Properties

Label 126.2.t
Level 126
Weight 2
Character orbit t
Rep. character \(\chi_{126}(47,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 16
Newform subspaces 1
Sturm bound 48
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 126.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(126, [\chi])\).

Total New Old
Modular forms 56 16 40
Cusp forms 40 16 24
Eisenstein series 16 0 16

Trace form

\( 16q + 8q^{4} + 2q^{7} - 6q^{9} + O(q^{10}) \) \( 16q + 8q^{4} + 2q^{7} - 6q^{9} - 6q^{13} - 6q^{14} - 18q^{15} - 8q^{16} + 18q^{17} + 12q^{18} - 18q^{21} - 6q^{24} + 16q^{25} - 12q^{26} - 36q^{27} - 2q^{28} + 6q^{29} - 18q^{30} + 6q^{31} + 18q^{33} - 30q^{35} - 2q^{37} - 30q^{39} + 6q^{41} + 30q^{42} - 2q^{43} + 12q^{44} + 12q^{45} + 6q^{46} - 18q^{47} + 10q^{49} - 12q^{50} + 36q^{53} + 18q^{54} + 6q^{57} - 12q^{58} + 30q^{59} - 6q^{60} - 60q^{61} - 36q^{62} + 42q^{63} - 16q^{64} + 42q^{65} + 48q^{66} + 14q^{67} + 36q^{68} + 42q^{69} + 30q^{75} - 18q^{77} - 16q^{79} + 54q^{81} - 18q^{84} - 12q^{85} - 48q^{87} + 24q^{89} - 18q^{90} - 12q^{91} + 6q^{92} + 30q^{93} - 66q^{95} - 6q^{96} - 6q^{97} + 24q^{98} + 18q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
126.2.t.a \(16\) \(1.006\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(2\) \(q+(-\beta _{1}+\beta _{6})q^{2}+(-\beta _{11}-\beta _{14})q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(126, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( ( 1 - T^{2} + T^{4} )^{4} \)
$3$ \( 1 + 3 T^{2} + 12 T^{3} - 9 T^{4} + 54 T^{5} + 45 T^{6} - 18 T^{7} + 441 T^{8} - 54 T^{9} + 405 T^{10} + 1458 T^{11} - 729 T^{12} + 2916 T^{13} + 2187 T^{14} + 6561 T^{16} \)
$5$ \( ( 1 + 16 T^{2} + 12 T^{3} + 133 T^{4} + 138 T^{5} + 943 T^{6} + 696 T^{7} + 5539 T^{8} + 3480 T^{9} + 23575 T^{10} + 17250 T^{11} + 83125 T^{12} + 37500 T^{13} + 250000 T^{14} + 390625 T^{16} )^{2} \)
$7$ \( 1 - 2 T - 3 T^{2} + 26 T^{3} - 67 T^{4} - 84 T^{5} + 355 T^{6} + 40 T^{7} - 675 T^{8} + 280 T^{9} + 17395 T^{10} - 28812 T^{11} - 160867 T^{12} + 436982 T^{13} - 352947 T^{14} - 1647086 T^{15} + 5764801 T^{16} \)
$11$ \( 1 - 68 T^{2} + 2622 T^{4} - 71710 T^{6} + 1545179 T^{8} - 27618072 T^{10} + 422760301 T^{12} - 5636332820 T^{14} + 66055843863 T^{16} - 681996271220 T^{18} + 6189633566941 T^{20} - 48927099250392 T^{22} + 331222841384699 T^{24} - 1859972718137710 T^{26} + 8228959203762462 T^{28} - 25822988683660388 T^{30} + 45949729863572161 T^{32} \)
$13$ \( 1 + 6 T + 47 T^{2} + 210 T^{3} + 888 T^{4} + 2658 T^{5} + 9181 T^{6} + 12564 T^{7} + 21641 T^{8} - 214770 T^{9} - 1221396 T^{10} - 6263526 T^{11} - 19011605 T^{12} - 72302586 T^{13} - 179114935 T^{14} - 742674348 T^{15} - 2320143696 T^{16} - 9654766524 T^{17} - 30270424015 T^{18} - 158848781442 T^{19} - 542990450405 T^{20} - 2325603359118 T^{21} - 5895445205364 T^{22} - 13476498996090 T^{23} + 17653228533161 T^{24} + 133234930122372 T^{25} + 1265678813665669 T^{26} + 4763562327350346 T^{27} + 20688699588763128 T^{28} + 63603772384373130 T^{29} + 185056690127866583 T^{30} + 307115358084544542 T^{31} + 665416609183179841 T^{32} \)
$17$ \( 1 - 18 T + 95 T^{2} + 42 T^{3} - 849 T^{4} - 7584 T^{5} + 29152 T^{6} + 139356 T^{7} - 154873 T^{8} - 2564070 T^{9} - 13186653 T^{10} + 89037906 T^{11} + 222290986 T^{12} - 933503742 T^{13} - 5890959001 T^{14} + 7644891330 T^{15} + 98422426836 T^{16} + 129963152610 T^{17} - 1702487151289 T^{18} - 4586303884446 T^{19} + 18565965441706 T^{20} + 126421094099442 T^{21} - 318293746666557 T^{22} - 1052137081279110 T^{23} - 1080356482159993 T^{24} + 16525932117115932 T^{25} + 58770254185889248 T^{26} - 259918061597088672 T^{27} - 494646279408067089 T^{28} + 415992277382049354 T^{29} + 15995893523143088255 T^{30} - 51523614927176684274 T^{31} + 48661191875666868481 T^{32} \)
$19$ \( 1 + 80 T^{2} + 3483 T^{4} - 882 T^{5} + 107770 T^{6} - 26190 T^{7} + 2596658 T^{8} + 477594 T^{9} + 51326154 T^{10} + 58243698 T^{11} + 858124540 T^{12} + 2331197604 T^{13} + 13169269781 T^{14} + 60976736712 T^{15} + 222780924306 T^{16} + 1158557997528 T^{17} + 4754106390941 T^{18} + 15989684365836 T^{19} + 111831648177340 T^{20} + 144217162374102 T^{21} + 2414684133271674 T^{22} + 426907779315966 T^{23} + 44100504838916978 T^{24} - 8451190804832010 T^{25} + 660745010603213770 T^{26} - 102744408348229158 T^{27} + 7708975863107438763 T^{28} + 63920534862630729680 T^{30} + \)\(28\!\cdots\!81\)\( T^{32} \)
$23$ \( 1 - 224 T^{2} + 24654 T^{4} - 1769830 T^{6} + 93146507 T^{8} - 3841107576 T^{10} + 129779286901 T^{12} - 3708814203716 T^{14} + 91488095720271 T^{16} - 1961962713765764 T^{18} + 36317565425662741 T^{20} - 568621774757795064 T^{22} + 7294394738653563467 T^{24} - 73317882341252409670 T^{26} + \)\(54\!\cdots\!34\)\( T^{28} - \)\(25\!\cdots\!16\)\( T^{30} + \)\(61\!\cdots\!61\)\( T^{32} \)
$29$ \( 1 - 6 T + 196 T^{2} - 1104 T^{3} + 19989 T^{4} - 108858 T^{5} + 1435478 T^{6} - 7594740 T^{7} + 81322766 T^{8} - 416245488 T^{9} + 3844091772 T^{10} - 18872529852 T^{11} + 155981060614 T^{12} - 727660406082 T^{13} + 5509975202215 T^{14} - 24244157784798 T^{15} + 170557455776958 T^{16} - 703080575759142 T^{17} + 4633889145062815 T^{18} - 17746909643933898 T^{19} + 110322440532130534 T^{20} - 387097271801319948 T^{21} + 2286555434049814812 T^{22} - 7180183182179343792 T^{23} + 40681421983566770126 T^{24} - \)\(11\!\cdots\!60\)\( T^{25} + \)\(60\!\cdots\!78\)\( T^{26} - \)\(13\!\cdots\!82\)\( T^{27} + \)\(70\!\cdots\!49\)\( T^{28} - \)\(11\!\cdots\!56\)\( T^{29} + \)\(58\!\cdots\!76\)\( T^{30} - \)\(51\!\cdots\!94\)\( T^{31} + \)\(25\!\cdots\!21\)\( T^{32} \)
$31$ \( 1 - 6 T + 164 T^{2} - 912 T^{3} + 14145 T^{4} - 82056 T^{5} + 882730 T^{6} - 5457276 T^{7} + 44537675 T^{8} - 289281588 T^{9} + 1950112812 T^{10} - 12838947000 T^{11} + 76837130221 T^{12} - 493000882878 T^{13} + 2756895706292 T^{14} - 16890347347524 T^{15} + 89911869890409 T^{16} - 523600767773244 T^{17} + 2649376773746612 T^{18} - 14686989301818498 T^{19} + 70960703338828141 T^{20} - 367568152343997000 T^{21} + 1730732299015260972 T^{22} - 7958892700061288268 T^{23} + 37985783835960089675 T^{24} - \)\(14\!\cdots\!96\)\( T^{25} + \)\(72\!\cdots\!30\)\( T^{26} - \)\(20\!\cdots\!36\)\( T^{27} + \)\(11\!\cdots\!45\)\( T^{28} - \)\(22\!\cdots\!92\)\( T^{29} + \)\(12\!\cdots\!44\)\( T^{30} - \)\(14\!\cdots\!06\)\( T^{31} + \)\(72\!\cdots\!81\)\( T^{32} \)
$37$ \( 1 + 2 T - 116 T^{2} - 656 T^{3} + 3854 T^{4} + 48538 T^{5} + 98460 T^{6} - 747702 T^{7} - 5251023 T^{8} - 50514234 T^{9} - 417738792 T^{10} + 801423570 T^{11} + 29966075382 T^{12} + 116541321036 T^{13} - 322717550496 T^{14} - 3343790405826 T^{15} - 14327838321804 T^{16} - 123720245015562 T^{17} - 441800326629024 T^{18} + 5903167534436508 T^{19} + 56161249804004502 T^{20} + 55573881576866490 T^{21} - 1071803450698157928 T^{22} - 4795411055555611122 T^{23} - 18444110399566611183 T^{24} - 97172652768258663054 T^{25} + \)\(47\!\cdots\!40\)\( T^{26} + \)\(86\!\cdots\!94\)\( T^{27} + \)\(25\!\cdots\!74\)\( T^{28} - \)\(15\!\cdots\!32\)\( T^{29} - \)\(10\!\cdots\!24\)\( T^{30} + \)\(66\!\cdots\!86\)\( T^{31} + \)\(12\!\cdots\!41\)\( T^{32} \)
$41$ \( 1 - 6 T - 223 T^{2} + 1686 T^{3} + 25980 T^{4} - 231654 T^{5} - 1971341 T^{6} + 20408106 T^{7} + 109216031 T^{8} - 1268388768 T^{9} - 4836103872 T^{10} + 57438167556 T^{11} + 192545389345 T^{12} - 1824668193534 T^{13} - 7677147470143 T^{14} + 27964729912410 T^{15} + 313424888729076 T^{16} + 1146553926408810 T^{17} - 12905284897310383 T^{18} - 125757956566556814 T^{19} + 544087251940916545 T^{20} + 6654567885439614756 T^{21} - 22971997512303721152 T^{22} - \)\(24\!\cdots\!08\)\( T^{23} + \)\(87\!\cdots\!51\)\( T^{24} + \)\(66\!\cdots\!66\)\( T^{25} - \)\(26\!\cdots\!41\)\( T^{26} - \)\(12\!\cdots\!14\)\( T^{27} + \)\(58\!\cdots\!80\)\( T^{28} + \)\(15\!\cdots\!06\)\( T^{29} - \)\(84\!\cdots\!03\)\( T^{30} - \)\(93\!\cdots\!06\)\( T^{31} + \)\(63\!\cdots\!41\)\( T^{32} \)
$43$ \( 1 + 2 T - 209 T^{2} - 602 T^{3} + 20774 T^{4} + 72052 T^{5} - 1457073 T^{6} - 4933350 T^{7} + 91147851 T^{8} + 235722522 T^{9} - 5466637218 T^{10} - 9144255228 T^{11} + 301177025103 T^{12} + 290829011802 T^{13} - 14773623661707 T^{14} - 4808085837138 T^{15} + 658882369500660 T^{16} - 206747690996934 T^{17} - 27316430150496243 T^{18} + 23122942241341614 T^{19} + 1029664314599161503 T^{20} - 1344282723462890004 T^{21} - 34556598512153357682 T^{22} + 64073768536679251854 T^{23} + \)\(10\!\cdots\!51\)\( T^{24} - \)\(24\!\cdots\!50\)\( T^{25} - \)\(31\!\cdots\!77\)\( T^{26} + \)\(66\!\cdots\!64\)\( T^{27} + \)\(83\!\cdots\!74\)\( T^{28} - \)\(10\!\cdots\!86\)\( T^{29} - \)\(15\!\cdots\!41\)\( T^{30} + \)\(63\!\cdots\!14\)\( T^{31} + \)\(13\!\cdots\!01\)\( T^{32} \)
$47$ \( 1 + 18 T - 55 T^{2} - 1722 T^{3} + 12957 T^{4} + 149790 T^{5} - 1485620 T^{6} - 10153800 T^{7} + 96840002 T^{8} + 357022848 T^{9} - 6832958010 T^{10} - 20400467106 T^{11} + 370230517390 T^{12} + 853239339180 T^{13} - 20043242784151 T^{14} - 7467517424682 T^{15} + 1132351959046185 T^{16} - 350973318960054 T^{17} - 44275523310189559 T^{18} + 88585867911685140 T^{19} + 1806606821328152590 T^{20} - 4678745271228839742 T^{21} - 73653925723805335290 T^{22} + \)\(18\!\cdots\!24\)\( T^{23} + \)\(23\!\cdots\!22\)\( T^{24} - \)\(11\!\cdots\!00\)\( T^{25} - \)\(78\!\cdots\!80\)\( T^{26} + \)\(37\!\cdots\!70\)\( T^{27} + \)\(15\!\cdots\!37\)\( T^{28} - \)\(94\!\cdots\!94\)\( T^{29} - \)\(14\!\cdots\!95\)\( T^{30} + \)\(21\!\cdots\!74\)\( T^{31} + \)\(56\!\cdots\!21\)\( T^{32} \)
$53$ \( 1 - 36 T + 766 T^{2} - 12024 T^{3} + 153999 T^{4} - 1662408 T^{5} + 15312632 T^{6} - 121481640 T^{7} + 835010600 T^{8} - 5038052724 T^{9} + 28358007246 T^{10} - 182105031078 T^{11} + 1622318702806 T^{12} - 17289317216124 T^{13} + 177226593270661 T^{14} - 1605696832118286 T^{15} + 12594715934262750 T^{16} - 85101932102269158 T^{17} + 497829500497286749 T^{18} - 2573981679184892748 T^{19} + 12800874900435389686 T^{20} - 76155503249444531454 T^{21} + \)\(62\!\cdots\!34\)\( T^{22} - \)\(59\!\cdots\!88\)\( T^{23} + \)\(51\!\cdots\!00\)\( T^{24} - \)\(40\!\cdots\!20\)\( T^{25} + \)\(26\!\cdots\!68\)\( T^{26} - \)\(15\!\cdots\!76\)\( T^{27} + \)\(75\!\cdots\!59\)\( T^{28} - \)\(31\!\cdots\!52\)\( T^{29} + \)\(10\!\cdots\!54\)\( T^{30} - \)\(26\!\cdots\!52\)\( T^{31} + \)\(38\!\cdots\!21\)\( T^{32} \)
$59$ \( 1 - 30 T + 200 T^{2} + 1272 T^{3} + 1905 T^{4} - 286356 T^{5} - 330074 T^{6} + 21958908 T^{7} + 129465491 T^{8} - 1641971784 T^{9} - 13037705556 T^{10} + 82617584088 T^{11} + 950143418149 T^{12} - 1952014889118 T^{13} - 70581518213368 T^{14} + 49596128462484 T^{15} + 4103530612541721 T^{16} + 2926171579286556 T^{17} - 245694264900734008 T^{18} - 400902865912165722 T^{19} + 11513230799485384789 T^{20} + 59065318389186954312 T^{21} - \)\(54\!\cdots\!96\)\( T^{22} - \)\(40\!\cdots\!96\)\( T^{23} + \)\(19\!\cdots\!11\)\( T^{24} + \)\(19\!\cdots\!12\)\( T^{25} - \)\(16\!\cdots\!74\)\( T^{26} - \)\(86\!\cdots\!04\)\( T^{27} + \)\(33\!\cdots\!05\)\( T^{28} + \)\(13\!\cdots\!88\)\( T^{29} + \)\(12\!\cdots\!00\)\( T^{30} - \)\(10\!\cdots\!70\)\( T^{31} + \)\(21\!\cdots\!41\)\( T^{32} \)
$61$ \( 1 + 60 T + 2036 T^{2} + 50160 T^{3} + 994527 T^{4} + 16748022 T^{5} + 247695826 T^{6} + 3290908266 T^{7} + 39930949007 T^{8} + 448092194298 T^{9} + 4697101745298 T^{10} + 46372941826116 T^{11} + 434191490396749 T^{12} + 3878280141400200 T^{13} + 33210009451501436 T^{14} + 273658668372668376 T^{15} + 2175265354887641205 T^{16} + 16693178770732770936 T^{17} + \)\(12\!\cdots\!56\)\( T^{18} + \)\(88\!\cdots\!00\)\( T^{19} + \)\(60\!\cdots\!09\)\( T^{20} + \)\(39\!\cdots\!16\)\( T^{21} + \)\(24\!\cdots\!78\)\( T^{22} + \)\(14\!\cdots\!58\)\( T^{23} + \)\(76\!\cdots\!67\)\( T^{24} + \)\(38\!\cdots\!06\)\( T^{25} + \)\(17\!\cdots\!26\)\( T^{26} + \)\(72\!\cdots\!42\)\( T^{27} + \)\(26\!\cdots\!67\)\( T^{28} + \)\(81\!\cdots\!60\)\( T^{29} + \)\(20\!\cdots\!76\)\( T^{30} + \)\(36\!\cdots\!60\)\( T^{31} + \)\(36\!\cdots\!61\)\( T^{32} \)
$67$ \( 1 - 14 T - 239 T^{2} + 5102 T^{3} + 20453 T^{4} - 910354 T^{5} + 617796 T^{6} + 105135588 T^{7} - 361795050 T^{8} - 8998911156 T^{9} + 52479815982 T^{10} + 604126066254 T^{11} - 5379501807402 T^{12} - 30548371355232 T^{13} + 457126004374545 T^{14} + 769012940073186 T^{15} - 33126987823382439 T^{16} + 51523866984903462 T^{17} + 2052038633637332505 T^{18} - 9187819813913642016 T^{19} - \)\(10\!\cdots\!42\)\( T^{20} + \)\(81\!\cdots\!78\)\( T^{21} + \)\(47\!\cdots\!58\)\( T^{22} - \)\(54\!\cdots\!88\)\( T^{23} - \)\(14\!\cdots\!50\)\( T^{24} + \)\(28\!\cdots\!36\)\( T^{25} + \)\(11\!\cdots\!04\)\( T^{26} - \)\(11\!\cdots\!82\)\( T^{27} + \)\(16\!\cdots\!33\)\( T^{28} + \)\(27\!\cdots\!74\)\( T^{29} - \)\(87\!\cdots\!31\)\( T^{30} - \)\(34\!\cdots\!02\)\( T^{31} + \)\(16\!\cdots\!81\)\( T^{32} \)
$71$ \( 1 - 650 T^{2} + 199389 T^{4} - 38930632 T^{6} + 5566228364 T^{8} - 640511863116 T^{10} + 63163988645884 T^{12} - 5475157404521894 T^{14} + 416179213677825948 T^{16} - 27600268476194867654 T^{18} + \)\(16\!\cdots\!04\)\( T^{20} - \)\(82\!\cdots\!36\)\( T^{22} + \)\(35\!\cdots\!04\)\( T^{24} - \)\(12\!\cdots\!32\)\( T^{26} + \)\(32\!\cdots\!49\)\( T^{28} - \)\(53\!\cdots\!50\)\( T^{30} + \)\(41\!\cdots\!21\)\( T^{32} \)
$73$ \( 1 + 434 T^{2} + 101253 T^{4} + 70380 T^{5} + 16361620 T^{6} + 29833866 T^{7} + 2027081504 T^{8} + 6817588704 T^{9} + 204710173188 T^{10} + 1064159524062 T^{11} + 17706469884892 T^{12} + 124668495857988 T^{13} + 1383495353685575 T^{14} + 11427374402737884 T^{15} + 102528286806790386 T^{16} + 834198331399865532 T^{17} + 7372646739790429175 T^{18} + 48498164253186917796 T^{19} + \)\(50\!\cdots\!72\)\( T^{20} + \)\(22\!\cdots\!66\)\( T^{21} + \)\(30\!\cdots\!32\)\( T^{22} + \)\(75\!\cdots\!88\)\( T^{23} + \)\(16\!\cdots\!24\)\( T^{24} + \)\(17\!\cdots\!58\)\( T^{25} + \)\(70\!\cdots\!80\)\( T^{26} + \)\(22\!\cdots\!60\)\( T^{27} + \)\(23\!\cdots\!13\)\( T^{28} + \)\(52\!\cdots\!06\)\( T^{30} + \)\(65\!\cdots\!61\)\( T^{32} \)
$79$ \( 1 + 16 T - 227 T^{2} - 5356 T^{3} + 15491 T^{4} + 818138 T^{5} + 465174 T^{6} - 79955730 T^{7} - 161428446 T^{8} + 5129891178 T^{9} + 6184544046 T^{10} - 147661653486 T^{11} + 2275304241738 T^{12} - 3934261822074 T^{13} - 453211437102513 T^{14} + 289666157971230 T^{15} + 45106559543464353 T^{16} + 22883626479727170 T^{17} - 2828492578956783633 T^{18} - 1939744514493542886 T^{19} + 88623284515338680778 T^{20} - \)\(45\!\cdots\!14\)\( T^{21} + \)\(15\!\cdots\!66\)\( T^{22} + \)\(98\!\cdots\!02\)\( T^{23} - \)\(24\!\cdots\!06\)\( T^{24} - \)\(95\!\cdots\!70\)\( T^{25} + \)\(44\!\cdots\!74\)\( T^{26} + \)\(61\!\cdots\!02\)\( T^{27} + \)\(91\!\cdots\!31\)\( T^{28} - \)\(25\!\cdots\!84\)\( T^{29} - \)\(83\!\cdots\!87\)\( T^{30} + \)\(46\!\cdots\!84\)\( T^{31} + \)\(23\!\cdots\!21\)\( T^{32} \)
$83$ \( 1 - 487 T^{2} - 312 T^{3} + 123774 T^{4} + 132990 T^{5} - 22183883 T^{6} - 29138634 T^{7} + 3170469341 T^{8} + 4110229572 T^{9} - 386467088226 T^{10} - 393115428402 T^{11} + 41656592194789 T^{12} + 25282823866380 T^{13} - 4030130568645907 T^{14} - 780079655467782 T^{15} + 351851707607703156 T^{16} - 64746611403825906 T^{17} - 27763569487401653323 T^{18} + 14456390010085821060 T^{19} + \)\(19\!\cdots\!69\)\( T^{20} - \)\(15\!\cdots\!86\)\( T^{21} - \)\(12\!\cdots\!94\)\( T^{22} + \)\(11\!\cdots\!44\)\( T^{23} + \)\(71\!\cdots\!81\)\( T^{24} - \)\(54\!\cdots\!02\)\( T^{25} - \)\(34\!\cdots\!67\)\( T^{26} + \)\(17\!\cdots\!30\)\( T^{27} + \)\(13\!\cdots\!14\)\( T^{28} - \)\(27\!\cdots\!56\)\( T^{29} - \)\(35\!\cdots\!23\)\( T^{30} + \)\(50\!\cdots\!81\)\( T^{32} \)
$89$ \( 1 - 24 T - 10 T^{2} + 3636 T^{3} + 1197 T^{4} - 543420 T^{5} + 1792912 T^{6} + 58468350 T^{7} - 544062388 T^{8} - 3510821196 T^{9} + 61278252588 T^{10} + 296095488138 T^{11} - 6613804791944 T^{12} - 16297764313308 T^{13} + 597103648531739 T^{14} - 218011613471172 T^{15} - 39896652829458150 T^{16} - 19403033598934308 T^{17} + 4729658000019904619 T^{18} - 11489418610188427452 T^{19} - \)\(41\!\cdots\!04\)\( T^{20} + \)\(16\!\cdots\!62\)\( T^{21} + \)\(30\!\cdots\!68\)\( T^{22} - \)\(15\!\cdots\!84\)\( T^{23} - \)\(21\!\cdots\!28\)\( T^{24} + \)\(20\!\cdots\!50\)\( T^{25} + \)\(55\!\cdots\!12\)\( T^{26} - \)\(15\!\cdots\!80\)\( T^{27} + \)\(29\!\cdots\!37\)\( T^{28} + \)\(79\!\cdots\!84\)\( T^{29} - \)\(19\!\cdots\!10\)\( T^{30} - \)\(41\!\cdots\!76\)\( T^{31} + \)\(15\!\cdots\!61\)\( T^{32} \)
$97$ \( 1 + 6 T + 395 T^{2} + 2298 T^{3} + 68379 T^{4} + 571872 T^{5} + 8922340 T^{6} + 109039644 T^{7} + 1233764039 T^{8} + 14418445794 T^{9} + 171203907675 T^{10} + 1605167799666 T^{11} + 21002714173786 T^{12} + 194363495836338 T^{13} + 2133943680044999 T^{14} + 22669145285986746 T^{15} + 200280216945639852 T^{16} + 2198907092740714362 T^{17} + 20078276085543395591 T^{18} + \)\(17\!\cdots\!74\)\( T^{19} + \)\(18\!\cdots\!66\)\( T^{20} + \)\(13\!\cdots\!62\)\( T^{21} + \)\(14\!\cdots\!75\)\( T^{22} + \)\(11\!\cdots\!22\)\( T^{23} + \)\(96\!\cdots\!79\)\( T^{24} + \)\(82\!\cdots\!48\)\( T^{25} + \)\(65\!\cdots\!60\)\( T^{26} + \)\(40\!\cdots\!16\)\( T^{27} + \)\(47\!\cdots\!39\)\( T^{28} + \)\(15\!\cdots\!46\)\( T^{29} + \)\(25\!\cdots\!55\)\( T^{30} + \)\(37\!\cdots\!58\)\( T^{31} + \)\(61\!\cdots\!21\)\( T^{32} \)
show more
show less