Sato-Tate group search results

Results (1-50 of 82 matches)

 

Label	Wt	Deg	$\mathrm{dim}_{\mathbb{R}}$	$\mathrm{G}^0$	Name	$\mathrm{G}/\mathrm{G}^0$	$\mathrm{Pr}[t\!=\!0]$	$\mathrm{E}[a_1^2]$	$\mathrm{E}[a_1^4]$	$\mathrm{E}[a_1^6]$	$\mathrm{E}[a_1^8]$	$\mathrm{E}[a_1^{10}]$	$\mathrm{E}[a_1^{12}]$	$\mathrm{E}[a_2]$	$\mathrm{E}[a_2^2]$	$\mathrm{E}[a_2^3]$	$\mathrm{E}[a_2^4]$	$\mathrm{E}[a_2^5]$	$\mathrm{E}[a_2^6]$	$\mathrm{E}[a_3^2]$	$\mathrm{E}[a_3^4]$	$\mathrm{E}[a_3^6]$	Maximal	Rational	Diagonal
1.4.A.1.1a	$1$	$4$	$10$	$\mathrm{USp}(4)$	$\mathrm{USp}(4)$	$1$	$0$	$1$	$3$	$14$	$84$	$594$	$594$	$1$	$2$	$4$	$10$	$27$	$82$				✓	✓	$[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]$
1.4.B.2.1a	$1$	$4$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)$	$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$	$2$	$1/2$	$1$	$5$	$35$	$294$	$2772$	$2772$	$1$	$3$	$7$	$23$	$76$	$287$				✓	✓	$[1, 1, 2, 2, 2, 3, 2, 4, 3, 4]$
1.4.D.4.1a	$1$	$4$	$2$	$\mathrm{U}(1)\times\mathrm{U}(1)$	$F_{ac}$	$4$	$3/4$	$1$	$9$	$100$	$1225$	$15876$	$15876$	$1$	$3$	$10$	$41$	$186$	$912$				✓	✓	$[1, 1, 2, 4, 6, 5, 7, 19, 20, 11]$
1.4.E.2.1a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$E_2$	$2$	$1/2$	$2$	$16$	$160$	$1792$	$21504$	$21504$	$1$	$6$	$17$	$78$	$322$	$1516$					✓	$[1, 2, 5, 6, 10, 14, 10, 29, 28, 30]$
1.4.E.3.1a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$E_3$	$3$	$0$	$2$	$12$	$110$	$1204$	$14364$	$14364$	$1$	$4$	$13$	$52$	$222$	$1014$					✓	$[1, 2, 3, 4, 8, 6, 8, 17, 20, 12]$
1.4.E.4.1a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$E_4$	$4$	$1/4$	$2$	$12$	$100$	$1008$	$11424$	$11424$	$1$	$4$	$11$	$46$	$182$	$824$					✓	$[1, 2, 3, 4, 6, 8, 6, 15, 16, 16]$
1.4.E.4.2a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$J(E_2)$	$4$	$3/4$	$1$	$8$	$80$	$896$	$10752$	$10752$	$1$	$4$	$10$	$42$	$166$	$768$					✓	$[1, 1, 3, 4, 5, 8, 5, 15, 14, 16]$
1.4.E.6.1a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$J(E_3)$	$6$	$1/2$	$1$	$6$	$55$	$602$	$7182$	$7182$	$1$	$3$	$8$	$29$	$116$	$517$					✓	$[1, 1, 2, 3, 4, 4, 4, 9, 10, 7]$
1.4.E.6.2a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$E_6$	$6$	$1/6$	$2$	$12$	$100$	$980$	$10584$	$10584$	$1$	$4$	$11$	$44$	$172$	$754$					✓	$[1, 2, 3, 4, 6, 6, 6, 13, 12, 12]$
1.4.E.8.3a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$J(E_4)$	$8$	$5/8$	$1$	$6$	$50$	$504$	$5712$	$5712$	$1$	$3$	$7$	$26$	$96$	$422$				✓	✓	$[1, 1, 2, 3, 3, 5, 3, 8, 8, 9]$
1.4.E.12.4a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$J(E_6)$	$12$	$7/12$	$1$	$6$	$50$	$490$	$5292$	$5292$	$1$	$3$	$7$	$25$	$91$	$387$				✓	✓	$[1, 1, 2, 3, 3, 4, 3, 7, 6, 7]$
1.4.F.2.1a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(C_1)$	$2$	$1/2$	$4$	$48$	$640$	$8960$	$129024$	$129024$	$1$	$11$	$40$	$235$	$1196$	$6650$					✓	$[1, 4, 10, 19, 40, 46, 52, 163, 184, 146]$
1.4.F.4.1a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_{4,1}$	$4$	$3/4$	$2$	$24$	$320$	$4480$	$64512$	$64512$	$1$	$5$	$22$	$115$	$606$	$3314$					✓	$[1, 2, 4, 9, 20, 16, 26, 77, 92, 52]$
1.4.F.4.2a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_2$	$4$	$3/4$	$2$	$24$	$320$	$4480$	$64512$	$64512$	$1$	$6$	$22$	$118$	$606$	$3324$					✓	$[1, 2, 5, 10, 20, 20, 26, 79, 92, 60]$
1.4.F.4.2b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(C_2)$	$4$	$3/4$	$2$	$24$	$320$	$4480$	$64512$	$64512$	$1$	$7$	$22$	$123$	$606$	$3346$					✓	$[1, 2, 6, 11, 20, 26, 26, 83, 92, 78]$
1.4.F.6.1a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_3$	$6$	$1/2$	$2$	$18$	$220$	$3010$	$43092$	$43092$	$1$	$5$	$17$	$85$	$421$	$2263$					✓	$[1, 2, 4, 7, 14, 14, 18, 53, 62, 41]$
1.4.F.6.2a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(C_3)$	$6$	$1/2$	$2$	$18$	$220$	$3010$	$43092$	$43092$	$1$	$5$	$16$	$85$	$416$	$2264$					✓	$[1, 2, 4, 7, 14, 16, 18, 55, 62, 50]$
1.4.F.6.2b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_{6,1}$	$6$	$1/2$	$2$	$18$	$220$	$3010$	$43092$	$43092$	$1$	$5$	$18$	$85$	$426$	$2264$					✓	$[1, 2, 4, 7, 14, 12, 18, 51, 62, 34]$
1.4.F.8.2a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(C_4)$	$8$	$5/8$	$2$	$18$	$200$	$2520$	$34272$	$34272$	$1$	$5$	$16$	$79$	$366$	$1904$					✓	$[1, 2, 4, 7, 12, 14, 14, 43, 48, 40]$
1.4.F.8.3a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{4,1}$	$8$	$7/8$	$1$	$12$	$160$	$2240$	$32256$	$32256$	$1$	$4$	$13$	$63$	$311$	$1678$					✓	$[1, 1, 3, 6, 10, 11, 13, 40, 46, 31]$
1.4.F.8.3b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_4$	$8$	$5/8$	$2$	$18$	$200$	$2520$	$34272$	$34272$	$1$	$5$	$16$	$78$	$366$	$1898$					✓	$[1, 2, 4, 7, 12, 13, 14, 42, 48, 35]$
1.4.F.8.5a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(D_2)$	$8$	$7/8$	$1$	$12$	$160$	$2240$	$32256$	$32256$	$1$	$5$	$13$	$67$	$311$	$1694$					✓	$[1, 1, 4, 7, 10, 16, 13, 43, 46, 44]$
1.4.F.12.3a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$T$	$12$	$1/4$	$2$	$12$	$120$	$1540$	$21672$	$21672$	$1$	$4$	$12$	$52$	$236$	$1202$					✓	$[1, 2, 3, 4, 8, 8, 10, 27, 32, 22]$
1.4.F.12.4a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(D_3)$	$12$	$3/4$	$1$	$9$	$110$	$1505$	$21546$	$21546$	$1$	$4$	$10$	$48$	$216$	$1153$					✓	$[1, 1, 3, 5, 7, 11, 9, 29, 31, 30]$
1.4.F.12.4b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{6,1}$	$12$	$3/4$	$1$	$9$	$110$	$1505$	$21546$	$21546$	$1$	$4$	$11$	$48$	$221$	$1153$					✓	$[1, 1, 3, 5, 7, 9, 9, 27, 31, 22]$
1.4.F.12.4c	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_6$	$12$	$7/12$	$2$	$18$	$200$	$2450$	$31752$	$31752$	$1$	$5$	$16$	$77$	$356$	$1803$					✓	$[1, 2, 4, 7, 12, 12, 14, 39, 40, 29]$
1.4.F.12.5a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(C_6)$	$12$	$7/12$	$2$	$18$	$200$	$2450$	$31752$	$31752$	$1$	$5$	$16$	$77$	$356$	$1804$					✓	$[1, 2, 4, 7, 12, 12, 14, 39, 40, 30]$
1.4.F.16.11a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(D_4)$	$16$	$13/16$	$1$	$9$	$100$	$1260$	$17136$	$17136$	$1$	$4$	$10$	$45$	$191$	$973$					✓	$[1, 1, 3, 5, 6, 10, 7, 23, 24, 25]$
1.4.F.24.12a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$O_1$	$24$	$5/8$	$1$	$6$	$60$	$770$	$10836$	$10836$	$1$	$3$	$8$	$30$	$126$	$617$					✓	$[1, 1, 2, 3, 4, 5, 5, 14, 16, 12]$
1.4.F.24.12b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$O$	$24$	$3/8$	$2$	$12$	$100$	$1050$	$12852$	$12852$	$1$	$4$	$11$	$45$	$181$	$837$					✓	$[1, 2, 3, 4, 6, 7, 6, 16, 18, 16]$
1.4.F.24.13a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(T)$	$24$	$5/8$	$1$	$6$	$60$	$770$	$10836$	$10836$	$1$	$3$	$7$	$29$	$121$	$612$					✓	$[1, 1, 2, 3, 4, 6, 5, 15, 16, 16]$
1.4.F.24.14a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(D_6)$	$24$	$19/24$	$1$	$9$	$100$	$1225$	$15876$	$15876$	$1$	$4$	$10$	$44$	$186$	$923$				✓	✓	$[1, 1, 3, 5, 6, 9, 7, 21, 20, 20]$
1.4.F.48.48a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(O)$	$48$	$11/16$	$1$	$6$	$50$	$525$	$6426$	$6426$	$1$	$3$	$7$	$26$	$96$	$432$				✓	✓	$[1, 1, 2, 3, 3, 5, 3, 9, 9, 11]$
1.6.A.1.1a	$1$	$6$	$21$	$\mathrm{USp}(6)$	$\mathrm{USp}(6)$	$1$	$0$	$1$	$3$	$15$	$104$	$909$	$909$	$1$	$2$	$5$	$16$	$62$	$282$	$2$	$23$	$684$	✓	✓	$[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]$
1.6.B.1.1a	$1$	$6$	$9$	$\mathrm{U}(3)$	$\mathrm{U}(3)$	$1$	$0$	$2$	$12$	$120$	$1610$	$25956$	$25956$	$1$	$4$	$18$	$107$	$743$	$5793$	$6$	$232$	$21260$		✓	$[1, 2, 3, 4, 4, 8, 9, 9, 12, 10, 6, 17, 22, 26, 40, 24, 19, 40, 30, 20]$
1.6.B.2.1a	$1$	$6$	$9$	$\mathrm{U}(3)$	$N(\mathrm{U}(3))$	$2$	$1/2$	$1$	$6$	$60$	$805$	$12978$	$12978$	$1$	$3$	$11$	$58$	$382$	$2922$	$3$	$116$	$10630$	✓	✓	$[1, 1, 2, 2, 3, 4, 5, 6, 6, 6, 3, 9, 11, 13, 20, 12, 11, 20, 16, 10]$
1.6.E.3.1a	$1$	$6$	$9$	$\mathrm{SU}(2)^3$	$E_{s}$	$3$	$2/3$	$1$	$8$	$95$	$1414$	$24402$	$24402$	$1$	$4$	$20$	$121$	$851$	$6703$	$5$	$244$	$24525$		✓	$[1, 1, 3, 2, 2, 8, 7, 9, 10, 4, 4, 15, 15, 30, 48, 19, 27, 40, 26, 8]$
1.6.E.6.1a	$1$	$6$	$9$	$\mathrm{SU}(2)^3$	$E_{s,t}$	$6$	$1/3$	$1$	$5$	$50$	$714$	$12222$	$12222$	$1$	$3$	$12$	$65$	$436$	$3377$	$3$	$124$	$12275$	✓	✓	$[1, 1, 2, 2, 2, 4, 5, 6, 6, 4, 3, 8, 10, 16, 24, 12, 15, 23, 15, 7]$
1.6.H.3.1a	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{s}$	$3$	$2/3$	$2$	$30$	$620$	$14910$	$390852$	$390852$	$1$	$7$	$61$	$615$	$6741$	$78043$	$12$	$1644$	$369720$		✓	$[1, 2, 6, 6, 9, 52, 52, 68, 114, 46, 32, 247, 284, 630, 1204, 562, 569, 1320, 1070, 294]$
1.6.H.6.2a	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{abc,s}$	$6$	$5/6$	$1$	$15$	$310$	$7455$	$195426$	$195426$	$1$	$5$	$35$	$321$	$3411$	$39143$	$6$	$822$	$184860$	✓	✓	$[1, 1, 4, 3, 6, 26, 27, 40, 57, 26, 16, 125, 142, 315, 602, 281, 298, 660, 541, 147]$
1.6.M.12.3a	$1$	$6$	$3$	$\mathrm{SU}(2)_{3}$	$M(A_4)$	$12$	$2/3$	$1$	$14$	$305$	$7658$	$206682$	$206682$	$1$	$5$	$37$	$353$	$3831$	$44475$	$7$	$928$	$213454$		✓	$[1, 1, 4, 4, 5, 28, 30, 44, 68, 30, 16, 129, 156, 363, 708, 339, 359, 812, 664, 187]$
1.6.M.24.12a	$1$	$6$	$3$	$\mathrm{SU}(2)_{3}$	$M(S_4)$	$24$	$1/3$	$1$	$8$	$155$	$3836$	$103362$	$103362$	$1$	$4$	$22$	$186$	$1941$	$22308$	$4$	$466$	$106744$	✓	✓	$[1, 1, 3, 3, 4, 14, 17, 26, 35, 19, 9, 66, 81, 183, 354, 174, 186, 410, 338, 100]$
1.6.N.9.2a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$C(3,1)$	$9$	$8/9$	$2$	$54$	$1620$	$51030$	$1653372$	$1653372$	$1$	$11$	$135$	$1755$	$23571$	$323109$	$20$	$5244$	$1717220$		✓	$[1, 2, 10, 10, 17, 144, 162, 250, 466, 196, 96, 1003, 1264, 3174, 6576, 3406, 3507, 8704, 7744, 2270]$
1.6.N.12.3a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$C(2,2)$	$12$	$2/3$	$2$	$42$	$1220$	$38290$	$1240092$	$1240092$	$1$	$9$	$103$	$1321$	$17691$	$242367$	$16$	$3944$	$1288060$		✓	$[1, 2, 8, 10, 15, 108, 128, 194, 354, 166, 76, 753, 976, 2386, 4932, 2594, 2641, 6588, 5840, 1790]$
1.6.N.18.3a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(C(3,1))$	$18$	$17/18$	$1$	$27$	$810$	$25515$	$826686$	$826686$	$1$	$7$	$72$	$891$	$11826$	$161676$	$10$	$2622$	$858610$		✓	$[1, 1, 6, 5, 10, 72, 82, 131, 233, 101, 48, 503, 632, 1587, 3288, 1703, 1767, 4352, 3878, 1135]$
1.6.N.18.4a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$D(3,1)$	$18$	$4/9$	$2$	$30$	$820$	$25550$	$826812$	$826812$	$1$	$7$	$71$	$887$	$11811$	$161625$	$12$	$2644$	$858900$		✓	$[1, 2, 6, 10, 13, 72, 94, 138, 242, 136, 56, 503, 688, 1598, 3288, 1782, 1775, 4472, 3936, 1310]$
1.6.N.21.1a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$C(1,7)$	$21$	$2/3$	$2$	$30$	$740$	$22190$	$710892$	$710892$	$1$	$7$	$67$	$791$	$10271$	$139225$	$12$	$2316$	$737820$		✓	$[1, 2, 6, 6, 9, 64, 72, 108, 202, 86, 44, 431, 544, 1362, 2822, 1462, 1507, 3732, 3322, 978]$
1.6.N.24.12a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J_s(C(2,2))$	$24$	$5/6$	$1$	$21$	$610$	$19145$	$620046$	$620046$	$1$	$7$	$58$	$681$	$8906$	$121366$	$8$	$1972$	$644030$		✓	$[1, 1, 6, 5, 10, 54, 66, 107, 177, 91, 38, 381, 488, 1193, 2466, 1297, 1343, 3294, 2938, 895]$
1.6.N.24.12b	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$D(2,2)$	$24$	$1/3$	$2$	$24$	$620$	$19180$	$620172$	$620172$	$1$	$6$	$55$	$670$	$8871$	$121254$	$10$	$1994$	$644320$		✓	$[1, 2, 5, 8, 10, 54, 71, 104, 182, 103, 42, 378, 516, 1200, 2466, 1338, 1332, 3354, 2954, 984]$
1.6.N.24.13a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(C(2,2))$	$24$	$5/6$	$1$	$21$	$610$	$19145$	$620046$	$620046$	$1$	$6$	$56$	$674$	$8886$	$121305$	$8$	$1972$	$644030$		✓	$[1, 1, 5, 5, 9, 54, 65, 103, 177, 86, 38, 378, 488, 1193, 2466, 1297, 1334, 3294, 2926, 895]$