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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 1286 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
77.1.j.a	$77$	$1$	77.j	77.j	$10$	$4$	$1$	$0.038$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$		$1$		$q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
88.1.l.a	$88$	$1$	88.l	88.l	$10$	$4$	$1$	$0.044$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$		$1$		$q-\zeta_{10}q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}+\zeta_{10}^{2}q^{4}+\cdots$
93.1.l.a	$93$	$1$	93.l	93.l	$10$	$4$	$1$	$0.046$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$		$1$		$q-\zeta_{10}q^{3}-\zeta_{10}^{3}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots$
100.1.j.a	$100$	$1$	100.j	100.j	$10$	$4$	$1$	$0.050$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-1$	$0$		$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{5}+\zeta_{10}^{4}q^{8}+\cdots$
17.2.d.a	$17$	$2$	17.d	17.d	$8$	$4$	$1$	$0.136$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$-4$	$-4$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots$
22.2.c.a	$22$	$2$	22.c	11.c	$5$	$4$	$1$	$0.176$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$-1$	$-4$	$-6$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots$
25.2.d.a	$25$	$2$	25.d	25.d	$5$	$4$	$1$	$0.200$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$-2$	$-1$	$-5$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots$
28.2.f.a	$28$	$2$	28.f	28.f	$6$	$4$	$2$	$0.224$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$-2$	$0$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}+\cdots)q^{3}+\cdots$
30.2.e.a	$30$	$2$	30.e	15.e	$4$	$4$	$2$	$0.240$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
31.2.c.a	$31$	$2$	31.c	31.c	$3$	$4$	$2$	$0.248$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$-4$	$2$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+\cdots$
31.2.d.a	$31$	$2$	31.d	31.d	$5$	$4$	$1$	$0.248$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$-3$	$1$	$-6$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\zeta_{10}^{2})q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
32.2.g.a	$32$	$2$	32.g	32.g	$8$	$4$	$1$	$0.256$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+(\zeta_{8}+\zeta_{8}^{2})q^{3}+\cdots$
33.2.e.a	$33$	$2$	33.e	11.c	$5$	$4$	$1$	$0.264$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$-3$	$-1$	$-1$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(\zeta_{10}+\cdots)q^{4}+\cdots$
33.2.e.b	$33$	$2$	33.e	11.c	$5$	$4$	$1$	$0.264$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$-1$	$1$	$-3$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+2\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{3}q^{3}+\cdots$
34.2.d.a	$34$	$2$	34.d	17.d	$8$	$4$	$1$	$0.271$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+\zeta_{8}^{3}q^{2}+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$
35.2.e.a	$35$	$2$	35.e	7.c	$3$	$4$	$2$	$0.279$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$-2$	$-2$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots$
35.2.f.a	$35$	$2$	35.f	35.f	$4$	$4$	$2$	$0.279$	$\Q(i, \sqrt{10})$	$_{}$	None	None		$4$	$0$	$-4$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}-\beta _{1}q^{5}+(-\beta _{1}+\cdots)q^{6}+\cdots$
35.2.j.a	$35$	$2$	35.j	35.j	$6$	$4$	$2$	$0.279$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots$
35.2.k.a	$35$	$2$	35.k	35.k	$12$	$4$	$1$	$0.279$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$-4$	$-2$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-1+\zeta_{12})q^{2}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots$
35.2.k.b	$35$	$2$	35.k	35.k	$12$	$4$	$1$	$0.279$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$2$	$-4$	$4$	$-10$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(1-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}+\cdots)q^{3}+\cdots$
37.2.e.a	$37$	$2$	37.e	37.e	$6$	$4$	$2$	$0.295$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$2$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots$
11.3.d.a	$11$	$3$	11.d	11.d	$10$	$4$	$1$	$0.300$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$-5$	$0$	$-4$	$10$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-2\zeta_{10}+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-2+\cdots)q^{3}+\cdots$
38.2.c.b	$38$	$2$	38.c	19.c	$3$	$4$	$2$	$0.303$	$\Q(\sqrt{-3}, \sqrt{7})$	$_{}$	None	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.b	$39$	$2$	39.e	13.c	$3$	$4$	$2$	$0.311$	$\Q(\sqrt{-3}, \sqrt{17})$	$_{}$	None	None		$2$	$0$	$-1$	$-2$	$-6$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}-\beta _{2}q^{3}+(-2+\beta _{1}+2\beta _{2}+\cdots)q^{4}+\cdots$
39.2.f.a	$39$	$2$	39.f	39.f	$4$	$4$	$2$	$0.311$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+(-1+\zeta_{8}+\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$
39.2.k.a	$39$	$2$	39.k	39.k	$12$	$4$	$1$	$0.311$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-10$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+2\zeta_{12}q^{4}+(-2+\cdots)q^{7}+\cdots$
40.2.d.a	$40$	$2$	40.d	8.b	$2$	$4$	$4$	$0.319$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}+\cdots)q^{3}+\cdots$
40.2.f.a	$40$	$2$	40.f	40.f	$2$	$4$	$4$	$0.319$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1+\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
42.2.d.a	$42$	$2$	42.d	21.c	$2$	$4$	$4$	$0.335$	$\Q(i, \sqrt{6})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$
42.2.f.a	$42$	$2$	42.f	21.g	$6$	$4$	$2$	$0.335$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-10$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
43.2.c.b	$43$	$2$	43.c	43.c	$3$	$4$	$2$	$0.343$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$-6$	$3$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2-\beta _{2})q^{2}+(1+\beta _{1}+\beta _{3})q^{3}+\cdots$
44.2.c.a	$44$	$2$	44.c	44.c	$2$	$4$	$4$	$0.351$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-1+\beta _{2})q^{4}-q^{5}+\cdots$
44.2.e.a	$44$	$2$	44.e	11.c	$5$	$4$	$1$	$0.351$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$-1$	$3$	$-7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}+2\zeta_{10}^{3})q^{3}+(1-\zeta_{10}^{3})q^{5}+\cdots$
13.3.d.a	$13$	$3$	13.d	13.d	$4$	$4$	$2$	$0.354$	$\Q(i, \sqrt{10})$	$_{}$	None	None		$2$	$0$	$-4$	$-4$	$8$	$-12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+\cdots$
13.3.f.a	$13$	$3$	13.f	13.f	$12$	$4$	$1$	$0.354$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$-2$	$-2$	$-14$	$16$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-1+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots$
45.2.f.a	$45$	$2$	45.f	15.e	$4$	$4$	$2$	$0.359$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}+(-\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots$
47.2.a.a	$47$	$2$	47.a	1.a	$1$	$4$	$4$	$0.375$	4.4.1957.1	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
14.3.d.a	$14$	$3$	14.d	7.d	$6$	$4$	$2$	$0.381$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$0$	$-6$	$-6$	$8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-2-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\cdots$
50.2.d.a	$50$	$2$	50.d	25.d	$5$	$4$	$1$	$0.399$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$1$	$-1$	$5$	$-12$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-1+\cdots)q^{3}+\cdots$
15.3.f.a	$15$	$3$	15.f	5.c	$4$	$4$	$2$	$0.409$	$\Q(i, \sqrt{6})$	$_{}$	None	None		$2$	$0$	$-4$	$0$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{3}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots$
52.2.l.a	$52$	$2$	52.l	52.l	$12$	$4$	$1$	$0.415$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$6$	$0$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots$
53.2.b.a	$53$	$2$	53.b	53.b	$2$	$4$	$4$	$0.423$	4.0.7168.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
55.2.b.a	$55$	$2$	55.b	5.b	$2$	$4$	$4$	$0.439$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-3$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(\beta _{1}-\beta _{3})q^{3}+\cdots$
55.2.e.a	$55$	$2$	55.e	55.e	$4$	$4$	$2$	$0.439$	$\Q(i, \sqrt{10})$	$_{}$	None	None		$4$	$0$	$0$	$-4$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+3\beta _{2}q^{4}+\cdots$
55.2.e.b	$55$	$2$	55.e	55.e	$4$	$4$	$2$	$0.439$	$\Q(i, \sqrt{11})$	$_{}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-1+\beta _{1}-\beta _{3})q^{3}+2\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
56.2.b.b	$56$	$2$	56.b	8.b	$2$	$4$	$4$	$0.447$	4.0.2312.1	$_{}$	None	None		$2$	$0$	$-1$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
56.2.e.b	$56$	$2$	56.e	56.e	$2$	$4$	$4$	$0.447$	$\Q(i, \sqrt{6})$	$_{}$	None	None		$4$	$0$	$-4$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}-2\beta _{1}q^{4}+\cdots$
57.2.d.a	$57$	$2$	57.d	57.d	$2$	$4$	$4$	$0.455$	$\Q(\sqrt{2}, \sqrt{-5})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-\beta _{1}q^{3}+\beta _{3}q^{5}+(-1-\beta _{3})q^{6}+\cdots$
60.2.h.a	$60$	$2$	60.h	60.h	$2$	$4$	$4$	$0.479$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{2}-\beta _{1}q^{3}-2q^{4}-\beta _{3}q^{5}+(-1+\cdots)q^{6}+\cdots$
60.2.h.b	$60$	$2$	60.h	60.h	$2$	$4$	$4$	$0.479$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+\beta _{3}q^{4}+\cdots$

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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.