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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 (1-50 of 122 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
62.2.a.a	$62$	$2$	62.a	1.a	$1$	$1$	$1$	$0.495$	$\Q$	None	✓	✓	✓	✓	62.2.a.a	$1$	$0$	$1$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+q^{8}-3q^{9}-2q^{10}+\cdots$
62.2.a.b	$62$	$2$	62.a	1.a	$1$	$2$	$2$	$0.495$	$\Q(\sqrt{3}) $	None	✓	✓	✓	✓	62.2.a.b	$1$	$0$	$-2$	$2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta )q^{3}+q^{4}-2\beta q^{5}+(-1+\cdots)q^{6}+\cdots$
62.2.c.a	$62$	$2$	62.c	31.c	$3$	$2$	$1$	$0.495$	$\Q(\sqrt{-3}) $	None		✓			62.2.c.a	$2$	$0$	$-2$	$-1$	$3$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(-1+\zeta_{6})q^{3}+q^{4}+3\zeta_{6}q^{5}+\cdots$
62.2.c.b	$62$	$2$	62.c	31.c	$3$	$2$	$1$	$0.495$	$\Q(\sqrt{-3}) $	None		✓			62.2.c.b	$2$	$0$	$2$	$-3$	$-1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-3+3\zeta_{6})q^{3}+q^{4}-\zeta_{6}q^{5}+\cdots$
62.2.d.a	$62$	$2$	62.d	31.d	$5$	$8$	$2$	$0.495$	8.0.511890625.1	None		✓			62.2.d.a	$2$	$0$	$-2$	$-4$	$-4$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$
62.2.d.b	$62$	$2$	62.d	31.d	$5$	$8$	$2$	$0.495$	8.0.1903140625.1	None		✓			62.2.d.b	$2$	$0$	$2$	$-2$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{6}q^{2}+\beta _{7}q^{3}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
62.2.g.a	$62$	$2$	62.g	31.g	$15$	$8$	$1$	$0.495$	$\Q(\zeta_{15})$	None		✓			62.2.g.a	$2$	$0$	$-2$	$3$	$1$	$2$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q+\zeta_{15}^{6}q^{2}+(\zeta_{15}+\zeta_{15}^{4}+\zeta_{15}^{7})q^{3}+\cdots$
62.2.g.b	$62$	$2$	62.g	31.g	$15$	$8$	$1$	$0.495$	$\Q(\zeta_{15})$	None		✓			62.2.g.b	$2$	$0$	$2$	$1$	$-3$	$-16$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q-\zeta_{15}^{6}q^{2}+(\zeta_{15}-\zeta_{15}^{4}+\zeta_{15}^{7})q^{3}+\cdots$
62.3.b.a	$62$	$3$	62.b	31.b	$2$	$4$	$4$	$1.689$	4.0.48128.1	None		✓	✓	✓	62.3.b.a	$2$	$0$	$0$	$0$	$-12$	$-12$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+\beta _{2}q^{3}+2q^{4}+(-3+2\beta _{3})q^{5}+\cdots$
62.3.e.a	$62$	$3$	62.e	31.e	$6$	$12$	$6$	$1.689$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓	✓	62.3.e.a	$2$	$0$	$0$	$-6$	$-6$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{4}q^{2}+(-1+\beta _{2})q^{3}+2q^{4}+(\beta _{5}+\cdots)q^{5}+\cdots$
62.3.f.a	$62$	$3$	62.f	31.f	$10$	$16$	$4$	$1.689$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓	✓	62.3.f.a	$2$	$0$	$0$	$0$	$12$	$-8$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(\beta _{1}-\beta _{2}-\beta _{4}+\beta _{11})q^{2}+(-\beta _{7}+\cdots)q^{3}+\cdots$
62.3.h.a	$62$	$3$	62.h	31.h	$30$	$48$	$6$	$1.689$		None		✓	✓	✓	62.3.h.a	$2$	$0$	$0$	$6$	$6$	$18$			$\mathrm{SU}(2)[C_{30}]$
62.4.a.a	$62$	$4$	62.a	1.a	$1$	$1$	$1$	$3.658$	$\Q$	None	✓	✓	✓	✓	62.4.a.a	$1$	$1$	$-2$	$-2$	$1$	$-11$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-2q^{3}+4q^{4}+q^{5}+4q^{6}+\cdots$
62.4.a.b	$62$	$4$	62.a	1.a	$1$	$1$	$1$	$3.658$	$\Q$	None	✓	✓	✓	✓	62.4.a.b	$1$	$1$	$2$	$-8$	$-3$	$-35$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-8q^{3}+4q^{4}-3q^{5}-2^{4}q^{6}+\cdots$
62.4.a.c	$62$	$4$	62.a	1.a	$1$	$3$	$3$	$3.658$	3.3.4364.1	None	✓	✓	✓	✓	62.4.a.c	$1$	$0$	$-6$	$4$	$1$	$17$	$+$	$2$	$\mathrm{SU}(2)$	$q-2q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+4q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots$
62.4.a.d	$62$	$4$	62.a	1.a	$1$	$3$	$3$	$3.658$	3.3.23964.1	None	✓	✓	✓	✓	62.4.a.d	$1$	$0$	$6$	$4$	$17$	$21$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(1+\beta _{1})q^{3}+4q^{4}+(6-\beta _{1}+\cdots)q^{5}+\cdots$
62.4.c.a	$62$	$4$	62.c	31.c	$3$	$8$	$4$	$3.658$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓			62.4.c.a	$2$	$0$	$-16$	$4$	$10$	$-6$		$2^{8}$	$\mathrm{SU}(2)[C_{3}]$	$q-2q^{2}+(1-\beta _{2}+\beta _{3})q^{3}+4q^{4}+(3\beta _{2}+\cdots)q^{5}+\cdots$
62.4.c.b	$62$	$4$	62.c	31.c	$3$	$8$	$4$	$3.658$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓			62.4.c.b	$2$	$0$	$16$	$10$	$-2$	$-16$		$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q+2q^{2}+(-3\beta _{1}+\beta _{5})q^{3}+4q^{4}+(-1+\cdots)q^{5}+\cdots$
62.4.d.a	$62$	$4$	62.d	31.d	$5$	$16$	$4$	$3.658$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			62.4.d.a	$2$	$0$	$-8$	$4$	$-14$	$-26$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-2\beta _{8}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots$
62.4.d.b	$62$	$4$	62.d	31.d	$5$	$16$	$4$	$3.658$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			62.4.d.b	$2$	$0$	$8$	$-2$	$-2$	$4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-2\beta _{2}q^{2}+(-2+\beta _{1}-2\beta _{2}+2\beta _{3}+\cdots)q^{3}+\cdots$
62.4.g.a	$62$	$4$	62.g	31.g	$15$	$32$	$4$	$3.658$		None		✓			62.4.g.a	$2$	$0$	$-16$	$-10$	$2$	$-19$			$\mathrm{SU}(2)[C_{15}]$
62.4.g.b	$62$	$4$	62.g	31.g	$15$	$32$	$4$	$3.658$		None		✓			62.4.g.b	$2$	$0$	$16$	$-4$	$-10$	$71$			$\mathrm{SU}(2)[C_{15}]$
62.5.b.a	$62$	$5$	62.b	31.b	$2$	$12$	$12$	$6.409$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓	✓	✓	62.5.b.a	$2$	$0$	$0$	$0$	$12$	$212$		$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{3}q^{3}+8q^{4}+(1-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots$
62.5.e.a	$62$	$5$	62.e	31.e	$6$	$20$	$10$	$6.409$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓	✓	62.5.e.a	$2$	$0$	$0$	$-18$	$6$	$122$		$2^{20}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{2}q^{2}+(-1+\beta _{7}+\beta _{9})q^{3}+8q^{4}+\cdots$
62.5.f.a	$62$	$5$	62.f	31.f	$10$	$48$	$12$	$6.409$		None		✓	✓	✓	62.5.f.a	$2$	$0$	$0$	$0$	$-12$	$-12$			$\mathrm{SU}(2)[C_{10}]$
62.5.h.a	$62$	$5$	62.h	31.h	$30$	$80$	$10$	$6.409$		None		✓	✓	✓	62.5.h.a	$2$	$0$	$0$	$18$	$-6$	$-322$			$\mathrm{SU}(2)[C_{30}]$
62.6.a.a	$62$	$6$	62.a	1.a	$1$	$2$	$2$	$9.944$	$\Q(\sqrt{94}) $	None	✓	✓	✓	✓	62.6.a.a	$1$	$1$	$-8$	$-8$	$2$	$-50$	$+$	$2$	$\mathrm{SU}(2)$	$q-4q^{2}+(-4+\beta )q^{3}+2^{4}q^{4}+(1-2\beta )q^{5}+\cdots$
62.6.a.b	$62$	$6$	62.a	1.a	$1$	$2$	$2$	$9.944$	$\Q(\sqrt{7}) $	None	✓	✓	✓	✓	62.6.a.b	$1$	$1$	$8$	$-8$	$-110$	$-126$	$+$	$2$	$\mathrm{SU}(2)$	$q+4q^{2}+(-4+\beta )q^{3}+2^{4}q^{4}+(-55+\cdots)q^{5}+\cdots$
62.6.a.c	$62$	$6$	62.a	1.a	$1$	$4$	$4$	$9.944$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	✓	✓	✓	62.6.a.c	$1$	$0$	$-16$	$10$	$2$	$146$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	$q-4q^{2}+(3+\beta _{2})q^{3}+2^{4}q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
62.6.a.d	$62$	$6$	62.a	1.a	$1$	$4$	$4$	$9.944$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	✓	✓	✓	62.6.a.d	$1$	$0$	$16$	$28$	$-10$	$266$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+4q^{2}+(7-\beta _{1})q^{3}+2^{4}q^{4}+(-3+\cdots)q^{5}+\cdots$
62.6.c.a	$62$	$6$	62.c	31.c	$3$	$14$	$7$	$9.944$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		✓			62.6.c.a	$2$	$0$	$-56$	$7$	$-91$	$79$		$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-4q^{2}+(1-\beta _{1}+\beta _{3})q^{3}+2^{4}q^{4}+\cdots$
62.6.c.b	$62$	$6$	62.c	31.c	$3$	$14$	$7$	$9.944$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		✓			62.6.c.b	$2$	$0$	$56$	$-11$	$33$	$101$		$2^{14}\cdot 3^{2}\cdot 11^{2}\cdot 17^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+4q^{2}+(2\beta _{1}-\beta _{3}+\beta _{4})q^{3}+2^{4}q^{4}+\cdots$
62.6.d.a	$62$	$6$	62.d	31.d	$5$	$24$	$6$	$9.944$		None		✓			62.6.d.a	$2$	$0$	$-24$	$-20$	$120$	$-180$			$\mathrm{SU}(2)[C_{5}]$
62.6.d.b	$62$	$6$	62.d	31.d	$5$	$24$	$6$	$9.944$		None		✓			62.6.d.b	$2$	$0$	$24$	$-2$	$-4$	$-246$			$\mathrm{SU}(2)[C_{5}]$
62.6.g.a	$62$	$6$	62.g	31.g	$15$	$56$	$7$	$9.944$		None		✓			62.6.g.a	$2$	$0$	$-56$	$11$	$-33$	$104$			$\mathrm{SU}(2)[C_{15}]$
62.6.g.b	$62$	$6$	62.g	31.g	$15$	$56$	$7$	$9.944$		None		✓			62.6.g.b	$2$	$0$	$56$	$-7$	$91$	$-94$			$\mathrm{SU}(2)[C_{15}]$
62.7.b.a	$62$	$7$	62.b	31.b	$2$	$16$	$16$	$14.263$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓	✓	62.7.b.a	$2$	$0$	$0$	$0$	$288$	$-328$		$2^{27}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{8}q^{3}+2^{5}q^{4}+(18-3\beta _{2}+\cdots)q^{5}+\cdots$
62.7.e.a	$62$	$7$	62.e	31.e	$6$	$32$	$16$	$14.263$		None		✓	✓	✓	62.7.e.a	$2$	$0$	$0$	$0$	$144$	$-524$			$\mathrm{SU}(2)[C_{6}]$
62.7.f.a	$62$	$7$	62.f	31.f	$10$	$64$	$16$	$14.263$		None		✓	✓	✓	62.7.f.a	$2$	$0$	$0$	$0$	$-288$	$-692$			$\mathrm{SU}(2)[C_{10}]$
62.7.h.a	$62$	$7$	62.h	31.h	$30$	$128$	$16$	$14.263$		None		✓	✓	✓	62.7.h.a	$2$	$0$	$0$	$0$	$-144$	$1544$			$\mathrm{SU}(2)[C_{30}]$
62.8.a.a	$62$	$8$	62.a	1.a	$1$	$3$	$3$	$19.368$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	62.8.a.a	$1$	$1$	$-24$	$-26$	$152$	$-1504$	$-$	$2$	$\mathrm{SU}(2)$	$q-8q^{2}+(-9-\beta _{1})q^{3}+2^{6}q^{4}+(50+\cdots)q^{5}+\cdots$
62.8.a.b	$62$	$8$	62.a	1.a	$1$	$4$	$4$	$19.368$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	✓	✓	✓	62.8.a.b	$1$	$1$	$32$	$-68$	$-334$	$-948$	$-$	$2$	$\mathrm{SU}(2)$	$q+8q^{2}+(-17+\beta _{1}+\beta _{3})q^{3}+2^{6}q^{4}+\cdots$
62.8.a.c	$62$	$8$	62.a	1.a	$1$	$5$	$5$	$19.368$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	✓	✓	✓	62.8.a.c	$1$	$0$	$-40$	$28$	$152$	$-132$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-8q^{2}+(6-\beta _{3})q^{3}+2^{6}q^{4}+(33-11\beta _{1}+\cdots)q^{5}+\cdots$
62.8.a.d	$62$	$8$	62.a	1.a	$1$	$6$	$6$	$19.368$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓	✓	✓	62.8.a.d	$1$	$0$	$48$	$40$	$166$	$1796$	$+$	$2^{5}$	$\mathrm{SU}(2)$	$q+8q^{2}+(7-\beta _{1})q^{3}+2^{6}q^{4}+(29-3\beta _{1}+\cdots)q^{5}+\cdots$
62.8.c.a	$62$	$8$	62.c	31.c	$3$	$18$	$9$	$19.368$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		✓			62.8.c.a	$2$	$0$	$-144$	$-53$	$-97$	$701$		$2^{26}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-8q^{2}+(-6-\beta _{1}-6\beta _{2}+\beta _{3})q^{3}+\cdots$
62.8.c.b	$62$	$8$	62.c	31.c	$3$	$18$	$9$	$19.368$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		✓			62.8.c.b	$2$	$0$	$144$	$1$	$-45$	$927$		$2^{26}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+8q^{2}+\beta _{1}q^{3}+2^{6}q^{4}+(5\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots$
62.8.d.a	$62$	$8$	62.d	31.d	$5$	$40$	$10$	$19.368$		None		✓			62.8.d.a	$2$	$0$	$-80$	$28$	$168$	$1402$			$\mathrm{SU}(2)[C_{5}]$
62.8.d.b	$62$	$8$	62.d	31.d	$5$	$40$	$10$	$19.368$		None		✓			62.8.d.b	$2$	$0$	$80$	$-26$	$116$	$724$			$\mathrm{SU}(2)[C_{5}]$
62.8.g.a	$62$	$8$	62.g	31.g	$15$	$72$	$9$	$19.368$		None		✓			62.8.g.a	$2$	$0$	$-144$	$-1$	$45$	$-1482$			$\mathrm{SU}(2)[C_{15}]$
62.8.g.b	$62$	$8$	62.g	31.g	$15$	$72$	$9$	$19.368$		None		✓			62.8.g.b	$2$	$0$	$144$	$53$	$97$	$-3516$			$\mathrm{SU}(2)[C_{15}]$

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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.