Properties

 Label 105.3.n Level 105 Weight 3 Character orbit n Rep. character $$\chi_{105}(31,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 20 Newform subspaces 2 Sturm bound 48 Trace bound 1

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$105 = 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 105.n (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$48$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(105, [\chi])$$.

Total New Old
Modular forms 72 20 52
Cusp forms 56 20 36
Eisenstein series 16 0 16

Trace form

 $$20q + 4q^{2} + 6q^{3} - 28q^{4} + 6q^{7} + 8q^{8} + 30q^{9} + O(q^{10})$$ $$20q + 4q^{2} + 6q^{3} - 28q^{4} + 6q^{7} + 8q^{8} + 30q^{9} + 40q^{11} - 48q^{12} + 16q^{14} - 84q^{16} - 96q^{17} - 12q^{18} - 6q^{19} + 84q^{21} + 40q^{22} + 64q^{23} + 108q^{24} + 50q^{25} + 156q^{26} - 248q^{28} - 200q^{29} - 18q^{31} - 72q^{32} - 60q^{35} - 168q^{36} - 114q^{37} + 240q^{38} - 54q^{39} + 204q^{42} + 228q^{43} + 216q^{44} + 196q^{46} + 24q^{47} - 22q^{49} + 40q^{50} - 60q^{51} - 492q^{52} - 152q^{53} + 308q^{56} - 12q^{57} - 92q^{58} - 324q^{59} - 456q^{61} - 54q^{63} + 696q^{64} - 120q^{65} + 108q^{66} + 166q^{67} - 204q^{68} - 300q^{70} - 464q^{71} + 12q^{72} + 582q^{73} + 104q^{74} + 30q^{75} - 44q^{77} - 168q^{78} - 98q^{79} + 480q^{80} - 90q^{81} + 684q^{82} - 60q^{84} - 120q^{85} + 308q^{86} - 544q^{88} + 96q^{89} + 330q^{91} + 168q^{92} + 234q^{93} + 60q^{94} - 120q^{95} - 432q^{96} - 176q^{98} + 240q^{99} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(105, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
105.3.n.a $$8$$ $$2.861$$ 8.0.$$\cdots$$.16 None $$2$$ $$-12$$ $$0$$ $$-16$$ $$q+\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$$
105.3.n.b $$12$$ $$2.861$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$2$$ $$18$$ $$0$$ $$22$$ $$q+(-\beta _{2}-\beta _{10})q^{2}+(2+\beta _{3})q^{3}+(4\beta _{3}+\cdots)q^{4}+\cdots$$

Decomposition of $$S_{3}^{\mathrm{old}}(105, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(105, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 2}$$

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 - 2 T - 3 T^{2} + 14 T^{3} - 13 T^{4} - 18 T^{5} + 70 T^{6} - 44 T^{7} - 156 T^{8} - 176 T^{9} + 1120 T^{10} - 1152 T^{11} - 3328 T^{12} + 14336 T^{13} - 12288 T^{14} - 32768 T^{15} + 65536 T^{16}$$)($$1 - 2 T + T^{2} - 18 T^{3} + 35 T^{4} - 10 T^{5} + 142 T^{6} - 148 T^{7} - 208 T^{8} - 424 T^{9} - 1176 T^{10} + 4080 T^{11} + 144 T^{12} + 16320 T^{13} - 18816 T^{14} - 27136 T^{15} - 53248 T^{16} - 151552 T^{17} + 581632 T^{18} - 163840 T^{19} + 2293760 T^{20} - 4718592 T^{21} + 1048576 T^{22} - 8388608 T^{23} + 16777216 T^{24}$$)
$3$ ($$( 1 + 3 T + 3 T^{2} )^{4}$$)($$( 1 - 3 T + 3 T^{2} )^{6}$$)
$5$ ($$( 1 - 5 T^{2} + 25 T^{4} )^{2}$$)($$( 1 - 5 T^{2} + 25 T^{4} )^{3}$$)
$7$ ($$1 + 16 T + 109 T^{2} + 784 T^{3} + 6664 T^{4} + 38416 T^{5} + 261709 T^{6} + 1882384 T^{7} + 5764801 T^{8}$$)($$1 - 22 T + 272 T^{2} - 2568 T^{3} + 19600 T^{4} - 138362 T^{5} + 991858 T^{6} - 6779738 T^{7} + 47059600 T^{8} - 302122632 T^{9} + 1568025872 T^{10} - 6214455478 T^{11} + 13841287201 T^{12}$$)
$11$ ($$1 - 20 T - 147 T^{2} + 2960 T^{3} + 57131 T^{4} - 519480 T^{5} - 8882912 T^{6} + 8003440 T^{7} + 1602642534 T^{8} + 968416240 T^{9} - 130054714592 T^{10} - 920290508280 T^{11} + 12246537230411 T^{12} + 76774776818960 T^{13} - 461348971377987 T^{14} - 7594996671664820 T^{15} + 45949729863572161 T^{16}$$)($$1 - 20 T - 77 T^{2} + 7872 T^{3} - 76264 T^{4} - 640168 T^{5} + 22115011 T^{6} - 150830740 T^{7} - 1492575946 T^{8} + 41825299028 T^{9} - 261075878769 T^{10} - 2649707325072 T^{11} + 64192943543664 T^{12} - 320614586333712 T^{13} - 3822411941056929 T^{14} + 74096068571342708 T^{15} - 319946909592076426 T^{16} - 3912160946263034740 T^{17} + 69406378073897058931 T^{18} -$$$$24\!\cdots\!88$$$$T^{19} -$$$$35\!\cdots\!04$$$$T^{20} +$$$$43\!\cdots\!32$$$$T^{21} -$$$$51\!\cdots\!77$$$$T^{22} -$$$$16\!\cdots\!20$$$$T^{23} +$$$$98\!\cdots\!41$$$$T^{24}$$)
$13$ ($$1 - 188 T^{2} + 39826 T^{4} - 8798048 T^{6} + 2113175419 T^{8} - 251281048928 T^{10} + 32487291694546 T^{12} - 4380040003026428 T^{14} + 665416609183179841 T^{16}$$)($$1 - 1050 T^{2} + 558861 T^{4} - 197481550 T^{6} + 52237691370 T^{8} - 11158031023650 T^{10} + 2025783626034165 T^{12} - 318684524066467650 T^{14} + 42611889644625577770 T^{16} -$$$$46\!\cdots\!50$$$$T^{18} +$$$$37\!\cdots\!01$$$$T^{20} -$$$$19\!\cdots\!50$$$$T^{22} +$$$$54\!\cdots\!61$$$$T^{24}$$)
$17$ ($$1 + 18 T + 766 T^{2} + 11844 T^{3} + 262438 T^{4} + 1906254 T^{5} + 22625848 T^{6} - 382636314 T^{7} - 5169040877 T^{8} - 110581894746 T^{9} + 1889733450808 T^{10} + 46012337456526 T^{11} + 1830703831301158 T^{12} + 23877431756917956 T^{13} + 446288633717996926 T^{14} + 3030800878069216722 T^{15} + 48661191875666868481 T^{16}$$)($$1 + 78 T + 3456 T^{2} + 111384 T^{3} + 2892825 T^{4} + 64908048 T^{5} + 1326815384 T^{6} + 25384395654 T^{7} + 459528789294 T^{8} + 7866410803470 T^{9} + 127737192900600 T^{10} + 2033291698334568 T^{11} + 33507834279238509 T^{12} + 587621300818690152 T^{13} + 10668738088251012600 T^{14} +$$$$18\!\cdots\!30$$$$T^{15} +$$$$32\!\cdots\!54$$$$T^{16} +$$$$51\!\cdots\!46$$$$T^{17} +$$$$77\!\cdots\!24$$$$T^{18} +$$$$10\!\cdots\!92$$$$T^{19} +$$$$14\!\cdots\!25$$$$T^{20} +$$$$15\!\cdots\!56$$$$T^{21} +$$$$14\!\cdots\!56$$$$T^{22} +$$$$91\!\cdots\!42$$$$T^{23} +$$$$33\!\cdots\!21$$$$T^{24}$$)
$19$ ($$1 + 598 T^{2} + 183481 T^{4} - 682560 T^{5} - 48973562 T^{6} - 501474240 T^{7} - 32269961996 T^{8} - 181032200640 T^{9} - 6382283573402 T^{10} - 32111636535360 T^{11} + 3116161130325721 T^{12} + 1323562321601564278 T^{14} +$$$$28\!\cdots\!81$$$$T^{16}$$)($$1 + 6 T + 1695 T^{2} + 10098 T^{3} + 1583475 T^{4} + 6257352 T^{5} + 993857576 T^{6} + 1495351404 T^{7} + 468684238005 T^{8} - 646226336898 T^{9} + 184440578012361 T^{10} - 649631264996682 T^{11} + 67037012122357518 T^{12} - 234516886663802202 T^{13} + 24036480567148897881 T^{14} - 30402287344769217138 T^{15} +$$$$79\!\cdots\!05$$$$T^{16} +$$$$91\!\cdots\!04$$$$T^{17} +$$$$21\!\cdots\!36$$$$T^{18} +$$$$49\!\cdots\!92$$$$T^{19} +$$$$45\!\cdots\!75$$$$T^{20} +$$$$10\!\cdots\!18$$$$T^{21} +$$$$63\!\cdots\!95$$$$T^{22} +$$$$81\!\cdots\!66$$$$T^{23} +$$$$48\!\cdots\!21$$$$T^{24}$$)
$23$ ($$1 - 62 T + 1497 T^{2} + 6014 T^{3} - 1196893 T^{4} + 31086552 T^{5} - 143771420 T^{6} - 13896561704 T^{7} + 513552019554 T^{8} - 7351281141416 T^{9} - 40233137944220 T^{10} + 4601925361264728 T^{11} - 93729870105931933 T^{12} + 249139038438885086 T^{13} + 32806192774734420537 T^{14} -$$$$71\!\cdots\!58$$$$T^{15} +$$$$61\!\cdots\!61$$$$T^{16}$$)($$1 - 2 T - 1961 T^{2} - 16242 T^{3} + 1952552 T^{4} + 28088402 T^{5} - 1236738581 T^{6} - 18913143826 T^{7} + 643866095426 T^{8} + 6409263044018 T^{9} - 382808809220061 T^{10} - 936062983320174 T^{11} + 225254373554835492 T^{12} - 495177318176372046 T^{13} -$$$$10\!\cdots\!01$$$$T^{14} +$$$$94\!\cdots\!02$$$$T^{15} +$$$$50\!\cdots\!06$$$$T^{16} -$$$$78\!\cdots\!74$$$$T^{17} -$$$$27\!\cdots\!01$$$$T^{18} +$$$$32\!\cdots\!18$$$$T^{19} +$$$$11\!\cdots\!72$$$$T^{20} -$$$$52\!\cdots\!98$$$$T^{21} -$$$$33\!\cdots\!61$$$$T^{22} -$$$$18\!\cdots\!58$$$$T^{23} +$$$$48\!\cdots\!41$$$$T^{24}$$)
$29$ ($$( 1 + 50 T + 1234 T^{2} - 15850 T^{3} - 1164374 T^{4} - 13329850 T^{5} + 872784754 T^{6} + 29741166050 T^{7} + 500246412961 T^{8} )^{2}$$)($$( 1 + 50 T + 4152 T^{2} + 144894 T^{3} + 7271923 T^{4} + 198551984 T^{5} + 7580628328 T^{6} + 166982218544 T^{7} + 5143292971363 T^{8} + 86186330272974 T^{9} + 2077023106614072 T^{10} + 21035361665010050 T^{11} + 353814783205469041 T^{12} )^{2}$$)
$31$ ($$1 + 126 T + 9883 T^{2} + 578466 T^{3} + 27206317 T^{4} + 1079090100 T^{5} + 38160094402 T^{6} + 1243487527488 T^{7} + 38998740329170 T^{8} + 1194991513915968 T^{9} + 35241648542229442 T^{10} + 957696435880658100 T^{11} + 23204023931078714797 T^{12} +$$$$47\!\cdots\!66$$$$T^{13} +$$$$77\!\cdots\!63$$$$T^{14} +$$$$95\!\cdots\!46$$$$T^{15} +$$$$72\!\cdots\!81$$$$T^{16}$$)($$1 - 108 T + 7296 T^{2} - 368064 T^{3} + 14679372 T^{4} - 497355660 T^{5} + 14549964692 T^{6} - 358253632404 T^{7} + 6912430087356 T^{8} - 59089176847584 T^{9} - 2401476398747496 T^{10} + 161517767136947820 T^{11} - 6040783753357557738 T^{12} +$$$$15\!\cdots\!20$$$$T^{13} -$$$$22\!\cdots\!16$$$$T^{14} -$$$$52\!\cdots\!04$$$$T^{15} +$$$$58\!\cdots\!96$$$$T^{16} -$$$$29\!\cdots\!04$$$$T^{17} +$$$$11\!\cdots\!12$$$$T^{18} -$$$$37\!\cdots\!60$$$$T^{19} +$$$$10\!\cdots\!32$$$$T^{20} -$$$$25\!\cdots\!24$$$$T^{21} +$$$$49\!\cdots\!96$$$$T^{22} -$$$$69\!\cdots\!88$$$$T^{23} +$$$$62\!\cdots\!21$$$$T^{24}$$)
$37$ ($$1 + 80 T + 1194 T^{2} + 28960 T^{3} + 3461705 T^{4} - 28416960 T^{5} - 6540374054 T^{6} - 198858748720 T^{7} - 6603314864556 T^{8} - 272237626997680 T^{9} - 12257713977418694 T^{10} - 72910144735496640 T^{11} + 12159167688035595305 T^{12} +$$$$13\!\cdots\!40$$$$T^{13} +$$$$78\!\cdots\!14$$$$T^{14} +$$$$72\!\cdots\!20$$$$T^{15} +$$$$12\!\cdots\!41$$$$T^{16}$$)($$1 + 34 T - 4909 T^{2} - 226690 T^{3} + 12133431 T^{4} + 708409644 T^{5} - 18171294956 T^{6} - 1398986295020 T^{7} + 16325526424229 T^{8} + 1786096223883250 T^{9} - 2380658436212215 T^{10} - 1019433693058130642 T^{11} - 10072912633170313306 T^{12} -$$$$13\!\cdots\!98$$$$T^{13} -$$$$44\!\cdots\!15$$$$T^{14} +$$$$45\!\cdots\!50$$$$T^{15} +$$$$57\!\cdots\!09$$$$T^{16} -$$$$67\!\cdots\!80$$$$T^{17} -$$$$11\!\cdots\!36$$$$T^{18} +$$$$63\!\cdots\!16$$$$T^{19} +$$$$14\!\cdots\!71$$$$T^{20} -$$$$38\!\cdots\!10$$$$T^{21} -$$$$11\!\cdots\!09$$$$T^{22} +$$$$10\!\cdots\!46$$$$T^{23} +$$$$43\!\cdots\!61$$$$T^{24}$$)
$41$ ($$1 - 10106 T^{2} + 48877645 T^{4} - 146585251874 T^{6} + 296639674915264 T^{8} - 414214887920726114 T^{10} +$$$$39\!\cdots\!45$$$$T^{12} -$$$$22\!\cdots\!86$$$$T^{14} +$$$$63\!\cdots\!41$$$$T^{16}$$)($$1 - 10494 T^{2} + 51364035 T^{4} - 152997660886 T^{6} + 310636210241223 T^{8} - 486286748354299068 T^{10} +$$$$74\!\cdots\!22$$$$T^{12} -$$$$13\!\cdots\!48$$$$T^{14} +$$$$24\!\cdots\!83$$$$T^{16} -$$$$34\!\cdots\!66$$$$T^{18} +$$$$32\!\cdots\!35$$$$T^{20} -$$$$18\!\cdots\!94$$$$T^{22} +$$$$50\!\cdots\!61$$$$T^{24}$$)
$43$ ($$( 1 - 176 T + 17017 T^{2} - 1139948 T^{3} + 56853640 T^{4} - 2107763852 T^{5} + 58177736617 T^{6} - 1112559896624 T^{7} + 11688200277601 T^{8} )^{2}$$)($$( 1 + 62 T + 7340 T^{2} + 336972 T^{3} + 27181828 T^{4} + 1019437474 T^{5} + 62011212778 T^{6} + 1884939889426 T^{7} + 92929260748228 T^{8} + 2130122349347628 T^{9} + 85791390037591340 T^{10} + 1339911903423623438 T^{11} + 39959630797262576401 T^{12} )^{2}$$)
$47$ ($$1 + 72 T + 10951 T^{2} + 664056 T^{3} + 65519473 T^{4} + 3342900456 T^{5} + 246192812578 T^{6} + 10750018584384 T^{7} + 651041931981118 T^{8} + 23746791052904256 T^{9} + 1201342389873427618 T^{10} + 36033843838636290024 T^{11} +$$$$15\!\cdots\!53$$$$T^{12} +$$$$34\!\cdots\!44$$$$T^{13} +$$$$12\!\cdots\!91$$$$T^{14} +$$$$18\!\cdots\!68$$$$T^{15} +$$$$56\!\cdots\!21$$$$T^{16}$$)($$1 - 96 T + 10053 T^{2} - 670176 T^{3} + 37816182 T^{4} - 1580720664 T^{5} + 53466325187 T^{6} - 1308296276496 T^{7} + 51809528884176 T^{8} - 4886895580883496 T^{9} + 455990427411620625 T^{10} - 31230646812310303944 T^{11} +$$$$16\!\cdots\!56$$$$T^{12} -$$$$68\!\cdots\!96$$$$T^{13} +$$$$22\!\cdots\!25$$$$T^{14} -$$$$52\!\cdots\!84$$$$T^{15} +$$$$12\!\cdots\!36$$$$T^{16} -$$$$68\!\cdots\!04$$$$T^{17} +$$$$62\!\cdots\!67$$$$T^{18} -$$$$40\!\cdots\!16$$$$T^{19} +$$$$21\!\cdots\!22$$$$T^{20} -$$$$83\!\cdots\!64$$$$T^{21} +$$$$27\!\cdots\!53$$$$T^{22} -$$$$58\!\cdots\!64$$$$T^{23} +$$$$13\!\cdots\!81$$$$T^{24}$$)
$53$ ($$1 + 76 T - 3069 T^{2} - 443764 T^{3} + 2229785 T^{4} + 1396117872 T^{5} + 34651196266 T^{6} - 1991894657480 T^{7} - 169369280357850 T^{8} - 5595232092861320 T^{9} + 273414605764143946 T^{10} + 30944060693658997488 T^{11} +$$$$13\!\cdots\!85$$$$T^{12} -$$$$77\!\cdots\!36$$$$T^{13} -$$$$15\!\cdots\!29$$$$T^{14} +$$$$10\!\cdots\!44$$$$T^{15} +$$$$38\!\cdots\!21$$$$T^{16}$$)($$1 + 76 T - 11231 T^{2} - 724524 T^{3} + 92836166 T^{4} + 4449767804 T^{5} - 540109351793 T^{6} - 16759328047612 T^{7} + 2565935011756424 T^{8} + 43462405312053452 T^{9} - 9681885823291571571 T^{10} - 46904208416898252492 T^{11} +$$$$30\!\cdots\!44$$$$T^{12} -$$$$13\!\cdots\!28$$$$T^{13} -$$$$76\!\cdots\!51$$$$T^{14} +$$$$96\!\cdots\!08$$$$T^{15} +$$$$15\!\cdots\!64$$$$T^{16} -$$$$29\!\cdots\!88$$$$T^{17} -$$$$26\!\cdots\!13$$$$T^{18} +$$$$61\!\cdots\!76$$$$T^{19} +$$$$35\!\cdots\!86$$$$T^{20} -$$$$78\!\cdots\!36$$$$T^{21} -$$$$34\!\cdots\!31$$$$T^{22} +$$$$65\!\cdots\!84$$$$T^{23} +$$$$24\!\cdots\!81$$$$T^{24}$$)
$59$ ($$1 + 54 T + 7198 T^{2} + 336204 T^{3} + 19932742 T^{4} - 202333950 T^{5} - 35478676088 T^{6} - 7641841019598 T^{7} - 385856896323245 T^{8} - 26601248589220638 T^{9} - 429907925960363768 T^{10} - 8534553984691411950 T^{11} +$$$$29\!\cdots\!82$$$$T^{12} +$$$$17\!\cdots\!04$$$$T^{13} +$$$$12\!\cdots\!38$$$$T^{14} +$$$$33\!\cdots\!94$$$$T^{15} +$$$$21\!\cdots\!41$$$$T^{16}$$)($$1 + 270 T + 48372 T^{2} + 6499440 T^{3} + 729674841 T^{4} + 72198474768 T^{5} + 6488082937652 T^{6} + 539451035302806 T^{7} + 41805568251303822 T^{8} + 3030722232785131878 T^{9} +$$$$20\!\cdots\!28$$$$T^{10} +$$$$13\!\cdots\!68$$$$T^{11} +$$$$80\!\cdots\!17$$$$T^{12} +$$$$46\!\cdots\!08$$$$T^{13} +$$$$25\!\cdots\!08$$$$T^{14} +$$$$12\!\cdots\!98$$$$T^{15} +$$$$61\!\cdots\!62$$$$T^{16} +$$$$27\!\cdots\!06$$$$T^{17} +$$$$11\!\cdots\!12$$$$T^{18} +$$$$44\!\cdots\!48$$$$T^{19} +$$$$15\!\cdots\!81$$$$T^{20} +$$$$48\!\cdots\!40$$$$T^{21} +$$$$12\!\cdots\!72$$$$T^{22} +$$$$24\!\cdots\!70$$$$T^{23} +$$$$31\!\cdots\!61$$$$T^{24}$$)
$61$ ($$1 + 396 T + 83164 T^{2} + 12233232 T^{3} + 1413738778 T^{4} + 136250283708 T^{5} + 11318984386192 T^{6} + 825650586150588 T^{7} + 53403008176121923 T^{8} + 3072245831066337948 T^{9} +$$$$15\!\cdots\!72$$$$T^{10} +$$$$70\!\cdots\!88$$$$T^{11} +$$$$27\!\cdots\!18$$$$T^{12} +$$$$87\!\cdots\!32$$$$T^{13} +$$$$22\!\cdots\!44$$$$T^{14} +$$$$39\!\cdots\!36$$$$T^{15} +$$$$36\!\cdots\!61$$$$T^{16}$$)($$1 + 60 T + 13086 T^{2} + 713160 T^{3} + 79444341 T^{4} + 3022528800 T^{5} + 251078089370 T^{6} + 4114433299500 T^{7} + 360604571968890 T^{8} - 6628548155521500 T^{9} + 198447695188114806 T^{10} - 25628280588886519440 T^{11} +$$$$58\!\cdots\!41$$$$T^{12} -$$$$95\!\cdots\!40$$$$T^{13} +$$$$27\!\cdots\!46$$$$T^{14} -$$$$34\!\cdots\!00$$$$T^{15} +$$$$69\!\cdots\!90$$$$T^{16} +$$$$29\!\cdots\!00$$$$T^{17} +$$$$66\!\cdots\!70$$$$T^{18} +$$$$29\!\cdots\!00$$$$T^{19} +$$$$29\!\cdots\!01$$$$T^{20} +$$$$97\!\cdots\!60$$$$T^{21} +$$$$66\!\cdots\!86$$$$T^{22} +$$$$11\!\cdots\!60$$$$T^{23} +$$$$70\!\cdots\!41$$$$T^{24}$$)
$67$ ($$1 - 184 T + 6231 T^{2} + 140176 T^{3} + 74370665 T^{4} - 7237038408 T^{5} + 24063966106 T^{6} - 15184872524680 T^{7} + 3087140085953070 T^{8} - 68164892763288520 T^{9} + 484915892741904826 T^{10} -$$$$65\!\cdots\!52$$$$T^{11} +$$$$30\!\cdots\!65$$$$T^{12} +$$$$25\!\cdots\!24$$$$T^{13} +$$$$50\!\cdots\!91$$$$T^{14} -$$$$67\!\cdots\!36$$$$T^{15} +$$$$16\!\cdots\!81$$$$T^{16}$$)($$1 + 18 T - 15576 T^{2} + 716224 T^{3} + 161647428 T^{4} - 11551101282 T^{5} - 593219478248 T^{6} + 115316141768802 T^{7} - 912928968126828 T^{8} - 541451373822575840 T^{9} + 35055175141983029184 T^{10} +$$$$12\!\cdots\!10$$$$T^{11} -$$$$20\!\cdots\!66$$$$T^{12} +$$$$55\!\cdots\!90$$$$T^{13} +$$$$70\!\cdots\!64$$$$T^{14} -$$$$48\!\cdots\!60$$$$T^{15} -$$$$37\!\cdots\!48$$$$T^{16} +$$$$21\!\cdots\!98$$$$T^{17} -$$$$48\!\cdots\!28$$$$T^{18} -$$$$42\!\cdots\!78$$$$T^{19} +$$$$26\!\cdots\!68$$$$T^{20} +$$$$53\!\cdots\!16$$$$T^{21} -$$$$51\!\cdots\!76$$$$T^{22} +$$$$26\!\cdots\!02$$$$T^{23} +$$$$66\!\cdots\!21$$$$T^{24}$$)
$71$ ($$( 1 - 82 T + 12166 T^{2} - 846262 T^{3} + 94594474 T^{4} - 4266006742 T^{5} + 309158511046 T^{6} - 10504223281522 T^{7} + 645753531245761 T^{8} )^{2}$$)($$( 1 + 314 T + 58704 T^{2} + 7369374 T^{3} + 727286203 T^{4} + 59185452824 T^{5} + 4395000293464 T^{6} + 298353867685784 T^{7} + 18481564986337243 T^{8} + 944018901720035454 T^{9} + 37908315298251153744 T^{10} +$$$$10\!\cdots\!14$$$$T^{11} +$$$$16\!\cdots\!41$$$$T^{12} )^{2}$$)
$73$ ($$1 - 348 T + 68263 T^{2} - 9707460 T^{3} + 1072498525 T^{4} - 96253557984 T^{5} + 7434307414846 T^{6} - 526544361727584 T^{7} + 37365046682274814 T^{8} - 2805954903646295136 T^{9} +$$$$21\!\cdots\!86$$$$T^{10} -$$$$14\!\cdots\!76$$$$T^{11} +$$$$86\!\cdots\!25$$$$T^{12} -$$$$41\!\cdots\!40$$$$T^{13} +$$$$15\!\cdots\!23$$$$T^{14} -$$$$42\!\cdots\!32$$$$T^{15} +$$$$65\!\cdots\!61$$$$T^{16}$$)($$1 - 234 T + 50280 T^{2} - 7494552 T^{3} + 1045125336 T^{4} - 124045277670 T^{5} + 13798749511760 T^{6} - 1393240344068466 T^{7} + 132320540590792632 T^{8} - 11749990134656584872 T^{9} +$$$$98\!\cdots\!48$$$$T^{10} -$$$$77\!\cdots\!58$$$$T^{11} +$$$$58\!\cdots\!42$$$$T^{12} -$$$$41\!\cdots\!82$$$$T^{13} +$$$$27\!\cdots\!68$$$$T^{14} -$$$$17\!\cdots\!08$$$$T^{15} +$$$$10\!\cdots\!92$$$$T^{16} -$$$$59\!\cdots\!34$$$$T^{17} +$$$$31\!\cdots\!60$$$$T^{18} -$$$$15\!\cdots\!30$$$$T^{19} +$$$$67\!\cdots\!96$$$$T^{20} -$$$$25\!\cdots\!88$$$$T^{21} +$$$$92\!\cdots\!80$$$$T^{22} -$$$$23\!\cdots\!86$$$$T^{23} +$$$$52\!\cdots\!41$$$$T^{24}$$)
$79$ ($$1 + 206 T + 5583 T^{2} - 659438 T^{3} + 124066817 T^{4} + 19494076044 T^{5} + 428008398310 T^{6} + 33090623674568 T^{7} + 7605703397631354 T^{8} + 206518582352978888 T^{9} + 16670961782854763110 T^{10} +$$$$47\!\cdots\!24$$$$T^{11} +$$$$18\!\cdots\!37$$$$T^{12} -$$$$62\!\cdots\!38$$$$T^{13} +$$$$32\!\cdots\!03$$$$T^{14} +$$$$75\!\cdots\!86$$$$T^{15} +$$$$23\!\cdots\!21$$$$T^{16}$$)($$1 - 108 T - 6108 T^{2} + 1752736 T^{3} - 90950172 T^{4} - 3971475972 T^{5} + 1036682005132 T^{6} - 72467068572108 T^{7} - 540849229955460 T^{8} + 549266052938802784 T^{9} - 33282724854561757956 T^{10} -$$$$11\!\cdots\!32$$$$T^{11} +$$$$26\!\cdots\!02$$$$T^{12} -$$$$70\!\cdots\!12$$$$T^{13} -$$$$12\!\cdots\!36$$$$T^{14} +$$$$13\!\cdots\!64$$$$T^{15} -$$$$82\!\cdots\!60$$$$T^{16} -$$$$68\!\cdots\!08$$$$T^{17} +$$$$61\!\cdots\!12$$$$T^{18} -$$$$14\!\cdots\!32$$$$T^{19} -$$$$20\!\cdots\!12$$$$T^{20} +$$$$25\!\cdots\!96$$$$T^{21} -$$$$54\!\cdots\!08$$$$T^{22} -$$$$60\!\cdots\!28$$$$T^{23} +$$$$34\!\cdots\!81$$$$T^{24}$$)
$83$ ($$1 - 20672 T^{2} + 223804480 T^{4} - 2182268545136 T^{6} + 17948924233578718 T^{8} -$$$$10\!\cdots\!56$$$$T^{10} +$$$$50\!\cdots\!80$$$$T^{12} -$$$$22\!\cdots\!92$$$$T^{14} +$$$$50\!\cdots\!81$$$$T^{16}$$)($$1 - 52956 T^{2} + 1343643534 T^{4} - 21859222482508 T^{6} + 258399723525197679 T^{8} -$$$$23\!\cdots\!76$$$$T^{10} +$$$$18\!\cdots\!16$$$$T^{12} -$$$$11\!\cdots\!96$$$$T^{14} +$$$$58\!\cdots\!39$$$$T^{16} -$$$$23\!\cdots\!88$$$$T^{18} +$$$$68\!\cdots\!54$$$$T^{20} -$$$$12\!\cdots\!56$$$$T^{22} +$$$$11\!\cdots\!21$$$$T^{24}$$)
$89$ ($$1 - 282 T + 59686 T^{2} - 9356196 T^{3} + 1240796086 T^{4} - 138656838366 T^{5} + 14271061565800 T^{6} - 1337157406377822 T^{7} + 121622616146107507 T^{8} - 10591623815918728062 T^{9} +$$$$89\!\cdots\!00$$$$T^{10} -$$$$68\!\cdots\!26$$$$T^{11} +$$$$48\!\cdots\!66$$$$T^{12} -$$$$29\!\cdots\!96$$$$T^{13} +$$$$14\!\cdots\!06$$$$T^{14} -$$$$55\!\cdots\!62$$$$T^{15} +$$$$15\!\cdots\!61$$$$T^{16}$$)($$1 + 186 T + 44532 T^{2} + 6138000 T^{3} + 889877673 T^{4} + 104389916664 T^{5} + 11976622429892 T^{6} + 1266314492339586 T^{7} + 128180246542580718 T^{8} + 12521360973919319370 T^{9} +$$$$11\!\cdots\!68$$$$T^{10} +$$$$10\!\cdots\!44$$$$T^{11} +$$$$99\!\cdots\!61$$$$T^{12} +$$$$86\!\cdots\!24$$$$T^{13} +$$$$74\!\cdots\!88$$$$T^{14} +$$$$62\!\cdots\!70$$$$T^{15} +$$$$50\!\cdots\!58$$$$T^{16} +$$$$39\!\cdots\!86$$$$T^{17} +$$$$29\!\cdots\!32$$$$T^{18} +$$$$20\!\cdots\!24$$$$T^{19} +$$$$13\!\cdots\!53$$$$T^{20} +$$$$75\!\cdots\!00$$$$T^{21} +$$$$43\!\cdots\!32$$$$T^{22} +$$$$14\!\cdots\!06$$$$T^{23} +$$$$61\!\cdots\!41$$$$T^{24}$$)
$97$ ($$1 - 44576 T^{2} + 925514428 T^{4} - 12414040936928 T^{6} + 128325632901816454 T^{8} -$$$$10\!\cdots\!68$$$$T^{10} +$$$$72\!\cdots\!08$$$$T^{12} -$$$$30\!\cdots\!16$$$$T^{14} +$$$$61\!\cdots\!21$$$$T^{16}$$)($$1 - 64740 T^{2} + 2084566242 T^{4} - 44252577868756 T^{6} + 697286703828717423 T^{8} -$$$$87\!\cdots\!56$$$$T^{10} +$$$$89\!\cdots\!48$$$$T^{12} -$$$$77\!\cdots\!36$$$$T^{14} +$$$$54\!\cdots\!03$$$$T^{16} -$$$$30\!\cdots\!96$$$$T^{18} +$$$$12\!\cdots\!82$$$$T^{20} -$$$$35\!\cdots\!40$$$$T^{22} +$$$$48\!\cdots\!81$$$$T^{24}$$)