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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 11723 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
18.2.c.a	$18$	$2$	18.c	9.c	$3$	$2$	$1$	$0.144$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$-3$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
21.2.e.a	$21$	$2$	21.e	7.c	$3$	$2$	$1$	$0.168$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-2$	$-1$	$2$	$-5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}-\zeta_{6}q^{3}-2\zeta_{6}q^{4}+\cdots$
26.2.c.a	$26$	$2$	26.c	13.c	$3$	$2$	$1$	$0.208$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$-2$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}-4\zeta_{6}q^{7}+\cdots$
28.2.e.a	$28$	$2$	28.e	7.c	$3$	$2$	$1$	$0.224$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$-1$	$-3$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{3}+(-3+3\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$
31.2.c.a	$31$	$2$	31.c	31.c	$3$	$4$	$2$	$0.248$	$\Q(\sqrt{2}, \sqrt{-3})$	None		$2$	$0$	$-4$	$2$	$-2$	$-2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+\cdots$
35.2.e.a	$35$	$2$	35.e	7.c	$3$	$4$	$2$	$0.279$	$\Q(\sqrt{2}, \sqrt{-3})$	None		$2$	$0$	$-2$	$-2$	$-2$	$2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots$
36.2.e.a	$36$	$2$	36.e	9.c	$3$	$2$	$1$	$0.287$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$0$	$-3$	$1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-2\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+\zeta_{6}q^{7}+\cdots$
37.2.c.a	$37$	$2$	37.c	37.c	$3$	$2$	$1$	$0.295$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$-1$	$-2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}-2\zeta_{6}q^{7}+\cdots$
38.2.c.a	$38$	$2$	38.c	19.c	$3$	$2$	$1$	$0.303$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-1$	$0$	$-8$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
38.2.c.b	$38$	$2$	38.c	19.c	$3$	$4$	$2$	$0.303$	$\Q(\sqrt{-3}, \sqrt{7})$	None		$2$	$0$	$-2$	$0$	$-2$	$4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
39.2.e.a	$39$	$2$	39.e	13.c	$3$	$2$	$1$	$0.311$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$1$	$-2$	$-2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
39.2.e.b	$39$	$2$	39.e	13.c	$3$	$4$	$2$	$0.311$	$\Q(\sqrt{-3}, \sqrt{17})$	None		$2$	$0$	$-1$	$-2$	$-6$	$3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}-\beta _{2}q^{3}+(-2+\beta _{1}+2\beta _{2}+\cdots)q^{4}+\cdots$
42.2.e.a	$42$	$2$	42.e	7.c	$3$	$2$	$1$	$0.335$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$1$	$-1$	$1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+(-1+\cdots)q^{5}+\cdots$
42.2.e.b	$42$	$2$	42.e	7.c	$3$	$2$	$1$	$0.335$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-1$	$-3$	$5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+(-3+\cdots)q^{5}+\cdots$
43.2.c.a	$43$	$2$	43.c	43.c	$3$	$2$	$1$	$0.343$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$-1$	$1$	$-3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-1+\zeta_{6})q^{3}-q^{4}+(1-\zeta_{6})q^{5}+\cdots$
43.2.c.b	$43$	$2$	43.c	43.c	$3$	$4$	$2$	$0.343$	$\Q(\sqrt{-3}, \sqrt{5})$	None		$2$	$0$	$-6$	$3$	$2$	$4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2-\beta _{2})q^{2}+(1+\beta _{1}+\beta _{3})q^{3}+\cdots$
45.2.e.a	$45$	$2$	45.e	9.c	$3$	$2$	$1$	$0.359$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$-3$	$1$	$3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
45.2.e.b	$45$	$2$	45.e	9.c	$3$	$6$	$3$	$0.359$	6.0.954288.1	None		$2$	$0$	$-1$	$1$	$-3$	$-5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{2}-\beta _{4}-\beta _{5})q^{2}+\beta _{4}q^{3}+\cdots$
49.2.c.a	$49$	$2$	49.c	7.c	$3$	$2$	$1$	$0.391$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-7}) $		$4$	$0$	$-1$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{3}]$	$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-3q^{8}+3\zeta_{6}q^{9}+\cdots$
7.4.c.a	$7$	$4$	7.c	7.c	$3$	$2$	$1$	$0.413$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-2$	$-7$	$-7$	$28$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}-7\zeta_{6}q^{3}+4\zeta_{6}q^{4}+\cdots$
52.2.e.a	$52$	$2$	52.e	13.c	$3$	$2$	$1$	$0.415$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$-3$	$4$	$-1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+3\zeta_{6})q^{3}+2q^{5}-\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots$
52.2.e.b	$52$	$2$	52.e	13.c	$3$	$2$	$1$	$0.415$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$2$	$-6$	$4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}-3q^{5}+4\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
54.2.c.a	$54$	$2$	54.c	9.c	$3$	$2$	$1$	$0.431$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{7}+\cdots$
56.2.i.a	$56$	$2$	56.i	7.c	$3$	$2$	$1$	$0.447$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$-3$	$1$	$4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-3\zeta_{6}q^{3}+(1-\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+\cdots$
56.2.i.b	$56$	$2$	56.i	7.c	$3$	$2$	$1$	$0.447$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$1$	$1$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{3}+(1-\zeta_{6})q^{5}+(-3+2\zeta_{6})q^{7}+\cdots$
57.2.e.a	$57$	$2$	57.e	19.c	$3$	$2$	$1$	$0.455$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$1$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
57.2.e.b	$57$	$2$	57.e	19.c	$3$	$6$	$3$	$0.455$	6.0.954288.1	None		$2$	$0$	$1$	$-3$	$-2$	$-2$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{4}+\beta _{5})q^{2}-\beta _{3}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots$
61.2.c.a	$61$	$2$	61.c	61.c	$3$	$8$	$4$	$0.487$	8.0.310217769.2	None		$2$	$0$	$0$	$-6$	$-2$	$-1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
62.2.c.a	$62$	$2$	62.c	31.c	$3$	$2$	$1$	$0.495$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-2$	$-1$	$3$	$1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(-1+\zeta_{6})q^{3}+q^{4}+3\zeta_{6}q^{5}+\cdots$
62.2.c.b	$62$	$2$	62.c	31.c	$3$	$2$	$1$	$0.495$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$-3$	$-1$	$3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-3+3\zeta_{6})q^{3}+q^{4}-\zeta_{6}q^{5}+\cdots$
63.2.e.a	$63$	$2$	63.e	7.c	$3$	$2$	$1$	$0.503$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$0$	$0$	$-1$	$1$	$\mathrm{U}(1)[D_{3}]$	$q+2\zeta_{6}q^{4}+(1-3\zeta_{6})q^{7}-7q^{13}+(-4+\cdots)q^{16}+\cdots$
63.2.e.b	$63$	$2$	63.e	7.c	$3$	$2$	$1$	$0.503$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$0$	$-2$	$-5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{5}+\cdots$
63.2.f.a	$63$	$2$	63.f	9.c	$3$	$6$	$3$	$0.503$	$\Q(\zeta_{18})$	None		$2$	$0$	$-3$	$0$	$-3$	$-3$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(-\zeta_{18}^{3}+\cdots)q^{3}+\cdots$
63.2.f.b	$63$	$2$	63.f	9.c	$3$	$6$	$3$	$0.503$	6.0.309123.1	None		$2$	$0$	$1$	$-4$	$5$	$3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots$
63.2.g.a	$63$	$2$	63.g	63.g	$3$	$2$	$1$	$0.503$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$-3$	$-2$	$1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
63.2.g.b	$63$	$2$	63.g	63.g	$3$	$10$	$5$	$0.503$	10.0.$\cdots$.1	None		$2$	$0$	$2$	$2$	$-8$	$-1$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{2}-\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
63.2.h.a	$63$	$2$	63.h	63.h	$3$	$2$	$1$	$0.503$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$0$	$1$	$4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+\zeta_{6}q^{5}+\cdots$
63.2.h.b	$63$	$2$	63.h	63.h	$3$	$10$	$5$	$0.503$	10.0.$\cdots$.1	None		$2$	$0$	$-4$	$-1$	$4$	$-4$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{5})q^{2}-\beta _{8}q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots$
65.2.e.a	$65$	$2$	65.e	13.c	$3$	$4$	$2$	$0.519$	$\Q(\sqrt{-3}, \sqrt{5})$	None		$2$	$0$	$-1$	$0$	$4$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-1+2\beta _{1}-\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
65.2.e.b	$65$	$2$	65.e	13.c	$3$	$4$	$2$	$0.519$	$\Q(\sqrt{-3}, \sqrt{13})$	None		$2$	$0$	$1$	$-2$	$-4$	$2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$
9.4.c.a	$9$	$4$	9.c	9.c	$3$	$4$	$2$	$0.531$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		$2$	$0$	$-3$	$-3$	$-15$	$-7$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
67.2.c.a	$67$	$2$	67.c	67.c	$3$	$10$	$5$	$0.535$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$2$	$-8$	$-6$	$2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{5})q^{2}+(-1+\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots$
70.2.e.a	$70$	$2$	70.e	7.c	$3$	$2$	$1$	$0.559$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$-3$	$1$	$1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
70.2.e.b	$70$	$2$	70.e	7.c	$3$	$2$	$1$	$0.559$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$2$	$1$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
70.2.e.c	$70$	$2$	70.e	7.c	$3$	$2$	$1$	$0.559$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-1$	$1$	$-1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
70.2.e.d	$70$	$2$	70.e	7.c	$3$	$2$	$1$	$0.559$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$2$	$-1$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
72.2.i.a	$72$	$2$	72.i	9.c	$3$	$2$	$1$	$0.575$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$0$	$1$	$3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+3\zeta_{6}q^{7}+\cdots$
72.2.i.b	$72$	$2$	72.i	9.c	$3$	$4$	$2$	$0.575$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		$2$	$0$	$0$	$1$	$1$	$-3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2}-2\beta _{3})q^{5}+(1-2\beta _{1}+\cdots)q^{7}+\cdots$
73.2.c.a	$73$	$2$	73.c	73.c	$3$	$8$	$4$	$0.583$	8.0.142635249.1	None		$2$	$0$	$1$	$-6$	$2$	$2$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{7}q^{2}+(-1+\beta _{5})q^{3}+(\beta _{1}+\beta _{4}+\cdots)q^{4}+\cdots$
74.2.c.a	$74$	$2$	74.c	37.c	$3$	$2$	$1$	$0.591$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-2$	$1$	$0$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-2\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$

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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.