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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 75 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
187.2.a.a	$187$	$2$	187.a	1.a	$1$	$1$	$1$	$1.493$	$\Q$	None	✓	✓			187.2.a.a	$1$	$0$	$0$	$1$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+3q^{5}+2q^{7}-2q^{9}+\cdots$
187.2.a.b	$187$	$2$	187.a	1.a	$1$	$1$	$1$	$1.493$	$\Q$	None	✓	✓			187.2.a.b	$1$	$0$	$2$	$0$	$4$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+4q^{5}-5q^{7}-3q^{9}+\cdots$
187.2.a.c	$187$	$2$	187.a	1.a	$1$	$2$	$2$	$1.493$	$\Q(\sqrt{3}) $	None	✓	✓	✓	✓	187.2.a.c	$1$	$1$	$-2$	$0$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-\beta q^{3}+(2-2\beta )q^{4}+\cdots$
187.2.a.d	$187$	$2$	187.a	1.a	$1$	$2$	$2$	$1.493$	$\Q(\sqrt{17}) $	None	✓	✓	✓		187.2.a.d	$1$	$0$	$4$	$-1$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-1+\beta )q^{3}+2q^{4}+(1-\beta )q^{5}+\cdots$
187.2.a.e	$187$	$2$	187.a	1.a	$1$	$3$	$3$	$1.493$	3.3.148.1	None	✓	✓	✓	✓	187.2.a.e	$1$	$1$	$-2$	$-3$	$-7$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots$
187.2.a.f	$187$	$2$	187.a	1.a	$1$	$4$	$4$	$1.493$	4.4.33844.1	None	✓	✓	✓		187.2.a.f	$1$	$0$	$1$	$1$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
187.2.d.a	$187$	$2$	187.d	17.b	$2$	$16$	$16$	$1.493$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓	✓	187.2.d.a	$2$	$0$	$-2$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{2}+\beta _{14}q^{3}+(1-\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots$
187.2.e.a	$187$	$2$	187.e	17.c	$4$	$4$	$2$	$1.493$	$\Q(\zeta_{8})$	None		✓			187.2.e.a	$2$	$0$	$0$	$-4$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+2\zeta_{8}^{2}q^{2}+(-1+2\zeta_{8}-\zeta_{8}^{2})q^{3}+\cdots$
187.2.e.b	$187$	$2$	187.e	17.c	$4$	$28$	$14$	$1.493$		None		✓	✓		187.2.e.b	$2$	$0$	$0$	$4$	$-16$	$0$			$\mathrm{SU}(2)[C_{4}]$
187.2.g.a	$187$	$2$	187.g	11.c	$5$	$4$	$1$	$1.493$	$\Q(\zeta_{10})$	None		✓			187.2.g.a	$2$	$1$	$-2$	$-5$	$-5$	$-8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}+(-2\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
187.2.g.b	$187$	$2$	187.g	11.c	$5$	$4$	$1$	$1.493$	$\Q(\zeta_{10})$	None		✓			187.2.g.b	$2$	$0$	$2$	$-4$	$-1$	$-8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+(-\zeta_{10}+2\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
187.2.g.c	$187$	$2$	187.g	11.c	$5$	$4$	$1$	$1.493$	$\Q(\zeta_{10})$	None		✓			187.2.g.c	$2$	$0$	$5$	$-1$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\cdots)q^{3}+\cdots$
187.2.g.d	$187$	$2$	187.g	11.c	$5$	$8$	$2$	$1.493$	8.0.324000000.3	None		✓			187.2.g.d	$2$	$0$	$-4$	$6$	$4$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots$
187.2.g.e	$187$	$2$	187.g	11.c	$5$	$8$	$2$	$1.493$	8.0.13140625.1	None		✓			187.2.g.e	$2$	$0$	$-1$	$3$	$-3$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}+\beta _{5})q^{2}+(-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots$
187.2.g.f	$187$	$2$	187.g	11.c	$5$	$36$	$9$	$1.493$		None		✓	✓		187.2.g.f	$2$	$0$	$-4$	$-1$	$1$	$1$			$\mathrm{SU}(2)[C_{5}]$
187.2.h.a	$187$	$2$	187.h	17.d	$8$	$56$	$14$	$1.493$		None		✓	✓	✓	187.2.h.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
187.2.j.a	$187$	$2$	187.j	187.j	$10$	$64$	$16$	$1.493$		None		✓	✓	✓	187.2.j.a	$4$	$0$	$-8$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
187.2.m.a	$187$	$2$	187.m	187.m	$16$	$128$	$16$	$1.493$		None		✓	✓	✓	187.2.m.a	$4$	$0$	$0$	$-16$	$-16$	$0$			$\mathrm{SU}(2)[C_{16}]$
187.2.p.a	$187$	$2$	187.p	187.p	$20$	$128$	$16$	$1.493$		None		✓	✓	✓	187.2.p.a	$4$	$0$	$0$	$-10$	$-2$	$0$			$\mathrm{SU}(2)[C_{20}]$
187.2.r.a	$187$	$2$	187.r	187.r	$40$	$256$	$16$	$1.493$		None		✓	✓	✓	187.2.r.a	$4$	$0$	$-12$	$-12$	$-20$	$-12$			$\mathrm{SU}(2)[C_{40}]$
187.2.t.a	$187$	$2$	187.t	187.t	$80$	$512$	$16$	$1.493$		None		✓	✓	✓	187.2.t.a	$4$	$0$	$-40$	$-24$	$-24$	$-40$			$\mathrm{SU}(2)[C_{80}]$
187.3.b.a	$187$	$3$	187.b	187.b	$2$	$1$	$1$	$5.095$	$\Q$	$\Q(\sqrt{-187}) $	✓	✓			187.3.b.a	$2$	$0$	$0$	$0$	$0$	$-3$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{4}-3q^{7}+9q^{9}+11q^{11}+2^{4}q^{16}+\cdots$
187.3.b.b	$187$	$3$	187.b	187.b	$2$	$1$	$1$	$5.095$	$\Q$	$\Q(\sqrt{-187}) $	✓	✓			187.3.b.a	$2$	$0$	$0$	$0$	$0$	$3$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{4}+3q^{7}+9q^{9}-11q^{11}+2^{4}q^{16}+\cdots$
187.3.b.c	$187$	$3$	187.b	187.b	$2$	$32$	$32$	$5.095$		None		✓	✓		187.3.b.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
187.3.c.a	$187$	$3$	187.c	11.b	$2$	$32$	$32$	$5.095$		None		✓	✓	✓	187.3.c.a	$2$	$0$	$0$	$-2$	$-6$	$0$			$\mathrm{SU}(2)[C_{2}]$
187.3.f.a	$187$	$3$	187.f	187.f	$4$	$68$	$34$	$5.095$		None		✓	✓	✓	187.3.f.a	$4$	$0$	$0$	$4$	$-8$	$0$			$\mathrm{SU}(2)[C_{4}]$
187.3.i.a	$187$	$3$	187.i	187.i	$8$	$136$	$34$	$5.095$		None		✓	✓	✓	187.3.i.a	$4$	$0$	$0$	$-8$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
187.3.k.a	$187$	$3$	187.k	11.d	$10$	$128$	$32$	$5.095$		None		✓	✓	✓	187.3.k.a	$2$	$0$	$0$	$2$	$6$	$0$			$\mathrm{SU}(2)[C_{10}]$
187.3.l.a	$187$	$3$	187.l	187.l	$10$	$136$	$34$	$5.095$		None		✓	✓	✓	187.3.l.a	$4$	$0$	$-10$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
187.3.n.a	$187$	$3$	187.n	17.e	$16$	$240$	$30$	$5.095$		None		✓	✓	✓	187.3.n.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
187.3.o.a	$187$	$3$	187.o	187.o	$20$	$272$	$34$	$5.095$		None		✓	✓	✓	187.3.o.a	$4$	$0$	$0$	$-14$	$-2$	$-40$			$\mathrm{SU}(2)[C_{20}]$
187.3.q.a	$187$	$3$	187.q	187.q	$40$	$544$	$34$	$5.095$		None		✓	✓	✓	187.3.q.a	$4$	$0$	$-20$	$-12$	$-20$	$-20$			$\mathrm{SU}(2)[C_{40}]$
187.3.s.a	$187$	$3$	187.s	187.s	$80$	$1088$	$34$	$5.095$		None		✓	✓	✓	187.3.s.a	$4$	$0$	$-24$	$-24$	$-24$	$-24$			$\mathrm{SU}(2)[C_{80}]$
187.4.a.a	$187$	$4$	187.a	1.a	$1$	$1$	$1$	$11.033$	$\Q$	None	✓	✓			187.4.a.a	$1$	$1$	$1$	$4$	$6$	$-24$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+4q^{3}-7q^{4}+6q^{5}+4q^{6}+\cdots$
187.4.a.b	$187$	$4$	187.a	1.a	$1$	$3$	$3$	$11.033$	3.3.138385.1	None	✓	✓			187.4.a.b	$1$	$1$	$-9$	$1$	$-19$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{2}+\beta _{1}q^{3}+q^{4}+(-6-\beta _{2})q^{5}+\cdots$
187.4.a.c	$187$	$4$	187.a	1.a	$1$	$4$	$4$	$11.033$	4.4.22000.1	None	✓	✓	✓		187.4.a.c	$1$	$1$	$2$	$-6$	$-10$	$16$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+\cdots$
187.4.a.d	$187$	$4$	187.a	1.a	$1$	$10$	$10$	$11.033$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓	✓	187.4.a.d	$1$	$1$	$-8$	$-9$	$-41$	$-63$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-1+\beta _{7})q^{3}+(4+\cdots)q^{4}+\cdots$
187.4.a.e	$187$	$4$	187.a	1.a	$1$	$10$	$10$	$11.033$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓	✓	187.4.a.e	$1$	$0$	$4$	$11$	$47$	$-17$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{1}-\beta _{5})q^{3}+(4+\beta _{1}+\cdots)q^{4}+\cdots$
187.4.a.f	$187$	$4$	187.a	1.a	$1$	$12$	$12$	$11.033$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓	✓	187.4.a.f	$1$	$0$	$10$	$3$	$29$	$39$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-\beta _{5}q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
187.4.d.a	$187$	$4$	187.d	17.b	$2$	$44$	$44$	$11.033$		None		✓	✓	✓	187.4.d.a	$2$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
187.4.e.a	$187$	$4$	187.e	17.c	$4$	$88$	$44$	$11.033$		None		✓	✓	✓	187.4.e.a	$2$	$0$	$0$	$0$	$-16$	$0$			$\mathrm{SU}(2)[C_{4}]$
187.4.g.a	$187$	$4$	187.g	11.c	$5$	$88$	$22$	$11.033$		None		✓			187.4.g.a	$2$	$0$	$2$	$14$	$42$	$16$			$\mathrm{SU}(2)[C_{5}]$
187.4.g.b	$187$	$4$	187.g	11.c	$5$	$104$	$26$	$11.033$		None		✓	✓		187.4.g.b	$2$	$0$	$2$	$-10$	$-50$	$36$			$\mathrm{SU}(2)[C_{5}]$
187.4.h.a	$187$	$4$	187.h	17.d	$8$	$184$	$46$	$11.033$		None		✓	✓	✓	187.4.h.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
187.4.j.a	$187$	$4$	187.j	187.j	$10$	$208$	$52$	$11.033$		None		✓	✓	✓	187.4.j.a	$4$	$0$	$-2$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
187.4.m.a	$187$	$4$	187.m	187.m	$16$	$416$	$52$	$11.033$		None		✓	✓	✓	187.4.m.a	$4$	$0$	$0$	$-16$	$-16$	$0$			$\mathrm{SU}(2)[C_{16}]$
187.4.p.a	$187$	$4$	187.p	187.p	$20$	$416$	$52$	$11.033$		None		✓	✓	✓	187.4.p.a	$4$	$0$	$0$	$-10$	$-22$	$6$			$\mathrm{SU}(2)[C_{20}]$
187.4.r.a	$187$	$4$	187.r	187.r	$40$	$832$	$52$	$11.033$		None		✓	✓	✓	187.4.r.a	$4$	$0$	$-12$	$-12$	$20$	$-12$			$\mathrm{SU}(2)[C_{40}]$
187.4.t.a	$187$	$4$	187.t	187.t	$80$	$1664$	$52$	$11.033$		None		✓	✓	✓	187.4.t.a	$4$	$0$	$-40$	$-24$	$-24$	$-40$			$\mathrm{SU}(2)[C_{80}]$
187.5.b.a	$187$	$5$	187.b	187.b	$2$	$1$	$1$	$19.330$	$\Q$	$\Q(\sqrt{-187}) $	✓	✓			187.5.b.a	$2$	$0$	$0$	$0$	$0$	$-89$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{4}-89q^{7}+3^{4}q^{9}+11^{2}q^{11}+\cdots$

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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.