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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 71 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
1805.1.f.a	$1805$	$1$	1805.f	5.c	$4$	$2$	$1$	$0.901$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$2$		$1$		$q+iq^{4}-q^{5}+(1-i)q^{7}-iq^{9}-q^{16}+\cdots$
1805.1.h.a	$1805$	$1$	1805.h	95.h	$6$	$2$	$1$	$0.901$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-19}) $, $\Q(\sqrt{-95}) $	$\Q(\sqrt{5}) $		$8$	$0$	$0$	$0$	$-1$	$0$		$1$		$q+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{9}-q^{11}+\cdots$
1805.1.h.b	$1805$	$1$	1805.h	95.h	$6$	$4$	$2$	$0.901$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\beta _{1}q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
1805.1.m.a	$1805$	$1$	1805.m	95.m	$12$	$4$	$1$	$0.901$	$\Q(\zeta_{12})$	$D_{4}$	$\Q(\sqrt{-19}) $	None		$8$	$0$	$0$	$0$	$2$	$4$		$1$		$q-\zeta_{12}^{5}q^{4}-\zeta_{12}^{4}q^{5}+(1-\zeta_{12}^{3}+\cdots)q^{7}+\cdots$
1805.1.o.a	$1805$	$1$	1805.o	95.o	$18$	$6$	$1$	$0.901$	$\Q(\zeta_{18})$	$D_{2}$	$\Q(\sqrt{-19}) $, $\Q(\sqrt{-95}) $	$\Q(\sqrt{5}) $		$24$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{2}q^{4}-\zeta_{18}^{7}q^{5}-\zeta_{18}^{8}q^{9}+\cdots$
1805.1.o.b	$1805$	$1$	1805.o	95.o	$18$	$12$	$2$	$0.901$	12.0.$\cdots$.2	$D_{4}$	$\Q(\sqrt{-95}) $	None		$24$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\beta _{5}+\beta _{11})q^{2}+\beta _{5}q^{3}+(-\beta _{4}-\beta _{10}+\cdots)q^{4}+\cdots$
1805.1.r.a	$1805$	$1$	1805.r	95.q	$36$	$12$	$1$	$0.901$	$\Q(\zeta_{36})$	$D_{4}$	$\Q(\sqrt{-19}) $	None		$24$	$0$	$0$	$0$	$0$	$-6$		$1$		$q-\zeta_{36}^{7}q^{4}+\zeta_{36}^{2}q^{5}+(\zeta_{36}^{3}+\zeta_{36}^{12}+\cdots)q^{7}+\cdots$
1805.2.a.a	$1805$	$2$	1805.a	1.a	$1$	$1$	$1$	$14.413$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{4}-q^{5}-4q^{7}+q^{9}+3q^{11}+\cdots$
1805.2.a.b	$1805$	$2$	1805.a	1.a	$1$	$1$	$1$	$14.413$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{4}-q^{5}-4q^{7}+q^{9}+3q^{11}+\cdots$
1805.2.a.c	$1805$	$2$	1805.a	1.a	$1$	$2$	$2$	$14.413$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$2$	$-3$	$-3$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots$
1805.2.a.d	$1805$	$2$	1805.a	1.a	$1$	$2$	$2$	$14.413$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$-2$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}+3q^{4}-q^{5}-2q^{7}-\beta q^{8}+\cdots$
1805.2.a.e	$1805$	$2$	1805.a	1.a	$1$	$2$	$2$	$14.413$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$3$	$3$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}-q^{5}+\cdots$
1805.2.a.f	$1805$	$2$	1805.a	1.a	$1$	$3$	$3$	$14.413$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-2$	$3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
1805.2.a.g	$1805$	$2$	1805.a	1.a	$1$	$3$	$3$	$14.413$	3.3.361.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$-1$	$-3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(2+\beta _{2})q^{4}+\cdots$
1805.2.a.h	$1805$	$2$	1805.a	1.a	$1$	$3$	$3$	$14.413$	3.3.361.1	$_{}$	None	None	✓	$1$	$1$	$1$	$1$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots$
1805.2.a.i	$1805$	$2$	1805.a	1.a	$1$	$4$	$4$	$14.413$	4.4.7537.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-3$	$4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(-1+\beta _{1})q^{3}+(1-\beta _{2}+\beta _{3})q^{4}+\cdots$
1805.2.a.j	$1805$	$2$	1805.a	1.a	$1$	$4$	$4$	$14.413$	4.4.2225.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-1$	$4$	$-11$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1+\beta _{1}+\beta _{3})q^{4}+\cdots$
1805.2.a.k	$1805$	$2$	1805.a	1.a	$1$	$4$	$4$	$14.413$	$\Q(\zeta_{20})^+$	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{3})q^{3}-2q^{4}-q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots$
1805.2.a.l	$1805$	$2$	1805.a	1.a	$1$	$4$	$4$	$14.413$	$\Q(\zeta_{20})^+$	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$-4$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{1}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
1805.2.a.m	$1805$	$2$	1805.a	1.a	$1$	$4$	$4$	$14.413$	4.4.7168.1	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$4$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
1805.2.a.n	$1805$	$2$	1805.a	1.a	$1$	$4$	$4$	$14.413$	4.4.2225.1	$_{}$	None	None	✓	$1$	$1$	$1$	$1$	$4$	$-11$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots$
1805.2.a.o	$1805$	$2$	1805.a	1.a	$1$	$4$	$4$	$14.413$	4.4.7537.1	$_{}$	None	None	✓	$1$	$0$	$1$	$3$	$4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{2}+\beta _{3})q^{4}+\cdots$
1805.2.a.p	$1805$	$2$	1805.a	1.a	$1$	$4$	$4$	$14.413$	4.4.11344.1	$_{}$	None	None	✓	$1$	$0$	$2$	$-2$	$-4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots$
1805.2.a.q	$1805$	$2$	1805.a	1.a	$1$	$6$	$6$	$14.413$	6.6.5822000.1	$_{}$	None	None	✓	$1$	$0$	$-2$	$-4$	$-6$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}-\beta _{3})q^{2}+(-1-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots$
1805.2.a.r	$1805$	$2$	1805.a	1.a	$1$	$6$	$6$	$14.413$	6.6.5822000.1	$_{}$	None	None	✓	$1$	$0$	$2$	$4$	$-6$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}+\beta _{3})q^{2}+(1+\beta _{3}-\beta _{4})q^{3}+\cdots$
1805.2.a.s	$1805$	$2$	1805.a	1.a	$1$	$9$	$9$	$14.413$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-6$	$-9$	$9$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-1+\beta _{7})q^{3}+(\beta _{4}+\cdots)q^{4}+\cdots$
1805.2.a.t	$1805$	$2$	1805.a	1.a	$1$	$9$	$9$	$14.413$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-9$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{5})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots$
1805.2.a.u	$1805$	$2$	1805.a	1.a	$1$	$9$	$9$	$14.413$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-9$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{5})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1805.2.a.v	$1805$	$2$	1805.a	1.a	$1$	$9$	$9$	$14.413$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$6$	$9$	$9$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{7})q^{3}+(\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots$
1805.2.a.w	$1805$	$2$	1805.a	1.a	$1$	$16$	$16$	$14.413$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$16$	$22$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{12}q^{3}+(2-\beta _{5}+\beta _{6})q^{4}+\cdots$
1805.2.b.a	$1805$	$2$	1805.b	5.b	$2$	$2$	$2$	$14.413$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-2q^{4}+(-1+i)q^{5}+2iq^{7}+\cdots$
1805.2.b.b	$1805$	$2$	1805.b	5.b	$2$	$2$	$2$	$14.413$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-2q^{4}+(-1-i)q^{5}-2iq^{7}+\cdots$
1805.2.b.c	$1805$	$2$	1805.b	5.b	$2$	$2$	$2$	$14.413$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{4}+(-1-2i)q^{5}+2iq^{7}+\cdots$
1805.2.b.d	$1805$	$2$	1805.b	5.b	$2$	$2$	$2$	$14.413$	$\Q(\sqrt{-19}) $	$_{}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{4}+(-1+\beta )q^{5}+(-1+2\beta )q^{7}+\cdots$
1805.2.b.e	$1805$	$2$	1805.b	5.b	$2$	$6$	$6$	$14.413$	6.0.16516096.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+(-\beta _{1}+\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots$
1805.2.b.f	$1805$	$2$	1805.b	5.b	$2$	$6$	$6$	$14.413$	6.0.4227136.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{5})q^{2}+(-\beta _{1}-\beta _{4}-\beta _{5})q^{3}+\cdots$
1805.2.b.g	$1805$	$2$	1805.b	5.b	$2$	$6$	$6$	$14.413$	6.0.4227136.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{5})q^{2}+(-\beta _{1}-\beta _{4}-\beta _{5})q^{3}+\cdots$
1805.2.b.h	$1805$	$2$	1805.b	5.b	$2$	$8$	$8$	$14.413$	8.0.$\cdots$.2	$_{}$	$\Q(\sqrt{-95}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-2+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$
1805.2.b.i	$1805$	$2$	1805.b	5.b	$2$	$16$	$16$	$14.413$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$
1805.2.b.j	$1805$	$2$	1805.b	5.b	$2$	$16$	$16$	$14.413$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots$
1805.2.b.k	$1805$	$2$	1805.b	5.b	$2$	$24$	$24$	$14.413$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-3$	$0$			$\mathrm{SU}(2)[C_{2}]$
1805.2.b.l	$1805$	$2$	1805.b	5.b	$2$	$24$	$24$	$14.413$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-3$	$0$			$\mathrm{SU}(2)[C_{2}]$
1805.2.b.m	$1805$	$2$	1805.b	5.b	$2$	$40$	$40$	$14.413$		$_{}$	None	None		$4$	$0$	$0$	$0$	$6$	$0$			$\mathrm{SU}(2)[C_{2}]$
1805.4.a.a	$1805$	$4$	1805.a	1.a	$1$	$1$	$1$	$106.498$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-5$	$-4$	$5$	$-32$	$+$	$1$	$\mathrm{SU}(2)$	$q-5q^{2}-4q^{3}+17q^{4}+5q^{5}+20q^{6}+\cdots$
1805.4.a.b	$1805$	$4$	1805.a	1.a	$1$	$1$	$1$	$106.498$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-5$	$5$	$5$	$-19$	$-$	$1$	$\mathrm{SU}(2)$	$q-5q^{2}+5q^{3}+17q^{4}+5q^{5}-5^{2}q^{6}+\cdots$
1805.4.a.c	$1805$	$4$	1805.a	1.a	$1$	$1$	$1$	$106.498$	$\Q$	$_{}$	None	None	✓	$1$	$2$	$-3$	$-7$	$5$	$11$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{2}-7q^{3}+q^{4}+5q^{5}+21q^{6}+\cdots$
1805.4.a.d	$1805$	$4$	1805.a	1.a	$1$	$1$	$1$	$106.498$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-3$	$5$	$-5$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{2}+5q^{3}+q^{4}-5q^{5}-15q^{6}+\cdots$
1805.4.a.e	$1805$	$4$	1805.a	1.a	$1$	$1$	$1$	$106.498$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-5$	$5$	$22$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-5q^{3}-7q^{4}+5q^{5}+5q^{6}+\cdots$
1805.4.a.f	$1805$	$4$	1805.a	1.a	$1$	$1$	$1$	$106.498$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$-5$	$-22$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{3}-8q^{4}-5q^{5}-22q^{7}-11q^{9}+\cdots$
1805.4.a.g	$1805$	$4$	1805.a	1.a	$1$	$1$	$1$	$106.498$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$5$	$5$	$22$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+5q^{3}-7q^{4}+5q^{5}+5q^{6}+\cdots$

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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.