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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 182 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	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
55.1.d.a	$55$	$1$	55.d	55.d	$2$	$1$	$1$	$0.027$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $	✓	✓	✓	✓	55.1.d.a	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-q^{4}-q^{5}+q^{9}-q^{11}+q^{16}+q^{20}+\cdots$
55.2.a.a	$55$	$2$	55.a	1.a	$1$	$1$	$1$	$0.439$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	55.2.a.a	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}-3q^{8}-3q^{9}+q^{10}+\cdots$
55.2.a.b	$55$	$2$	55.a	1.a	$1$	$2$	$2$	$0.439$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓	✓	55.2.a.b	$1$	$0$	$2$	$0$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-2\beta q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots$
55.2.b.a	$55$	$2$	55.b	5.b	$2$	$4$	$4$	$0.439$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		✓	✓	✓	55.2.b.a	$2$	$0$	$0$	$0$	$-3$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(\beta _{1}-\beta _{3})q^{3}+\cdots$
55.2.e.a	$55$	$2$	55.e	55.e	$4$	$4$	$2$	$0.439$	$\Q(i, \sqrt{10})$	$_{}$	None	None		✓			55.2.e.a	$4$	$0$	$0$	$-4$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+3\beta _{2}q^{4}+\cdots$
55.2.e.b	$55$	$2$	55.e	55.e	$4$	$4$	$2$	$0.439$	$\Q(i, \sqrt{11})$	$_{}$	$\Q(\sqrt{-11}) $	None		✓			55.2.e.b	$4$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-1+\beta _{1}-\beta _{3})q^{3}+2\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
55.2.g.a	$55$	$2$	55.g	11.c	$5$	$8$	$2$	$0.439$	8.0.159390625.1	$_{}$	None	None		✓			55.2.g.a	$2$	$0$	$-4$	$1$	$-2$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}-\beta _{2}+\beta _{4})q^{2}+\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots$
55.2.g.b	$55$	$2$	55.g	11.c	$5$	$8$	$2$	$0.439$	8.0.13140625.1	$_{}$	None	None		✓			55.2.g.b	$2$	$0$	$-2$	$-5$	$2$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$
55.2.j.a	$55$	$2$	55.j	55.j	$10$	$16$	$4$	$0.439$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓	✓	55.2.j.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(\beta _{1}-\beta _{12}-\beta _{13})q^{2}+(\beta _{5}+\beta _{13}+\cdots)q^{3}+\cdots$
55.2.l.a	$55$	$2$	55.l	55.l	$20$	$32$	$4$	$0.439$		$_{}$	None	None		✓	✓	✓	55.2.l.a	$4$	$0$	$-10$	$-4$	$-2$	$0$			$\mathrm{SU}(2)[C_{20}]$
55.3.c.a	$55$	$3$	55.c	11.b	$2$	$8$	$8$	$1.499$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		✓	✓	✓	55.3.c.a	$2$	$0$	$0$	$8$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(-4+\beta _{2})q^{4}+\cdots$
55.3.d.a	$55$	$3$	55.d	55.d	$2$	$2$	$2$	$1.499$	$\Q(\sqrt{-11}) $	$_{}$	$\Q(\sqrt{-11}) $	None		✓			55.3.d.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(1-2\beta )q^{3}-4q^{4}+(2-3\beta )q^{5}-2q^{9}+\cdots$
55.3.d.b	$55$	$3$	55.d	55.d	$2$	$2$	$2$	$1.499$	$\Q(\sqrt{5}) $	$_{}$	$\Q(\sqrt{-55}) $	None	✓	✓			55.3.d.b	$4$	$0$	$0$	$0$	$10$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{2}+q^{4}+5q^{5}+2\beta q^{7}+3\beta q^{8}+\cdots$
55.3.d.c	$55$	$3$	55.d	55.d	$2$	$2$	$2$	$1.499$	$\Q(\sqrt{11}) $	$_{}$	$\Q(\sqrt{-55}) $	None	✓	✓			55.3.d.c	$4$	$0$	$0$	$0$	$-10$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}+7q^{4}-5q^{5}-4\beta q^{7}+3\beta q^{8}+\cdots$
55.3.d.d	$55$	$3$	55.d	55.d	$2$	$4$	$4$	$1.499$	$\Q(\sqrt{5}, \sqrt{-21})$	$_{}$	None	None		✓	✓		55.3.d.d	$4$	$0$	$0$	$0$	$-8$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-\beta _{1}q^{3}+q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots$
55.3.f.a	$55$	$3$	55.f	5.c	$4$	$20$	$10$	$1.499$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓	✓	✓	55.3.f.a	$2$	$0$	$-4$	$-2$	$-8$	$0$		$2^{8}\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{5}q^{2}-\beta _{4}q^{3}+(-2\beta _{8}-\beta _{16})q^{4}+\cdots$
55.3.h.a	$55$	$3$	55.h	55.h	$10$	$40$	$10$	$1.499$		$_{}$	None	None		✓	✓	✓	55.3.h.a	$4$	$0$	$0$	$0$	$2$	$0$			$\mathrm{SU}(2)[C_{10}]$
55.3.i.a	$55$	$3$	55.i	11.d	$10$	$4$	$1$	$1.499$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			55.3.i.a	$2$	$0$	$-5$	$4$	$-5$	$15$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-2\zeta_{10}+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(4+\cdots)q^{3}+\cdots$
55.3.i.b	$55$	$3$	55.i	11.d	$10$	$4$	$1$	$1.499$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			55.3.i.b	$2$	$0$	$5$	$-6$	$5$	$30$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(2+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-4+3\zeta_{10}+\cdots)q^{3}+\cdots$
55.3.i.c	$55$	$3$	55.i	11.d	$10$	$12$	$3$	$1.499$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			55.3.i.c	$2$	$0$	$-5$	$7$	$15$	$-40$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}+\beta _{7}-\beta _{11})q^{2}+\cdots$
55.3.i.d	$55$	$3$	55.i	11.d	$10$	$12$	$3$	$1.499$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			55.3.i.d	$2$	$0$	$5$	$-13$	$-15$	$-5$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(1+\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}-\beta _{10})q^{2}+\cdots$
55.3.k.a	$55$	$3$	55.k	55.k	$20$	$80$	$10$	$1.499$		$_{}$	None	None		✓	✓	✓	55.3.k.a	$4$	$0$	$-6$	$-8$	$-2$	$-40$			$\mathrm{SU}(2)[C_{20}]$
55.4.a.a	$55$	$4$	55.a	1.a	$1$	$1$	$1$	$3.245$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	55.4.a.a	$1$	$1$	$1$	$-3$	$-5$	$-9$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}-7q^{4}-5q^{5}-3q^{6}+\cdots$
55.4.a.b	$55$	$4$	55.a	1.a	$1$	$2$	$2$	$3.245$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓	✓	55.4.a.b	$1$	$1$	$-7$	$-3$	$10$	$-25$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-3-\beta )q^{2}+(-1-\beta )q^{3}+(5+7\beta )q^{4}+\cdots$
55.4.a.c	$55$	$4$	55.a	1.a	$1$	$3$	$3$	$3.245$	3.3.568.1	$_{}$	None	None	✓	✓	✓	✓	55.4.a.c	$1$	$0$	$5$	$-3$	$-15$	$-15$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1}-\beta _{2})q^{2}+(-2-3\beta _{2})q^{3}+\cdots$
55.4.a.d	$55$	$4$	55.a	1.a	$1$	$4$	$4$	$3.245$	4.4.1539480.1	$_{}$	None	None	✓	✓	✓	✓	55.4.a.d	$1$	$0$	$1$	$9$	$20$	$9$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2-\beta _{2})q^{3}+(5+\beta _{1}+\beta _{3})q^{4}+\cdots$
55.4.b.a	$55$	$4$	55.b	5.b	$2$	$6$	$6$	$3.245$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	$_{}$	None	None		✓			55.4.b.a	$2$	$0$	$0$	$0$	$-4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{5})q^{3}+(1+\beta _{3})q^{4}+\cdots$
55.4.b.b	$55$	$4$	55.b	5.b	$2$	$10$	$10$	$3.245$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		✓	✓		55.4.b.b	$2$	$0$	$0$	$0$	$14$	$0$		$2^{3}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-6+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
55.4.e.a	$55$	$4$	55.e	55.e	$4$	$4$	$2$	$3.245$	$\Q(i, \sqrt{11})$	$_{}$	$\Q(\sqrt{-11}) $	None		✓			55.4.e.a	$4$	$0$	$0$	$16$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{4}]$	$q+(4+4\beta _{1}+\beta _{2}+\beta _{3})q^{3}-8\beta _{1}q^{4}+\cdots$
55.4.e.b	$55$	$4$	55.e	55.e	$4$	$28$	$14$	$3.245$		$_{}$	None	None		✓	✓		55.4.e.b	$4$	$0$	$0$	$-16$	$12$	$0$			$\mathrm{SU}(2)[C_{4}]$
55.4.g.a	$55$	$4$	55.g	11.c	$5$	$24$	$6$	$3.245$		$_{}$	None	None		✓			55.4.g.a	$2$	$0$	$2$	$-8$	$30$	$-53$			$\mathrm{SU}(2)[C_{5}]$
55.4.g.b	$55$	$4$	55.g	11.c	$5$	$24$	$6$	$3.245$		$_{}$	None	None		✓			55.4.g.b	$2$	$0$	$6$	$4$	$-30$	$81$			$\mathrm{SU}(2)[C_{5}]$
55.4.j.a	$55$	$4$	55.j	55.j	$10$	$64$	$16$	$3.245$		$_{}$	None	None		✓	✓	✓	55.4.j.a	$4$	$0$	$0$	$0$	$-15$	$0$			$\mathrm{SU}(2)[C_{10}]$
55.4.l.a	$55$	$4$	55.l	55.l	$20$	$128$	$16$	$3.245$		$_{}$	None	None		✓	✓	✓	55.4.l.a	$4$	$0$	$-10$	$-10$	$-22$	$10$			$\mathrm{SU}(2)[C_{20}]$
55.5.c.a	$55$	$5$	55.c	11.b	$2$	$16$	$16$	$5.685$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓	✓	55.5.c.a	$2$	$0$	$0$	$-16$	$0$	$0$		$2^{10}\cdot 5^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{5})q^{3}+(-9+\beta _{2}+\cdots)q^{4}+\cdots$
55.5.d.a	$55$	$5$	55.d	55.d	$2$	$1$	$1$	$5.685$	$\Q$	$_{}$	$\Q(\sqrt{-55}) $	None	✓	✓			55.5.d.a	$2$	$0$	$-3$	$0$	$25$	$-78$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{2}-7q^{4}+5^{2}q^{5}-78q^{7}+69q^{8}+\cdots$
55.5.d.b	$55$	$5$	55.d	55.d	$2$	$1$	$1$	$5.685$	$\Q$	$_{}$	$\Q(\sqrt{-55}) $	None	✓	✓			55.5.d.a	$2$	$0$	$3$	$0$	$25$	$78$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{2}-7q^{4}+5^{2}q^{5}+78q^{7}-69q^{8}+\cdots$
55.5.d.c	$55$	$5$	55.d	55.d	$2$	$2$	$2$	$5.685$	$\Q(\sqrt{-11}) $	$_{}$	$\Q(\sqrt{-11}) $	None		✓			55.5.d.c	$4$	$0$	$0$	$0$	$49$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(5-10\beta )q^{3}-2^{4}q^{4}+(26-3\beta )q^{5}+\cdots$
55.5.d.d	$55$	$5$	55.d	55.d	$2$	$2$	$2$	$5.685$	$\Q(\sqrt{55}) $	$_{}$	$\Q(\sqrt{-55}) $	None	✓	✓			55.5.d.d	$4$	$0$	$0$	$0$	$-50$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}+39q^{4}-5^{2}q^{5}+8\beta q^{7}+23\beta q^{8}+\cdots$
55.5.d.e	$55$	$5$	55.d	55.d	$2$	$16$	$16$	$5.685$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓		55.5.d.e	$4$	$0$	$0$	$0$	$-30$	$0$		$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{2}-\beta _{7}q^{3}+(8-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots$
55.5.f.a	$55$	$5$	55.f	5.c	$4$	$40$	$20$	$5.685$		$_{}$	None	None		✓	✓	✓	55.5.f.a	$2$	$0$	$0$	$10$	$-48$	$0$			$\mathrm{SU}(2)[C_{4}]$
55.5.h.a	$55$	$5$	55.h	55.h	$10$	$88$	$22$	$5.685$		$_{}$	None	None		✓	✓	✓	55.5.h.a	$4$	$0$	$0$	$0$	$-24$	$0$			$\mathrm{SU}(2)[C_{10}]$
55.5.i.a	$55$	$5$	55.i	11.d	$10$	$4$	$1$	$5.685$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			55.5.i.a	$2$	$0$	$5$	$-30$	$-25$	$150$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(2+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-4-9\zeta_{10}+\cdots)q^{3}+\cdots$
55.5.i.b	$55$	$5$	55.i	11.d	$10$	$28$	$7$	$5.685$		$_{}$	None	None		✓			55.5.i.b	$2$	$0$	$-5$	$43$	$-175$	$-90$			$\mathrm{SU}(2)[C_{10}]$
55.5.i.c	$55$	$5$	55.i	11.d	$10$	$32$	$8$	$5.685$		$_{}$	None	None		✓	✓		55.5.i.c	$2$	$0$	$0$	$3$	$200$	$-60$			$\mathrm{SU}(2)[C_{10}]$
55.5.k.a	$55$	$5$	55.k	55.k	$20$	$176$	$22$	$5.685$		$_{}$	None	None		✓	✓	✓	55.5.k.a	$4$	$0$	$-6$	$4$	$-42$	$244$			$\mathrm{SU}(2)[C_{20}]$
55.6.a.a	$55$	$6$	55.a	1.a	$1$	$3$	$3$	$8.821$	3.3.21865.1	$_{}$	None	None	✓	✓	✓	✓	55.6.a.a	$1$	$1$	$-7$	$-36$	$75$	$-102$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2-\beta _{2})q^{2}+(-11-3\beta _{1})q^{3}+\cdots$
55.6.a.b	$55$	$6$	55.a	1.a	$1$	$4$	$4$	$8.821$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	55.6.a.b	$1$	$1$	$-5$	$0$	$-100$	$-90$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(15+\cdots)q^{4}+\cdots$
55.6.a.c	$55$	$6$	55.a	1.a	$1$	$5$	$5$	$8.821$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	55.6.a.c	$1$	$0$	$9$	$0$	$125$	$70$	$-$	$2$	$\mathrm{SU}(2)$	$q+(2-\beta _{1})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(24-3\beta _{1}+\cdots)q^{4}+\cdots$
55.6.a.d	$55$	$6$	55.a	1.a	$1$	$6$	$6$	$8.821$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	55.6.a.d	$1$	$0$	$3$	$0$	$-150$	$-66$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(20+\cdots)q^{4}+\cdots$

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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.