Sato-Tate group search results

Weight	Degree	Include irrational	$\mathrm{ST}^0$	Maximal
Components	Component group	$\mathrm{Pr}[a_1=0]$	Second trace moment	Fourth trace moment
First $a_2$ moment

Results (1-50 of 410 matches)

Label	Wt	Deg	$\mathrm{dim}_{\mathbb{R}}$	$\mathrm{G}^0$	Name	$\mathrm{G}/\mathrm{G}^0$	$\#\mathrm{G}/\mathrm{G^0}$	$\mathrm{Pr}[t\!=\!0]$	Trace moments
1.6.A.1.1a	$1$	$6$	$21$	$\mathrm{USp}(6)$	$\mathrm{USp}(6)$	$C_1$	$1$	$0$	$1$	$0$	$1$	$0$	$3$	$0$	$15$	$0$	$104$
1.6.B.1.1a	$1$	$6$	$9$	$\mathrm{U}(3)$	$\mathrm{U}(3)$	$C_1$	$1$	$0$	$1$	$0$	$2$	$0$	$12$	$0$	$120$	$0$	$1610$
1.6.B.2.1a	$1$	$6$	$9$	$\mathrm{U}(3)$	$N(\mathrm{U}(3))$	$C_2$	$2$	$1/2$	$1$	$0$	$1$	$0$	$6$	$0$	$60$	$0$	$805$
1.6.C.1.1a	$1$	$6$	$13$	$\mathrm{SU}(2)\times\mathrm{USp}(4)$	$\mathrm{SU}(2)\times \mathrm{USp}(4)$	$C_1$	$1$	$0$	$1$	$0$	$2$	$0$	$11$	$0$	$94$	$0$	$1050$
1.6.D.1.1a	$1$	$6$	$11$	$\mathrm{U}(1)\times\mathrm{USp}(4)$	$\mathrm{U}(1)\times \mathrm{USp}(4)$	$C_1$	$1$	$0$	$1$	$0$	$3$	$0$	$21$	$0$	$214$	$0$	$2758$
1.6.D.2.1a	$1$	$6$	$11$	$\mathrm{U}(1)\times\mathrm{USp}(4)$	$N(\mathrm{U}(1)\times \mathrm{USp}(4))$	$C_2$	$2$	$0$	$1$	$0$	$2$	$0$	$12$	$0$	$114$	$0$	$1421$
1.6.E.1.1a	$1$	$6$	$9$	$\mathrm{SU}(2)^3$	$E$	$C_1$	$1$	$0$	$1$	$0$	$3$	$0$	$24$	$0$	$285$	$0$	$4242$
1.6.E.2.1a	$1$	$6$	$9$	$\mathrm{SU}(2)^3$	$E_{t}$	$C_2$	$2$	$0$	$1$	$0$	$2$	$0$	$13$	$0$	$145$	$0$	$2128$
1.6.E.3.1a	$1$	$6$	$9$	$\mathrm{SU}(2)^3$	$E_{s}$	$C_3$	$3$	$2/3$	$1$	$0$	$1$	$0$	$8$	$0$	$95$	$0$	$1414$
1.6.E.6.1a	$1$	$6$	$9$	$\mathrm{SU}(2)^3$	$E_{s,t}$	$S_3$	$6$	$1/3$	$1$	$0$	$1$	$0$	$5$	$0$	$50$	$0$	$714$
1.6.F.1.1a	$1$	$6$	$7$	$\mathrm{U}(1)\times\mathrm{SU}(2)^2$	$F$	$C_1$	$1$	$0$	$1$	$0$	$4$	$0$	$40$	$0$	$570$	$0$	$9898$
1.6.F.2.1a	$1$	$6$	$7$	$\mathrm{U}(1)\times\mathrm{SU}(2)^2$	$F_{at}$	$C_2$	$2$	$1/2$	$1$	$0$	$2$	$0$	$20$	$0$	$285$	$0$	$4949$
1.6.F.2.1b	$1$	$6$	$7$	$\mathrm{U}(1)\times\mathrm{SU}(2)^2$	$F_{t}$	$C_2$	$2$	$0$	$1$	$0$	$3$	$0$	$23$	$0$	$295$	$0$	$4984$
1.6.F.2.1c	$1$	$6$	$7$	$\mathrm{U}(1)\times\mathrm{SU}(2)^2$	$F_{a}$	$C_2$	$2$	$0$	$1$	$0$	$3$	$0$	$25$	$0$	$320$	$0$	$5243$
1.6.F.4.2a	$1$	$6$	$7$	$\mathrm{U}(1)\times\mathrm{SU}(2)^2$	$F_{a,t}$	$C_2^2$	$4$	$1/4$	$1$	$0$	$2$	$0$	$14$	$0$	$165$	$0$	$2639$
1.6.G.1.1a	$1$	$6$	$5$	$\mathrm{U}(1)^2\times\mathrm{SU}(2)$	$F\times \mathrm{SU}(2)$	$C_1$	$1$	$0$	$1$	$0$	$5$	$0$	$62$	$0$	$1065$	$0$	$21714$
1.6.G.2.1a	$1$	$6$	$5$	$\mathrm{U}(1)^2\times\mathrm{SU}(2)$	$F_{ab}\times \mathrm{SU}(2)$	$C_2$	$2$	$0$	$1$	$0$	$3$	$0$	$32$	$0$	$535$	$0$	$10864$
1.6.G.2.1b	$1$	$6$	$5$	$\mathrm{U}(1)^2\times\mathrm{SU}(2)$	$F_{a}\times \mathrm{SU}(2)$	$C_2$	$2$	$0$	$1$	$0$	$4$	$0$	$41$	$0$	$620$	$0$	$11739$
1.6.G.4.1a	$1$	$6$	$5$	$\mathrm{U}(1)^2\times\mathrm{SU}(2)$	$F_{ac}\times \mathrm{SU}(2)$	$C_4$	$4$	$0$	$1$	$0$	$2$	$0$	$17$	$0$	$270$	$0$	$5439$
1.6.G.4.2a	$1$	$6$	$5$	$\mathrm{U}(1)^2\times\mathrm{SU}(2)$	$F_{a,b}\times \mathrm{SU}(2)$	$C_2^2$	$4$	$0$	$1$	$0$	$3$	$0$	$26$	$0$	$355$	$0$	$6314$
1.6.H.1.1a	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H$	$C_1$	$1$	$0$	$1$	$0$	$6$	$0$	$90$	$0$	$1860$	$0$	$44730$
1.6.H.2.1a	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{abc}$	$C_2$	$2$	$1/2$	$1$	$0$	$3$	$0$	$45$	$0$	$930$	$0$	$22365$
1.6.H.2.1b	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{ab}$	$C_2$	$2$	$0$	$1$	$0$	$4$	$0$	$48$	$0$	$940$	$0$	$22400$
1.6.H.2.1c	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{a}$	$C_2$	$2$	$0$	$1$	$0$	$5$	$0$	$63$	$0$	$1130$	$0$	$24815$
1.6.H.3.1a	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{s}$	$C_3$	$3$	$2/3$	$1$	$0$	$2$	$0$	$30$	$0$	$620$	$0$	$14910$
1.6.H.4.1a	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{act}$	$C_4$	$4$	$1/2$	$1$	$0$	$2$	$0$	$24$	$0$	$470$	$0$	$11200$
1.6.H.4.1b	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{at}$	$C_4$	$4$	$0$	$1$	$0$	$3$	$0$	$27$	$0$	$480$	$0$	$11235$
1.6.H.4.2a	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{ab,bc}$	$C_2^2$	$4$	$0$	$1$	$0$	$3$	$0$	$27$	$0$	$480$	$0$	$11235$
1.6.H.4.2b	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{a,bc}$	$C_2^2$	$4$	$1/4$	$1$	$0$	$3$	$0$	$33$	$0$	$570$	$0$	$12425$
1.6.H.4.2c	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{a,b}$	$C_2^2$	$4$	$0$	$1$	$0$	$4$	$0$	$42$	$0$	$670$	$0$	$13650$
1.6.H.6.2a	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{abc,s}$	$C_6$	$6$	$5/6$	$1$	$0$	$1$	$0$	$15$	$0$	$310$	$0$	$7455$
1.6.H.8.2a	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{c,at}$	$C_2\times C_4$	$8$	$3/8$	$1$	$0$	$2$	$0$	$18$	$0$	$290$	$0$	$6230$
1.6.H.8.5a	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{a,b,c}$	$C_2^3$	$8$	$1/8$	$1$	$0$	$3$	$0$	$27$	$0$	$390$	$0$	$7455$
1.6.I.1.1a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times E_1$	$C_1$	$1$	$0$	$1$	$0$	$5$	$0$	$58$	$0$	$925$	$0$	$17598$
1.6.I.2.1a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times E_2$	$C_2$	$2$	$0$	$1$	$0$	$3$	$0$	$30$	$0$	$465$	$0$	$8806$
1.6.I.2.1b	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times J(E_1)$	$C_2$	$2$	$0$	$1$	$0$	$3$	$0$	$30$	$0$	$465$	$0$	$8806$
1.6.I.3.1a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times E_3$	$C_3$	$3$	$0$	$1$	$0$	$3$	$0$	$26$	$0$	$355$	$0$	$6258$
1.6.I.4.1a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times E_4$	$C_4$	$4$	$0$	$1$	$0$	$3$	$0$	$26$	$0$	$345$	$0$	$5782$
1.6.I.4.2a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times J(E_2)$	$C_2^2$	$4$	$0$	$1$	$0$	$2$	$0$	$16$	$0$	$235$	$0$	$4410$
1.6.I.6.1a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times J(E_3)$	$S_3$	$6$	$0$	$1$	$0$	$2$	$0$	$14$	$0$	$180$	$0$	$3136$
1.6.I.6.2a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times E_6$	$C_6$	$6$	$0$	$1$	$0$	$3$	$0$	$26$	$0$	$345$	$0$	$5754$
1.6.I.8.3a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times J(E_4)$	$D_4$	$8$	$0$	$1$	$0$	$2$	$0$	$14$	$0$	$175$	$0$	$2898$
1.6.I.12.4a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times J(E_6)$	$D_6$	$12$	$0$	$1$	$0$	$2$	$0$	$14$	$0$	$175$	$0$	$2884$
1.6.J.1.1a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_1(E_1)$	$C_1$	$1$	$0$	$1$	$0$	$6$	$0$	$86$	$0$	$1660$	$0$	$37254$
1.6.J.2.1a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J(E_2,E_1)$	$C_2$	$2$	$1/2$	$1$	$0$	$3$	$0$	$43$	$0$	$830$	$0$	$18627$
1.6.J.2.1b	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_1(E_2)$	$C_2$	$2$	$0$	$1$	$0$	$4$	$0$	$46$	$0$	$840$	$0$	$18662$
1.6.J.2.1c	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J(J(E_1),E_1)$	$C_2$	$2$	$1/2$	$1$	$0$	$3$	$0$	$43$	$0$	$830$	$0$	$18627$
1.6.J.2.1d	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_1(J(E_1))$	$C_2$	$2$	$0$	$1$	$0$	$4$	$0$	$46$	$0$	$840$	$0$	$18662$
1.6.J.2.1e	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_2(E_1)$	$C_2$	$2$	$0$	$1$	$0$	$5$	$0$	$59$	$0$	$990$	$0$	$20419$
1.6.J.3.1a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_1(E_3)$	$C_3$	$3$	$0$	$1$	$0$	$4$	$0$	$42$	$0$	$670$	$0$	$13594$