Sato-Tate group search results

Results (1-50 of 154 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
0.1.1	$0$	$1$	$0$	$\mathrm{SO}(1)$	$\mu(1)$	$1$	$0$	$1$	$1$	$1$	$1$	$1$	$1$											✓
0.1.2	$0$	$1$	$0$	$\mathrm{SO}(1)$	$\mu(2)$	$2$	$0$	$1$	$1$	$1$	$1$	$1$	$1$										✓	✓
1.2.A.1.1a	$1$	$2$	$3$	$\mathrm{SU}(2)$	$\mathrm{SU}(2)$	$1$	$0$	$1$	$2$	$5$	$14$	$42$	$42$										✓	✓
1.2.B.1.1a	$1$	$2$	$1$	$\mathrm{U}(1)$	$\mathrm{U}(1)$	$1$	$0$	$2$	$6$	$20$	$70$	$252$	$252$											✓
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.1.1a	$1$	$4$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)$	$\mathrm{SU}(2)\times\mathrm{SU}(2)$	$1$	$0$	$2$	$10$	$70$	$588$	$5544$	$5544$	$2$	$5$	$14$	$44$	$152$	$569$					✓	$[1, 2, 2, 3, 4, 3, 4, 6, 6, 4]$
1.4.C.1.1a	$1$	$4$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)$	$\mathrm{U}(1)\times\mathrm{SU}(2)$	$1$	$0$	$3$	$20$	$175$	$1764$	$19404$	$19404$	$2$	$6$	$20$	$76$	$312$	$1364$					✓	$[1, 3, 3, 6, 10, 6, 10, 21, 21, 10]$
1.4.C.2.1a	$1$	$4$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)$	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$	$2$	$0$	$2$	$11$	$90$	$889$	$9723$	$9723$	$2$	$5$	$14$	$46$	$172$	$714$				✓	✓	$[1, 2, 2, 4, 5, 4, 6, 11, 11, 6]$
1.4.D.1.1a	$1$	$4$	$2$	$\mathrm{U}(1)\times\mathrm{U}(1)$	$F$	$1$	$0$	$4$	$36$	$400$	$4900$	$63504$	$63504$	$2$	$8$	$32$	$148$	$712$	$3584$				✓	✓	$[1, 4, 5, 12, 24, 16, 28, 73, 80, 40]$
1.4.D.2.1b	$1$	$4$	$2$	$\mathrm{U}(1)\times\mathrm{U}(1)$	$F_a$	$2$	$0$	$3$	$21$	$210$	$2485$	$31878$	$31878$	$2$	$6$	$20$	$82$	$372$	$1824$					✓	$[1, 3, 3, 7, 12, 9, 15, 37, 42, 21]$
1.4.E.1.1a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$E_1$	$1$	$0$	$4$	$32$	$320$	$3584$	$43008$	$43008$	$3$	$10$	$37$	$150$	$654$	$3012$					✓	$[1, 4, 5, 10, 20, 14, 20, 49, 56, 30]$
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.F.1.1a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_1$	$1$	$0$	$8$	$96$	$1280$	$17920$	$258048$	$258048$	$4$	$18$	$88$	$454$	$2424$	$13236$					✓	$[1, 8, 11, 34, 80, 56, 104, 301, 368, 192]$
1.4.F.3.1a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_3$	$3$	$0$	$4$	$36$	$440$	$6020$	$86184$	$86184$	$2$	$8$	$34$	$164$	$842$	$4506$					✓	$[1, 4, 5, 12, 28, 20, 36, 101, 124, 66]$
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.C.1.1a	$1$	$6$	$13$	$\mathrm{SU}(2)\times\mathrm{USp}(4)$	$\mathrm{SU}(2)\times \mathrm{USp}(4)$	$1$	$0$	$2$	$11$	$94$	$1050$	$14076$	$14076$	$2$	$6$	$23$	$109$	$613$	$3941$	$6$	$188$	$12226$	✓	✓	$[1, 2, 3, 2, 3, 6, 5, 6, 6, 3, 4, 9, 8, 12, 16, 8, 10, 12, 9, 4]$
1.6.D.1.1a	$1$	$6$	$11$	$\mathrm{U}(1)\times\mathrm{USp}(4)$	$\mathrm{U}(1)\times \mathrm{USp}(4)$	$1$	$0$	$3$	$21$	$214$	$2758$	$41796$	$41796$	$2$	$7$	$32$	$181$	$1193$	$8801$	$8$	$348$	$29536$		✓	$[1, 3, 4, 3, 6, 13, 11, 10, 13, 6, 10, 27, 24, 34, 50, 24, 20, 34, 27, 10]$
1.6.D.2.1a	$1$	$6$	$11$	$\mathrm{U}(1)\times\mathrm{USp}(4)$	$N(\mathrm{U}(1)\times \mathrm{USp}(4))$	$2$	$0$	$2$	$12$	$114$	$1421$	$21195$	$21195$	$2$	$6$	$23$	$112$	$668$	$4656$	$6$	$198$	$15216$	✓	✓	$[1, 2, 3, 2, 4, 7, 6, 7, 7, 4, 6, 15, 13, 18, 25, 13, 13, 18, 15, 6]$
1.6.E.1.1a	$1$	$6$	$9$	$\mathrm{SU}(2)^3$	$E$	$1$	$0$	$3$	$24$	$285$	$4242$	$73206$	$73206$	$3$	$12$	$60$	$363$	$2553$	$20109$	$13$	$728$	$73565$		✓	$[1, 3, 7, 4, 6, 22, 19, 27, 30, 10, 10, 45, 45, 88, 140, 57, 77, 118, 78, 20]$
1.6.E.2.1a	$1$	$6$	$9$	$\mathrm{SU}(2)^3$	$E_{t}$	$2$	$0$	$2$	$13$	$145$	$2128$	$36624$	$36624$	$2$	$7$	$32$	$186$	$1287$	$10080$	$7$	$366$	$36795$		✓	$[1, 2, 4, 3, 4, 11, 11, 15, 16, 7, 6, 23, 25, 45, 70, 31, 40, 62, 41, 13]$
1.6.F.1.1a	$1$	$6$	$7$	$\mathrm{U}(1)\times\mathrm{SU}(2)^2$	$F$	$1$	$0$	$4$	$40$	$570$	$9898$	$195216$	$195216$	$3$	$14$	$84$	$607$	$4993$	$45009$	$18$	$1384$	$181460$		✓	$[1, 4, 9, 6, 10, 44, 39, 47, 66, 22, 20, 121, 124, 244, 420, 174, 179, 358, 258, 62]$
1.6.F.2.1b	$1$	$6$	$7$	$\mathrm{U}(1)\times\mathrm{SU}(2)^2$	$F_{t}$	$2$	$0$	$3$	$23$	$295$	$4984$	$97734$	$97734$	$2$	$8$	$44$	$308$	$2507$	$22530$	$10$	$698$	$90780$		✓	$[1, 3, 5, 5, 7, 22, 24, 26, 35, 17, 13, 61, 73, 125, 210, 99, 92, 191, 135, 45]$
1.6.F.2.1c	$1$	$6$	$7$	$\mathrm{U}(1)\times\mathrm{SU}(2)^2$	$F_{a}$	$2$	$0$	$3$	$25$	$320$	$5243$	$100380$	$100380$	$3$	$12$	$60$	$373$	$2783$	$23759$	$13$	$772$	$92970$		✓	$[1, 3, 7, 4, 7, 24, 21, 30, 34, 13, 13, 65, 65, 125, 210, 90, 104, 182, 135, 34]$
1.6.G.1.1a	$1$	$6$	$5$	$\mathrm{U}(1)^2\times\mathrm{SU}(2)$	$F\times \mathrm{SU}(2)$	$1$	$0$	$5$	$62$	$1065$	$21714$	$492366$	$492366$	$3$	$17$	$123$	$1053$	$10023$	$102549$	$24$	$2600$	$446720$		✓	$[1, 5, 12, 9, 17, 84, 78, 96, 149, 52, 45, 313, 333, 689, 1240, 537, 537, 1177, 894, 221]$
1.6.G.2.1a	$1$	$6$	$5$	$\mathrm{U}(1)^2\times\mathrm{SU}(2)$	$F_{ab}\times \mathrm{SU}(2)$	$2$	$0$	$3$	$32$	$535$	$10864$	$246204$	$246204$	$3$	$13$	$75$	$567$	$5133$	$51639$	$14$	$1316$	$223520$		✓	$[1, 3, 8, 5, 11, 42, 40, 58, 75, 30, 25, 161, 169, 347, 620, 271, 291, 591, 456, 113]$
1.6.G.2.1b	$1$	$6$	$5$	$\mathrm{U}(1)^2\times\mathrm{SU}(2)$	$F_{a}\times \mathrm{SU}(2)$	$2$	$0$	$4$	$41$	$620$	$11739$	$255885$	$255885$	$3$	$14$	$84$	$627$	$5493$	$53714$	$18$	$1460$	$228960$		✓	$[1, 4, 9, 6, 11, 47, 42, 53, 76, 28, 26, 164, 170, 349, 620, 273, 278, 592, 456, 115]$
1.6.G.4.1a	$1$	$6$	$5$	$\mathrm{U}(1)^2\times\mathrm{SU}(2)$	$F_{ac}\times \mathrm{SU}(2)$	$4$	$0$	$2$	$17$	$270$	$5439$	$123123$	$123123$	$2$	$7$	$38$	$284$	$2567$	$25820$	$7$	$658$	$111760$	✓	✓	$[1, 2, 4, 3, 6, 21, 21, 29, 38, 15, 13, 81, 85, 174, 310, 136, 146, 296, 229, 57]$
1.6.G.4.2a	$1$	$6$	$5$	$\mathrm{U}(1)^2\times\mathrm{SU}(2)$	$F_{a,b}\times \mathrm{SU}(2)$	$4$	$0$	$3$	$26$	$355$	$6314$	$132804$	$132804$	$3$	$12$	$60$	$384$	$3048$	$28259$	$13$	$818$	$117360$	✓	✓	$[1, 3, 7, 4, 8, 26, 23, 34, 39, 17, 16, 88, 88, 178, 310, 140, 155, 299, 237, 61]$
1.6.H.1.1a	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H$	$1$	$0$	$6$	$90$	$1860$	$44730$	$1172556$	$1172556$	$3$	$21$	$183$	$1845$	$20223$	$234129$	$32$	$4920$	$1109120$		✓	$[1, 6, 16, 14, 27, 152, 154, 204, 342, 132, 92, 741, 852, 1886, 3600, 1686, 1695, 3956, 3210, 862]$
1.6.H.2.1b	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{ab}$	$2$	$0$	$4$	$48$	$940$	$22400$	$586404$	$586404$	$3$	$15$	$105$	$963$	$10233$	$117429$	$20$	$2508$	$555200$		✓	$[1, 4, 10, 8, 15, 76, 78, 108, 172, 70, 48, 375, 428, 948, 1800, 848, 861, 1980, 1614, 436]$
1.6.H.2.1c	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{a}$	$2$	$0$	$5$	$63$	$1130$	$24815$	$618030$	$618030$	$3$	$17$	$123$	$1089$	$11043$	$122489$	$24$	$2748$	$567360$		✓	$[1, 5, 12, 9, 18, 88, 83, 108, 173, 68, 54, 393, 434, 953, 1800, 853, 854, 1986, 1631, 441]$
1.6.H.4.1b	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{at}$	$4$	$0$	$3$	$27$	$480$	$11235$	$293328$	$293328$	$2$	$8$	$53$	$482$	$5117$	$58715$	$10$	$1254$	$277600$		✓	$[1, 3, 5, 5, 9, 38, 42, 54, 87, 35, 26, 188, 216, 475, 900, 425, 432, 992, 810, 219]$
1.6.H.4.2a	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{ab,bc}$	$4$	$0$	$3$	$27$	$480$	$11235$	$293328$	$293328$	$3$	$12$	$66$	$522$	$5238$	$59079$	$14$	$1302$	$278240$		✓	$[1, 3, 7, 5, 9, 38, 40, 60, 87, 39, 26, 192, 216, 479, 900, 429, 444, 992, 816, 223]$
1.6.H.4.2c	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{a,b}$	$4$	$0$	$4$	$42$	$670$	$13650$	$324954$	$324954$	$3$	$14$	$84$	$648$	$6048$	$64139$	$18$	$1542$	$290400$		✓	$[1, 4, 9, 6, 12, 50, 45, 60, 88, 37, 32, 210, 222, 484, 900, 434, 437, 998, 833, 228]$
1.6.I.1.1a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times E_1$	$1$	$0$	$5$	$58$	$925$	$17598$	$374850$	$374850$	$4$	$21$	$137$	$1059$	$9250$	$88075$	$26$	$2444$	$366740$		✓	$[1, 5, 14, 9, 15, 76, 70, 96, 133, 44, 35, 235, 251, 535, 940, 399, 449, 887, 642, 155]$
1.6.I.2.1a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times E_2$	$2$	$0$	$3$	$30$	$465$	$8806$	$187446$	$187446$	$2$	$11$	$69$	$531$	$4628$	$44045$	$14$	$1228$	$183420$		✓	$[1, 3, 8, 7, 9, 38, 38, 52, 71, 30, 19, 119, 135, 269, 470, 209, 231, 463, 334, 97]$
1.6.I.2.1b	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times J(E_1)$	$2$	$0$	$3$	$30$	$465$	$8806$	$187446$	$187446$	$3$	$13$	$75$	$547$	$4673$	$44171$	$14$	$1228$	$183420$		✓	$[1, 3, 8, 5, 9, 38, 36, 52, 67, 24, 19, 119, 127, 269, 470, 201, 231, 445, 324, 79]$
1.6.I.3.1a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times E_3$	$3$	$0$	$3$	$26$	$355$	$6258$	$128646$	$128646$	$2$	$9$	$53$	$385$	$3238$	$30163$	$12$	$872$	$124190$		✓	$[1, 3, 6, 5, 7, 28, 26, 34, 47, 18, 15, 81, 87, 181, 318, 137, 153, 299, 218, 57]$
1.6.I.4.1a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times E_4$	$4$	$0$	$3$	$26$	$345$	$5782$	$112686$	$112686$	$2$	$9$	$51$	$359$	$2908$	$26103$	$12$	$812$	$105080$		✓	$[1, 3, 6, 5, 7, 26, 24, 30, 41, 18, 13, 71, 75, 147, 250, 113, 121, 239, 176, 53]$
1.6.I.4.2a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times J(E_2)$	$4$	$0$	$2$	$16$	$235$	$4410$	$93744$	$93744$	$2$	$8$	$41$	$283$	$2362$	$22156$	$8$	$620$	$91760$		✓	$[1, 2, 5, 4, 6, 19, 20, 30, 36, 17, 11, 61, 69, 136, 235, 106, 122, 233, 170, 50]$
1.6.I.6.1a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times J(E_3)$	$6$	$0$	$2$	$14$	$180$	$3136$	$64344$	$64344$	$2$	$7$	$33$	$210$	$1667$	$15215$	$7$	$442$	$62145$		✓	$[1, 2, 4, 3, 5, 14, 14, 21, 24, 11, 9, 42, 45, 92, 159, 70, 83, 151, 112, 30]$
1.6.I.6.2a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times E_6$	$6$	$0$	$3$	$26$	$345$	$5754$	$110586$	$110586$	$2$	$9$	$51$	$357$	$2868$	$25403$	$12$	$808$	$101370$		✓	$[1, 3, 6, 5, 7, 26, 24, 28, 39, 16, 13, 69, 73, 135, 230, 99, 101, 201, 146, 43]$
1.6.I.8.3a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times J(E_4)$	$8$	$0$	$2$	$14$	$175$	$2898$	$56364$	$56364$	$2$	$7$	$32$	$197$	$1502$	$13185$	$7$	$412$	$52590$	✓	✓	$[1, 2, 4, 3, 5, 13, 13, 19, 21, 11, 8, 37, 39, 75, 125, 58, 67, 121, 91, 28]$
1.6.I.12.4a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times J(E_6)$	$12$	$0$	$2$	$14$	$175$	$2884$	$55314$	$55314$	$2$	$7$	$32$	$196$	$1482$	$12835$	$7$	$410$	$50735$	✓	✓	$[1, 2, 4, 3, 5, 13, 13, 18, 20, 10, 8, 36, 38, 69, 115, 51, 57, 102, 76, 23]$
1.6.J.1.1a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_1(E_1)$	$1$	$0$	$6$	$86$	$1660$	$37254$	$916020$	$916020$	$4$	$25$	$197$	$1811$	$18370$	$199015$	$36$	$4676$	$913040$		✓	$[1, 6, 18, 14, 23, 140, 140, 186, 302, 110, 68, 571, 656, 1450, 2752, 1262, 1269, 2880, 2288, 590]$
1.6.J.2.1b	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_1(E_2)$	$2$	$0$	$4$	$46$	$840$	$18662$	$458136$	$458136$	$2$	$13$	$99$	$907$	$9188$	$99515$	$20$	$2356$	$456720$		✓	$[1, 4, 10, 12, 15, 70, 80, 102, 160, 82, 40, 287, 368, 732, 1376, 680, 649, 1520, 1188, 396]$
1.6.J.2.1d	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_1(J(E_1))$	$2$	$0$	$4$	$46$	$840$	$18662$	$458136$	$458136$	$3$	$15$	$105$	$923$	$9233$	$99641$	$20$	$2356$	$456720$		✓	$[1, 4, 10, 8, 13, 70, 72, 96, 152, 58, 36, 287, 332, 728, 1376, 636, 639, 1444, 1148, 300]$
1.6.J.2.1e	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_2(E_1)$	$2$	$0$	$5$	$59$	$990$	$20419$	$479514$	$479514$	$4$	$21$	$137$	$1091$	$10130$	$104555$	$26$	$2594$	$466760$		✓	$[1, 5, 14, 9, 16, 80, 75, 106, 153, 58, 42, 303, 336, 735, 1376, 641, 664, 1448, 1169, 305]$
1.6.J.3.1a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_1(E_3)$	$3$	$0$	$4$	$42$	$670$	$13594$	$318276$	$318276$	$2$	$11$	$77$	$661$	$6438$	$68173$	$16$	$1656$	$308840$		✓	$[1, 4, 8, 8, 13, 52, 54, 66, 108, 44, 34, 201, 234, 490, 932, 438, 431, 970, 780, 210]$