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Results (1-50 of 1955 matches)

 

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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
47.1.b.a	$47$	$1$	47.b	47.b	$2$	$2$	$2$	$0.023$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-47}) \)	None	✓	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(-1\)		$1$		\(q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots\)
52.1.j.a	$52$	$1$	52.j	52.j	$6$	$2$	$1$	$0.026$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(-2\)	\(0\)		$1$		\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots\)
57.1.h.a	$57$	$1$	57.h	57.h	$6$	$2$	$1$	$0.028$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)		$1$		\(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{7}-\zeta_{6}q^{9}+q^{12}+\cdots\)
68.1.f.a	$68$	$1$	68.f	68.f	$4$	$2$	$1$	$0.034$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$1$		\(q+iq^{2}-q^{4}+(-1-i)q^{5}-iq^{8}+\cdots\)
72.1.p.a	$72$	$1$	72.p	72.p	$6$	$2$	$1$	$0.036$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(-1\)	\(-1\)	\(0\)	\(0\)		$1$		\(q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots\)
79.1.b.a	$79$	$1$	79.b	79.b	$2$	$2$	$2$	$0.039$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-79}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(0\)		$1$		\(q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{5}-q^{8}+\cdots\)
84.1.p.a	$84$	$1$	84.p	21.h	$6$	$2$	$1$	$0.042$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$1$		\(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}-q^{13}+\cdots\)
95.1.d.b	$95$	$1$	95.d	95.d	$2$	$2$	$2$	$0.047$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-95}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$1$		\(q-\beta q^{2}+\beta q^{3}+q^{4}-q^{5}-2q^{6}+q^{9}+\cdots\)
99.1.h.a	$99$	$1$	99.h	99.h	$6$	$2$	$1$	$0.049$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$1$		\(q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+\cdots\)
13.2.e.a	$13$	$2$	13.e	13.e	$6$	$2$	$1$	$0.104$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(-3\)	\(-2\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
16.2.e.a	$16$	$2$	16.e	16.e	$4$	$2$	$1$	$0.128$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-i)q^{2}+(-1+i)q^{3}+2iq^{4}+\cdots\)
18.2.c.a	$18$	$2$	18.c	9.c	$3$	$2$	$1$	$0.144$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(-1\)	\(-3\)	\(0\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
20.2.e.a	$20$	$2$	20.e	20.e	$4$	$2$	$1$	$0.160$	\(\Q(\sqrt{-1}) \)	$_{}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(-2\)	\(0\)	\(-4\)	\(0\)		$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-1-i)q^{2}+2iq^{4}+(-2+i)q^{5}+\cdots\)
21.2.e.a	$21$	$2$	21.e	7.c	$3$	$2$	$1$	$0.168$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(-2\)	\(-1\)	\(2\)	\(-5\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{2}-\zeta_{6}q^{3}-2\zeta_{6}q^{4}+\cdots\)
21.2.g.a	$21$	$2$	21.g	21.g	$6$	$2$	$1$	$0.168$	\(\Q(\sqrt{-3}) \)	$_{}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(-3\)	\(0\)	\(1\)		$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(2+\cdots)q^{7}+\cdots\)
23.2.a.a	$23$	$2$	23.a	1.a	$1$	$2$	$2$	$0.184$	\(\Q(\sqrt{5}) \)	$_{}$	None	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
24.2.d.a	$24$	$2$	24.d	8.b	$2$	$2$	$2$	$0.192$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+i)q^{2}+iq^{3}-2iq^{4}-2iq^{5}+\cdots\)
24.2.f.a	$24$	$2$	24.f	24.f	$2$	$2$	$2$	$0.192$	\(\Q(\sqrt{-2}) \)	$_{}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}+(-1-\beta )q^{3}-2q^{4}+(2-\beta )q^{6}+\cdots\)
26.2.b.a	$26$	$2$	26.b	13.b	$2$	$2$	$2$	$0.208$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{3}-q^{4}-3iq^{5}-iq^{6}+\cdots\)
26.2.c.a	$26$	$2$	26.c	13.c	$3$	$2$	$1$	$0.208$	\(\Q(\sqrt{-3}) \)	$_{}$	None	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.d.a	$28$	$2$	28.d	28.d	$2$	$2$	$2$	$0.224$	\(\Q(\sqrt{-7}) \)	$_{}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{2}+(-2+\beta )q^{4}+(-1+2\beta )q^{7}+\cdots\)
28.2.e.a	$28$	$2$	28.e	7.c	$3$	$2$	$1$	$0.224$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(-1\)	\(-3\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{3}+(-3+3\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
29.2.a.a	$29$	$2$	29.a	1.a	$1$	$2$	$2$	$0.232$	\(\Q(\sqrt{2}) \)	$_{}$	None	None	✓	$1$	$0$	\(-2\)	\(2\)	\(-2\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)
29.2.b.a	$29$	$2$	29.b	29.b	$2$	$2$	$2$	$0.232$	\(\Q(\sqrt{-5}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-\beta q^{3}-3q^{4}-3q^{5}+5q^{6}+\cdots\)
30.2.c.a	$30$	$2$	30.c	5.b	$2$	$2$	$2$	$0.240$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}-q^{4}+(-2+i)q^{5}+\cdots\)
31.2.a.a	$31$	$2$	31.a	1.a	$1$	$2$	$2$	$0.248$	\(\Q(\sqrt{5}) \)	$_{}$	None	None	✓	$1$	$0$	\(1\)	\(-2\)	\(2\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-2\beta q^{3}+(-1+\beta )q^{4}+q^{5}+\cdots\)
33.2.d.a	$33$	$2$	33.d	33.d	$2$	$2$	$2$	$0.264$	\(\Q(\sqrt{-11}) \)	$_{}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{3}-2q^{4}+(1-2\beta )q^{5}+(-3+\beta )q^{9}+\cdots\)
34.2.b.a	$34$	$2$	34.b	17.b	$2$	$2$	$2$	$0.271$	\(\Q(\sqrt{-2}) \)	$_{}$	None	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}-q^{8}+\cdots\)
34.2.c.a	$34$	$2$	34.c	17.c	$4$	$2$	$1$	$0.271$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(-2\)	\(4\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-iq^{2}+(-1-i)q^{3}-q^{4}+(2+2i)q^{5}+\cdots\)
34.2.c.b	$34$	$2$	34.c	17.c	$4$	$2$	$1$	$0.271$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+iq^{2}-q^{4}+(-1-i)q^{5}-iq^{8}+\cdots\)
35.2.a.b	$35$	$2$	35.a	1.a	$1$	$2$	$2$	$0.279$	\(\Q(\sqrt{17}) \)	$_{}$	None	None	✓	$1$	$0$	\(-1\)	\(-1\)	\(2\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{3}+(2+\beta )q^{4}+q^{5}+\cdots\)
35.2.b.a	$35$	$2$	35.b	5.b	$2$	$2$	$2$	$0.279$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-iq^{3}-2q^{4}+(-2-i)q^{5}+\cdots\)
36.2.b.a	$36$	$2$	36.b	12.b	$2$	$2$	$2$	$0.287$	\(\Q(\sqrt{-2}) \)	$_{}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}-2q^{4}-\beta q^{5}-2\beta q^{8}+2q^{10}+\cdots\)
36.2.e.a	$36$	$2$	36.e	9.c	$3$	$2$	$1$	$0.287$	\(\Q(\sqrt{-3}) \)	$_{}$	None	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.b.a	$37$	$2$	37.b	37.b	$2$	$2$	$2$	$0.295$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(6\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-q^{3}-2q^{4}-2iq^{5}-2iq^{6}+\cdots\)
37.2.c.a	$37$	$2$	37.c	37.c	$3$	$2$	$1$	$0.295$	\(\Q(\sqrt{-3}) \)	$_{}$	None	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	None		$2$	$0$	\(1\)	\(-1\)	\(0\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
39.2.a.b	$39$	$2$	39.a	1.a	$1$	$2$	$2$	$0.311$	\(\Q(\sqrt{2}) \)	$_{}$	None	None	✓	$1$	$0$	\(-2\)	\(2\)	\(0\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}-2\beta q^{5}+\cdots\)
39.2.b.a	$39$	$2$	39.b	13.b	$2$	$2$	$2$	$0.311$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{2}-q^{3}-q^{4}+\zeta_{6}q^{6}+2\zeta_{6}q^{7}+\cdots\)
39.2.e.a	$39$	$2$	39.e	13.c	$3$	$2$	$1$	$0.311$	\(\Q(\sqrt{-3}) \)	$_{}$	None	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.j.a	$39$	$2$	39.j	13.e	$6$	$2$	$1$	$0.311$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(1\)	\(0\)	\(-3\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+(-2+4\zeta_{6})q^{5}+\cdots\)
40.2.c.a	$40$	$2$	40.c	5.b	$2$	$2$	$2$	$0.319$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(-1-i)q^{5}-iq^{7}-q^{9}+\cdots\)
12.3.d.a	$12$	$3$	12.d	4.b	$2$	$2$	$2$	$0.327$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(-2\)	\(0\)	\(-4\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
41.2.b.a	$41$	$2$	41.b	41.b	$2$	$2$	$2$	$0.327$	\(\Q(\sqrt{-2}) \)	$_{}$	None	None		$2$	$0$	\(-2\)	\(0\)	\(4\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta q^{3}-q^{4}+2q^{5}-\beta q^{6}-\beta q^{7}+\cdots\)
42.2.e.a	$42$	$2$	42.e	7.c	$3$	$2$	$1$	$0.335$	\(\Q(\sqrt{-3}) \)	$_{}$	None	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	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.a.b	$43$	$2$	43.a	1.a	$1$	$2$	$2$	$0.343$	\(\Q(\sqrt{2}) \)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-\beta q^{3}+(2-\beta )q^{5}-2q^{6}+(-2+\cdots)q^{7}+\cdots\)
43.2.c.a	$43$	$2$	43.c	43.c	$3$	$2$	$1$	$0.343$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(2\)	\(-1\)	\(1\)	\(-3\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(-1+\zeta_{6})q^{3}-q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
45.2.b.a	$45$	$2$	45.b	5.b	$2$	$2$	$2$	$0.359$	\(\Q(\sqrt{-5}) \)	$_{}$	\(\Q(\sqrt{-15}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}-3q^{4}-\beta q^{5}-\beta q^{8}+5q^{10}+\cdots\)
45.2.e.a	$45$	$2$	45.e	9.c	$3$	$2$	$1$	$0.359$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(-1\)	\(-3\)	\(1\)	\(3\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)