$0$	$-5$	$6$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
104.3.p.a	$104$	$3$	104.p	104.p	$6$	$2$	$1$	$2.834$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-4$	$-1$	$4$	$-5$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-2q^{2}+(-1+\zeta_{6})q^{3}+4q^{4}+2q^{5}+\cdots$
104.3.p.b	$104$	$3$	104.p	104.p	$6$	$2$	$1$	$2.834$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-2$	$-1$	$-4$	$5$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-2\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots$
104.3.p.c	$104$	$3$	104.p	104.p	$6$	$4$	$2$	$2.834$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		$4$	$0$	$3$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{1})q^{2}+(2+2\beta _{2})q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots$
104.3.p.d	$104$	$3$	104.p	104.p	$6$	$44$	$22$	$2.834$		$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
104.3.v.a	$104$	$3$	104.v	13.f	$12$	$4$	$1$	$2.834$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$4$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(\zeta_{12}+2\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+(3+6\zeta_{12}+\cdots)q^{5}+\cdots$
104.3.v.b	$104$	$3$	104.v	13.f	$12$	$4$	$1$	$2.834$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$4$	$6$	$16$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-2\zeta_{12}+2\zeta_{12}^{2}-2\zeta_{12}^{3})q^{3}+\cdots$
104.3.v.c	$104$	$3$	104.v	13.f	$12$	$8$	$2$	$2.834$	8.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$-8$	$-2$	$-36$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-2-\beta _{2}-2\beta _{3}+\beta _{5})q^{3}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
104.3.v.d	$104$	$3$	104.v	13.f	$12$	$12$	$3$	$2.834$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$6$		$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+\beta _{7}q^{3}+(-1+\beta _{2}-\beta _{3}+2\beta _{4}+2\beta _{5}+\cdots)q^{5}+\cdots$
104.3.x.a	$104$	$3$	104.x	104.x	$12$	$104$	$26$	$2.834$		$_{}$	None	None		$4$	$0$	$-4$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{12}]$
104.4.a.a	$104$	$4$	104.a	1.a	$1$	$1$	$1$	$6.136$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-7$	$-21$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-7q^{5}-21q^{7}-26q^{9}+6q^{11}+\cdots$
104.4.a.b	$104$	$4$	104.a	1.a	$1$	$1$	$1$	$6.136$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$5$	$19$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+5q^{3}+19q^{5}-3q^{7}-2q^{9}-2q^{11}+\cdots$
104.4.a.c	$104$	$4$	104.a	1.a	$1$	$2$	$2$	$6.136$	$\Q(\sqrt{73}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-3$	$-25$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(-3+3\beta )q^{5}+(-13+\cdots)q^{7}+\cdots$
104.4.a.d	$104$	$4$	104.a	1.a	$1$	$2$	$2$	$6.136$	$\Q(\sqrt{321}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-11$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-6+\beta )q^{5}+(2-3\beta )q^{7}+\cdots$
104.4.a.e	$104$	$4$	104.a	1.a	$1$	$3$	$3$	$6.136$	3.3.18257.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-8$	$36$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-3-2\beta _{1}-\beta _{2})q^{5}+(12+\cdots)q^{7}+\cdots$
104.4.b.a	$104$	$4$	104.b	8.b	$2$	$2$	$2$	$6.136$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$4$	$0$	$0$	$-58$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2+2i)q^{2}-iq^{3}+8iq^{4}+11iq^{5}+\cdots$
104.4.b.b	$104$	$4$	104.b	8.b	$2$	$34$	$34$	$6.136$		$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$86$			$\mathrm{SU}(2)[C_{2}]$
104.4.e.a	$104$	$4$	104.e	104.e	$2$	$40$	$40$	$6.136$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
104.4.f.a	$104$	$4$	104.f	13.b	$2$	$10$	$10$	$6.136$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$6$	$0$	$0$		$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{1})q^{3}+\beta _{8}q^{5}-\beta _{7}q^{7}+(8-\beta _{1}+\cdots)q^{9}+\cdots$
104.4.i.a	$104$	$4$	104.i	13.c	$3$	$2$	$1$	$6.136$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$-8$	$-18$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-8+8\zeta_{6})q^{3}-9q^{5}+4\zeta_{6}q^{7}+\cdots$

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