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 52 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
1.4.A.1.1a	$1$	$4$	$10$	$\mathrm{USp}(4)$	$\mathrm{USp}(4)$	$C_1$	$1$	$0$	$1$	$0$	$1$	$0$	$3$	$0$	$14$	$0$	$84$
1.4.B.1.1a	$1$	$4$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)$	$G_{3,3}$	$C_1$	$1$	$0$	$1$	$0$	$2$	$0$	$10$	$0$	$70$	$0$	$588$
1.4.B.2.1a	$1$	$4$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)$	$N(G_{3,3})$	$C_2$	$2$	$1/2$	$1$	$0$	$1$	$0$	$5$	$0$	$35$	$0$	$294$
1.4.C.1.1a	$1$	$4$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)$	$G_{1,3}$	$C_1$	$1$	$0$	$1$	$0$	$3$	$0$	$20$	$0$	$175$	$0$	$1764$
1.4.C.2.1a	$1$	$4$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)$	$N(G_{1,3})$	$C_2$	$2$	$0$	$1$	$0$	$2$	$0$	$11$	$0$	$90$	$0$	$889$
1.4.D.1.1a	$1$	$4$	$2$	$\mathrm{U}(1)\times\mathrm{U}(1)$	$F$	$C_1$	$1$	$0$	$1$	$0$	$4$	$0$	$36$	$0$	$400$	$0$	$4900$
1.4.D.2.1a	$1$	$4$	$2$	$\mathrm{U}(1)\times\mathrm{U}(1)$	$F_{ab}$	$C_2$	$2$	$1/2$	$1$	$0$	$2$	$0$	$18$	$0$	$200$	$0$	$2450$
1.4.D.2.1b	$1$	$4$	$2$	$\mathrm{U}(1)\times\mathrm{U}(1)$	$F_a$	$C_2$	$2$	$0$	$1$	$0$	$3$	$0$	$21$	$0$	$210$	$0$	$2485$
1.4.D.4.1a	$1$	$4$	$2$	$\mathrm{U}(1)\times\mathrm{U}(1)$	$F_{ac}$	$C_4$	$4$	$3/4$	$1$	$0$	$1$	$0$	$9$	$0$	$100$	$0$	$1225$
1.4.D.4.2a	$1$	$4$	$2$	$\mathrm{U}(1)\times\mathrm{U}(1)$	$F_{a,b}$	$C_2^2$	$4$	$1/4$	$1$	$0$	$2$	$0$	$12$	$0$	$110$	$0$	$1260$
1.4.E.1.1a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$E_1$	$C_1$	$1$	$0$	$1$	$0$	$4$	$0$	$32$	$0$	$320$	$0$	$3584$
1.4.E.2.1a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$E_2$	$C_2$	$2$	$1/2$	$1$	$0$	$2$	$0$	$16$	$0$	$160$	$0$	$1792$
1.4.E.2.1b	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$J(E_1)$	$C_2$	$2$	$1/2$	$1$	$0$	$2$	$0$	$16$	$0$	$160$	$0$	$1792$
1.4.E.3.1a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$E_3$	$C_3$	$3$	$0$	$1$	$0$	$2$	$0$	$12$	$0$	$110$	$0$	$1204$
1.4.E.4.1a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$E_4$	$C_4$	$4$	$1/4$	$1$	$0$	$2$	$0$	$12$	$0$	$100$	$0$	$1008$
1.4.E.4.2a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$J(E_2)$	$C_2^2$	$4$	$3/4$	$1$	$0$	$1$	$0$	$8$	$0$	$80$	$0$	$896$
1.4.E.6.1a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$J(E_3)$	$S_3$	$6$	$1/2$	$1$	$0$	$1$	$0$	$6$	$0$	$55$	$0$	$602$
1.4.E.6.2a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$E_6$	$C_6$	$6$	$1/6$	$1$	$0$	$2$	$0$	$12$	$0$	$100$	$0$	$980$
1.4.E.8.3a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$J(E_4)$	$D_4$	$8$	$5/8$	$1$	$0$	$1$	$0$	$6$	$0$	$50$	$0$	$504$
1.4.E.12.4a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$J(E_6)$	$D_6$	$12$	$7/12$	$1$	$0$	$1$	$0$	$6$	$0$	$50$	$0$	$490$
1.4.F.1.1a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_1$	$C_1$	$1$	$0$	$1$	$0$	$8$	$0$	$96$	$0$	$1280$	$0$	$17920$
1.4.F.2.1a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(C_1)$	$C_2$	$2$	$1/2$	$1$	$0$	$4$	$0$	$48$	$0$	$640$	$0$	$8960$
1.4.F.2.1b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_2$	$C_2$	$2$	$1/2$	$1$	$0$	$4$	$0$	$48$	$0$	$640$	$0$	$8960$
1.4.F.2.1c	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_{2,1}$	$C_2$	$2$	$1/2$	$1$	$0$	$4$	$0$	$48$	$0$	$640$	$0$	$8960$
1.4.F.3.1a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_3$	$C_3$	$3$	$0$	$1$	$0$	$4$	$0$	$36$	$0$	$440$	$0$	$6020$
1.4.F.4.1a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_{4,1}$	$C_4$	$4$	$3/4$	$1$	$0$	$2$	$0$	$24$	$0$	$320$	$0$	$4480$
1.4.F.4.1b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_4$	$C_4$	$4$	$1/4$	$1$	$0$	$4$	$0$	$36$	$0$	$400$	$0$	$5040$
1.4.F.4.2a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_2$	$C_2^2$	$4$	$3/4$	$1$	$0$	$2$	$0$	$24$	$0$	$320$	$0$	$4480$
1.4.F.4.2b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(C_2)$	$C_2^2$	$4$	$3/4$	$1$	$0$	$2$	$0$	$24$	$0$	$320$	$0$	$4480$
1.4.F.4.2c	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{2,1}$	$C_2^2$	$4$	$3/4$	$1$	$0$	$2$	$0$	$24$	$0$	$320$	$0$	$4480$
1.4.F.6.1a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_3$	$S_3$	$6$	$1/2$	$1$	$0$	$2$	$0$	$18$	$0$	$220$	$0$	$3010$
1.4.F.6.1b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{3,2}$	$S_3$	$6$	$1/2$	$1$	$0$	$2$	$0$	$18$	$0$	$220$	$0$	$3010$
1.4.F.6.2a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(C_3)$	$C_6$	$6$	$1/2$	$1$	$0$	$2$	$0$	$18$	$0$	$220$	$0$	$3010$
1.4.F.6.2b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_{6,1}$	$C_6$	$6$	$1/2$	$1$	$0$	$2$	$0$	$18$	$0$	$220$	$0$	$3010$
1.4.F.6.2c	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_6$	$C_6$	$6$	$1/6$	$1$	$0$	$4$	$0$	$36$	$0$	$400$	$0$	$4900$
1.4.F.8.2a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(C_4)$	$C_2\times C_4$	$8$	$5/8$	$1$	$0$	$2$	$0$	$18$	$0$	$200$	$0$	$2520$
1.4.F.8.3a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{4,1}$	$D_4$	$8$	$7/8$	$1$	$0$	$1$	$0$	$12$	$0$	$160$	$0$	$2240$
1.4.F.8.3b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_4$	$D_4$	$8$	$5/8$	$1$	$0$	$2$	$0$	$18$	$0$	$200$	$0$	$2520$
1.4.F.8.3c	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{4,2}$	$D_4$	$8$	$5/8$	$1$	$0$	$2$	$0$	$18$	$0$	$200$	$0$	$2520$
1.4.F.8.5a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(D_2)$	$C_2^3$	$8$	$7/8$	$1$	$0$	$1$	$0$	$12$	$0$	$160$	$0$	$2240$
1.4.F.12.3a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$T$	$A_4$	$12$	$1/4$	$1$	$0$	$2$	$0$	$12$	$0$	$120$	$0$	$1540$
1.4.F.12.4a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(D_3)$	$D_6$	$12$	$3/4$	$1$	$0$	$1$	$0$	$9$	$0$	$110$	$0$	$1505$
1.4.F.12.4b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{6,1}$	$D_6$	$12$	$3/4$	$1$	$0$	$1$	$0$	$9$	$0$	$110$	$0$	$1505$
1.4.F.12.4c	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_6$	$D_6$	$12$	$7/12$	$1$	$0$	$2$	$0$	$18$	$0$	$200$	$0$	$2450$
1.4.F.12.4d	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{6,2}$	$D_6$	$12$	$7/12$	$1$	$0$	$2$	$0$	$18$	$0$	$200$	$0$	$2450$
1.4.F.12.5a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(C_6)$	$C_2\times C_6$	$12$	$7/12$	$1$	$0$	$2$	$0$	$18$	$0$	$200$	$0$	$2450$
1.4.F.16.11a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(D_4)$	$C_2\times D_4$	$16$	$13/16$	$1$	$0$	$1$	$0$	$9$	$0$	$100$	$0$	$1260$
1.4.F.24.12a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$O_1$	$S_4$	$24$	$5/8$	$1$	$0$	$1$	$0$	$6$	$0$	$60$	$0$	$770$
1.4.F.24.12b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$O$	$S_4$	$24$	$3/8$	$1$	$0$	$2$	$0$	$12$	$0$	$100$	$0$	$1050$
1.4.F.24.13a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(T)$	$C_2\times A_4$	$24$	$5/8$	$1$	$0$	$1$	$0$	$6$	$0$	$60$	$0$	$770$