Sato-Tate group search results

Results (23 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	$0$	$1$	$0$	$\mathrm{SO}(1)$	$\mu(1)$	$1$	$0$	$1$	$1$	$1$	$1$	$1$	$1$											✓
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.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.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.F.1.1a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_1$	$1$	$0$	$8$	$96$	$1280$	$17920$	$258048$	$258048$	$4$	$18$	$88$	$454$	$2424$	$13236$					✓	$[1, 8, 11, 34, 80, 56, 104, 301, 368, 192]$
1.6.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.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.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.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.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.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.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.K.1.1a	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times C_1$	$1$	$0$	$9$	$146$	$2965$	$68334$	$1707930$	$1707930$	$5$	$35$	$299$	$2899$	$30495$	$339085$	$50$	$7436$	$1543940$		✓	$[1, 9, 26, 19, 43, 240, 228, 304, 485, 170, 147, 1099, 1187, 2603, 4768, 2123, 2205, 4909, 3824, 965]$
1.6.L.1.1a	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L_1(C_1)$	$1$	$0$	$10$	$198$	$4900$	$134470$	$3912300$	$3912300$	$5$	$43$	$443$	$5059$	$61295$	$771445$	$68$	$14244$	$3866000$		✓	$[1, 10, 34, 30, 61, 416, 444, 636, 1122, 446, 264, 2435, 2924, 6898, 13696, 6734, 6859, 16500, 14000, 3906]$
1.6.M.1.1a	$1$	$6$	$3$	$\mathrm{SU}(2)_{3}$	$M(C_1)$	$1$	$0$	$9$	$162$	$3645$	$91854$	$2480058$	$2480058$	$6$	$45$	$405$	$4131$	$45684$	$532899$	$65$	$11076$	$2561186$		✓	$[1, 9, 34, 26, 45, 320, 334, 486, 810, 300, 164, 1539, 1836, 4325, 8448, 4023, 4191, 9680, 7920, 2101]$
1.6.N.1.1a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$A(1,1)$	$1$	$0$	$18$	$486$	$14580$	$459270$	$14880348$	$14880348$	$9$	$99$	$1215$	$15795$	$212139$	$2907981$	$164$	$47148$	$15454820$		✓	$[1, 18, 82, 74, 153, 1280, 1450, 2250, 4194, 1740, 848, 9027, 11376, 28550, 59136, 30654, 31515, 78320, 69696, 20350]$