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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 192 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
120.1.i.a	$120$	$1$	120.i	120.i	$2$	$2$	$2$	$0.060$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{10}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}-iq^{3}-q^{4}+iq^{5}-q^{6}+iq^{8}+\cdots$
120.2.a.a	$120$	$2$	120.a	1.a	$1$	$1$	$1$	$0.958$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+4q^{7}+q^{9}-6q^{13}-q^{15}+\cdots$
120.2.a.b	$120$	$2$	120.a	1.a	$1$	$1$	$1$	$0.958$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots$
120.2.b.a	$120$	$2$	120.b	24.f	$2$	$8$	$8$	$0.958$	8.0.1649659456.5	$_{}$	None	None		$2$	$0$	$-1$	$0$	$8$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-\beta _{6}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots$
120.2.b.b	$120$	$2$	120.b	24.f	$2$	$8$	$8$	$0.958$	8.0.1649659456.5	$_{}$	None	None		$2$	$0$	$1$	$0$	$-8$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots$
120.2.d.a	$120$	$2$	120.d	40.f	$2$	$6$	$6$	$0.958$	6.0.839056.1	$_{}$	None	None		$2$	$0$	$-1$	$6$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+q^{3}+(-\beta _{1}-\beta _{2})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$
120.2.d.b	$120$	$2$	120.d	40.f	$2$	$6$	$6$	$0.958$	6.0.839056.1	$_{}$	None	None		$2$	$0$	$1$	$-6$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-q^{3}+(\beta _{1}-\beta _{3})q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$
120.2.f.a	$120$	$2$	120.f	5.b	$2$	$2$	$2$	$0.958$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(2-i)q^{5}+2iq^{7}-q^{9}+2q^{11}+\cdots$
120.2.k.a	$120$	$2$	120.k	8.b	$2$	$2$	$2$	$0.958$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+i)q^{2}-iq^{3}+2iq^{4}+iq^{5}+\cdots$
120.2.k.b	$120$	$2$	120.k	8.b	$2$	$6$	$6$	$0.958$	6.0.399424.1	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{1}q^{3}+(\beta _{1}+\beta _{5})q^{4}+\beta _{1}q^{5}+\cdots$
120.2.m.a	$120$	$2$	120.m	120.m	$2$	$4$	$4$	$0.958$	$\Q(\sqrt{3}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots$
120.2.m.b	$120$	$2$	120.m	120.m	$2$	$16$	$16$	$0.958$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{13}q^{3}-\beta _{11}q^{4}+\beta _{7}q^{5}+\cdots$
120.2.r.a	$120$	$2$	120.r	15.e	$4$	$4$	$2$	$0.958$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots$
120.2.r.b	$120$	$2$	120.r	15.e	$4$	$4$	$2$	$0.958$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$-4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+(-1+2\zeta_{8})q^{5}+(-1+\cdots)q^{7}+\cdots$
120.2.r.c	$120$	$2$	120.r	15.e	$4$	$4$	$2$	$0.958$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$4$	$4$	$-4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\zeta_{8}^{2})q^{3}+(1-2\zeta_{8})q^{5}+(-1+\cdots)q^{7}+\cdots$
120.2.v.a	$120$	$2$	120.v	40.k	$4$	$24$	$12$	$0.958$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
120.2.w.a	$120$	$2$	120.w	120.w	$4$	$4$	$2$	$0.958$	$\Q(i, \sqrt{6})$	$_{}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$-4$	$0$	$4$	$-4$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+\cdots$
120.2.w.b	$120$	$2$	120.w	120.w	$4$	$4$	$2$	$0.958$	$\Q(i, \sqrt{6})$	$_{}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$4$	$0$	$-4$	$-4$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(1-\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots$
120.2.w.c	$120$	$2$	120.w	120.w	$4$	$32$	$16$	$0.958$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
120.3.c.a	$120$	$3$	120.c	15.d	$2$	$12$	$12$	$3.270$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{15}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{8}q^{5}-\beta _{9}q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots$
120.3.g.a	$120$	$3$	120.g	8.d	$2$	$16$	$16$	$3.270$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$-4$	$0$	$0$	$0$		$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots$
120.3.i.a	$120$	$3$	120.i	120.i	$2$	$1$	$1$	$3.270$	$\Q$	$_{}$	$\Q(\sqrt{-30}) $	None	✓	$2$	$0$	$-2$	$-3$	$-5$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}-3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots$
120.3.i.b	$120$	$3$	120.i	120.i	$2$	$1$	$1$	$3.270$	$\Q$	$_{}$	$\Q(\sqrt{-30}) $	None	✓	$2$	$0$	$-2$	$3$	$5$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots$
120.3.i.c	$120$	$3$	120.i	120.i	$2$	$1$	$1$	$3.270$	$\Q$	$_{}$	$\Q(\sqrt{-30}) $	None	✓	$2$	$0$	$2$	$-3$	$5$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}-3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots$
120.3.i.d	$120$	$3$	120.i	120.i	$2$	$1$	$1$	$3.270$	$\Q$	$_{}$	$\Q(\sqrt{-30}) $	None	✓	$2$	$0$	$2$	$3$	$-5$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots$
120.3.i.e	$120$	$3$	120.i	120.i	$2$	$4$	$4$	$3.270$	$\Q(i, \sqrt{6})$	$_{}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q-2\beta _{1}q^{2}+3\beta _{1}q^{3}-4q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
120.3.i.f	$120$	$3$	120.i	120.i	$2$	$4$	$4$	$3.270$	$\Q(i, \sqrt{15})$	$_{}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}-3\beta _{2}q^{3}+(4+\beta _{3})q^{4}-5\beta _{2}q^{5}+\cdots$
120.3.i.g	$120$	$3$	120.i	120.i	$2$	$32$	$32$	$3.270$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
120.3.l.a	$120$	$3$	120.l	3.b	$2$	$8$	$8$	$3.270$	8.0.$\cdots$.5	$_{}$	None	None		$2$	$0$	$0$	$-4$	$0$	$16$		$2^{5}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+\beta _{6}q^{5}+(1+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots$
120.3.n.a	$120$	$3$	120.n	24.h	$2$	$32$	$32$	$3.270$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
120.3.p.a	$120$	$3$	120.p	40.e	$2$	$24$	$24$	$3.270$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
120.3.q.a	$120$	$3$	120.q	120.q	$4$	$88$	$44$	$3.270$		$_{}$	None	None		$8$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
120.3.t.a	$120$	$3$	120.t	40.i	$4$	$48$	$24$	$3.270$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
120.3.u.a	$120$	$3$	120.u	5.c	$4$	$4$	$2$	$3.270$	$\Q(i, \sqrt{6})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$-12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{3}+(1+\beta _{1}+3\beta _{2}-2\beta _{3})q^{5}+\cdots$
120.3.u.b	$120$	$3$	120.u	5.c	$4$	$8$	$4$	$3.270$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-12$	$4$		$2\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{3}+(-2+\beta _{1}+\beta _{6})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
120.4.a.a	$120$	$4$	120.a	1.a	$1$	$1$	$1$	$7.080$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$-5$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-5q^{5}+4q^{7}+9q^{9}+72q^{11}+\cdots$
120.4.a.b	$120$	$4$	120.a	1.a	$1$	$1$	$1$	$7.080$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-5$	$20$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-5q^{5}+20q^{7}+9q^{9}-56q^{11}+\cdots$
120.4.a.c	$120$	$4$	120.a	1.a	$1$	$1$	$1$	$7.080$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$5$	$-16$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+5q^{5}-2^{4}q^{7}+9q^{9}-28q^{11}+\cdots$
120.4.a.d	$120$	$4$	120.a	1.a	$1$	$1$	$1$	$7.080$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$5$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+5q^{5}+9q^{9}+4q^{11}+54q^{13}+\cdots$
120.4.a.e	$120$	$4$	120.a	1.a	$1$	$1$	$1$	$7.080$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-5$	$20$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-5q^{5}+20q^{7}+9q^{9}+2^{4}q^{11}+\cdots$
120.4.a.f	$120$	$4$	120.a	1.a	$1$	$1$	$1$	$7.080$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$5$	$8$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+5q^{5}+8q^{7}+9q^{9}+20q^{11}+\cdots$
120.4.b.a	$120$	$4$	120.b	24.f	$2$	$24$	$24$	$7.080$		$_{}$	None	None		$2$	$0$	$-3$	$0$	$120$	$0$			$\mathrm{SU}(2)[C_{2}]$
120.4.b.b	$120$	$4$	120.b	24.f	$2$	$24$	$24$	$7.080$		$_{}$	None	None		$2$	$0$	$3$	$0$	$-120$	$0$			$\mathrm{SU}(2)[C_{2}]$
120.4.d.a	$120$	$4$	120.d	40.f	$2$	$18$	$18$	$7.080$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		$2$	$0$	$-1$	$54$	$0$	$0$		$2^{25}\cdot 3^{4}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+3q^{3}+\beta _{2}q^{4}+\beta _{10}q^{5}+\cdots$
120.4.d.b	$120$	$4$	120.d	40.f	$2$	$18$	$18$	$7.080$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		$2$	$0$	$1$	$-54$	$0$	$0$		$2^{25}\cdot 3^{4}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}-3q^{3}-\beta _{7}q^{4}+\beta _{11}q^{5}+\cdots$
120.4.f.a	$120$	$4$	120.f	5.b	$2$	$2$	$2$	$7.080$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$1$	$0$	$0$	$-20$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{3}+(-10+5i)q^{5}-10iq^{7}+\cdots$
120.4.f.b	$120$	$4$	120.f	5.b	$2$	$2$	$2$	$7.080$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{3}+(-2-11i)q^{5}-10iq^{7}+\cdots$
120.4.f.c	$120$	$4$	120.f	5.b	$2$	$2$	$2$	$7.080$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$10$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{3}+(5+10i)q^{5}+4iq^{7}-9q^{9}+\cdots$
120.4.f.d	$120$	$4$	120.f	5.b	$2$	$4$	$4$	$7.080$	$\Q(i, \sqrt{129})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$22$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-3\beta _{1}q^{3}+(6+5\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
120.4.k.a	$120$	$4$	120.k	8.b	$2$	$2$	$2$	$7.080$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$-4$	$0$	$0$	$52$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2+2i)q^{2}+3iq^{3}-8iq^{4}+5iq^{5}+\cdots$

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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.