Properties

Label 1.64
Level 1
Weight 64
Dimension 5
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 64 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{64}(\Gamma_1(1))\).

Total New Old
Modular forms 6 6 0
Cusp forms 5 5 0
Eisenstein series 1 1 0

Trace form

\( 5q + 507315096q^{2} + 953245351116252q^{3} + 6772922881670488640q^{4} - 501184199539643271930q^{5} + 1068627718494014524169760q^{6} + 376817877722086399439439256q^{7} + 7373083738744782322804569600q^{8} + 637396295620644432934325521785q^{9} + O(q^{10}) \) \( 5q + 507315096q^{2} + 953245351116252q^{3} + 6772922881670488640q^{4} - 501184199539643271930q^{5} + 1068627718494014524169760q^{6} + 376817877722086399439439256q^{7} + 7373083738744782322804569600q^{8} + 637396295620644432934325521785q^{9} + 34805720696971516624169126640720q^{10} - 540229094938924469136867622360140q^{11} - 2623634227414171572600561756413184q^{12} + 108181792532202432266404872185866462q^{13} - 54084971043930392944098441496816320q^{14} - 348660153327675947104166235548634360q^{15} - 15159504282791660159626289035944325120q^{16} + 233526732797217220125532397644743920826q^{17} - 878288957740682168785729261423496761608q^{18} - 7865422683256304571013031795593188000500q^{19} + 119732404991815793713722982154585901682560q^{20} + 129742883997422764536533691448958694051360q^{21} + 522423012385730886331292903044579480248672q^{22} + 15741757721943761462993254761236931413817672q^{23} + 81420550986598778904562391448937582504396800q^{24} + 292140347366023827983252525250222472224504275q^{25} + 1839051975856323981143175281915543784076214160q^{26} + 5995620820889371589085528605465633389174051800q^{27} + 20537937802314435233418391499696666641793064448q^{28} + 50794057939113445336173371211400804999575041550q^{29} + 119599751674209323591694650465650283116522069440q^{30} + 159433862626305294394996530486509737703620382560q^{31} - 288839096991246799804118797555409689201302994944q^{32} - 1985039125536508051580230500373193506662510782736q^{33} - 7795229014190619843231021275250308444731969968720q^{34} - 10557440874563511263423843961508717076049161308080q^{35} - 37204859885919911089599455494799964973968364182720q^{36} - 17147796860746064343272909856513075508644081479834q^{37} + 96961175243860213325076480378784661216846555556000q^{38} + 492167917497720661901422065953515470410075070510120q^{39} + 896446641636036625169137129815741762131481186432000q^{40} + 1559678150469731047687963466434444190641664714862210q^{41} + 2081496056204279968289878006271140331858037130897152q^{42} - 2983480654504430801847803264567818556163926831907308q^{43} - 18694374606435020769086358744659889563339255880625920q^{44} - 42915794659164783458146544031317844487388645901128610q^{45} - 51138823220473279961598851250008086980240261547467840q^{46} - 48803318103437656200328895986865036348129901500078064q^{47} + 105030731921033071573566542229505770762259930957135872q^{48} + 339954400631541607259125157882259489058114941961211565q^{49} + 1145766254187619060443643128490826898486806978223935400q^{50} + 1573856653389132533580410794526319320841950113639520760q^{51} + 1100089067926371487906797270480194411314440787489242496q^{52} - 692620923468041120314769654783046236221069399596219498q^{53} - 12241254713499812360048511900337793888058128715691896000q^{54} - 20518321028364082359377216700393318257347660689712574760q^{55} - 23023175950768775440489799736204099376922285452382515200q^{56} - 17165930318654624911621905238013222730357511047458838000q^{57} + 24263146187335234519264617757094026741989307665448630800q^{58} + 105022627362831482575423381645924825912298204628844229700q^{59} + 348815801318717337128814346317462318028682012888660421120q^{60} + 392008741666961324913019363738714690637509013784647052910q^{61} + 517886811617172418873631635177191658868452247595279666432q^{62} - 688525987399009316135147212418376806290326301310285121288q^{63} - 2180009675566773867746832715393348298244228612034924380160q^{64} - 1790351395436014012859210003100506705478557202772387149660q^{65} - 5560362505883676488751771192389016447628360456591147025280q^{66} - 4772918882566263586387384393016421637717756025307890516324q^{67} - 1217235811705845972574871765837936700542360337637019524992q^{68} + 17361351448150889077637265817219083285785250426768721895520q^{69} + 40370459686415885897530019946258677235420585269803429288320q^{70} + 50262977800159315724835086683846685501725736129988791785560q^{71} + 61741978698481390141302726420710704640623611541551890419200q^{72} - 29866935912976824238577353448611378509570684111927150030878q^{73} - 141849784351445213753933251006028603295768815102096738143920q^{74} - 201957285133938827818209142762872334198535626872978135872700q^{75} - 459524449626729728237506845156327517313622138193176308998400q^{76} - 584903691091230632807084878932757448595860972050144651202208q^{77} - 22402086294347989122673287092781322891691396539029809599296q^{78} + 585575205089660590838265168880022777028257388453771607481200q^{79} + 1073190252220259266057147746504064677993096991374081580523520q^{80} + 4533130095818971466699734318425466519486071025110491052925005q^{81} + 3942135409805155170887010182148436012685330945941771799686512q^{82} + 2788245690403819754860784912585317051147818763920351702275532q^{83} - 126919894267453303311398867974653650894429551428194565150720q^{84} - 12285625873772156133384209670234539029240309631211205889028180q^{85} - 25827853637025878857294346599932142285683441775204060440193440q^{86} - 16639728321686122963829124023195021859110126733857984457365400q^{87} - 37714047968515707622032367000426709169856663409503596568012800q^{88} + 3261564182425241052169353984916675793465907809562936240181650q^{89} + 3967145115564708643943604045640844654494980994165877917975440q^{90} + 108036910334048530340065483166305935475510347360713558662966160q^{91} + 166995545147622332685032938656047356744592976712074780741106176q^{92} + 379916756753184270638361497392906589593938589120992563130336384q^{93} - 20439950593005273708597610879292286110217691498870249996014720q^{94} + 135646904668873700623162464290893387798407178357502623630425000q^{95} - 903336283885608238754961378979276328179547455316018655408291840q^{96} - 171116727826062583131545726181696338626852935879476361892307414q^{97} - 1942373455669362555509787890732368496523562886191617825973826472q^{98} - 126634984461121539221842595814731567513779549557792846854185980q^{99} + O(q^{100}) \)

Decomposition of \(S_{64}^{\mathrm{new}}(\Gamma_1(1))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1.64.a \(\chi_{1}(1, \cdot)\) 1.64.a.a 5 1

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 507315096 T + 19800652954616439808 T^{2} - \)\(10\!\cdots\!00\)\( T^{3} + \)\(21\!\cdots\!28\)\( T^{4} - \)\(54\!\cdots\!88\)\( T^{5} + \)\(19\!\cdots\!24\)\( T^{6} - \)\(92\!\cdots\!00\)\( T^{7} + \)\(15\!\cdots\!96\)\( T^{8} - \)\(36\!\cdots\!16\)\( T^{9} + \)\(66\!\cdots\!68\)\( T^{10} \)
$3$ \( 1 - 953245351116252 T + \)\(29\!\cdots\!27\)\( T^{2} - \)\(42\!\cdots\!00\)\( T^{3} + \)\(50\!\cdots\!58\)\( T^{4} - \)\(67\!\cdots\!16\)\( T^{5} + \)\(57\!\cdots\!66\)\( T^{6} - \)\(55\!\cdots\!00\)\( T^{7} + \)\(44\!\cdots\!41\)\( T^{8} - \)\(16\!\cdots\!32\)\( T^{9} + \)\(19\!\cdots\!07\)\( T^{10} \)
$5$ \( 1 + \)\(50\!\cdots\!30\)\( T + \)\(12\!\cdots\!25\)\( T^{2} - \)\(28\!\cdots\!00\)\( T^{3} + \)\(20\!\cdots\!50\)\( T^{4} + \)\(56\!\cdots\!00\)\( T^{5} + \)\(22\!\cdots\!50\)\( T^{6} - \)\(33\!\cdots\!00\)\( T^{7} + \)\(15\!\cdots\!25\)\( T^{8} + \)\(69\!\cdots\!50\)\( T^{9} + \)\(14\!\cdots\!25\)\( T^{10} \)
$7$ \( 1 - \)\(37\!\cdots\!56\)\( T + \)\(33\!\cdots\!43\)\( T^{2} - \)\(31\!\cdots\!00\)\( T^{3} + \)\(24\!\cdots\!98\)\( T^{4} + \)\(82\!\cdots\!12\)\( T^{5} + \)\(43\!\cdots\!14\)\( T^{6} - \)\(95\!\cdots\!00\)\( T^{7} + \)\(17\!\cdots\!01\)\( T^{8} - \)\(34\!\cdots\!56\)\( T^{9} + \)\(16\!\cdots\!43\)\( T^{10} \)
$11$ \( 1 + \)\(54\!\cdots\!40\)\( T + \)\(12\!\cdots\!95\)\( T^{2} + \)\(42\!\cdots\!80\)\( T^{3} + \)\(70\!\cdots\!10\)\( T^{4} + \)\(17\!\cdots\!48\)\( T^{5} + \)\(28\!\cdots\!10\)\( T^{6} + \)\(70\!\cdots\!80\)\( T^{7} + \)\(84\!\cdots\!45\)\( T^{8} + \)\(14\!\cdots\!40\)\( T^{9} + \)\(10\!\cdots\!51\)\( T^{10} \)
$13$ \( 1 - \)\(10\!\cdots\!62\)\( T + \)\(25\!\cdots\!97\)\( T^{2} - \)\(21\!\cdots\!00\)\( T^{3} + \)\(59\!\cdots\!18\)\( T^{4} - \)\(62\!\cdots\!16\)\( T^{5} + \)\(90\!\cdots\!46\)\( T^{6} - \)\(49\!\cdots\!00\)\( T^{7} + \)\(88\!\cdots\!81\)\( T^{8} - \)\(55\!\cdots\!22\)\( T^{9} + \)\(78\!\cdots\!57\)\( T^{10} \)
$17$ \( 1 - \)\(23\!\cdots\!26\)\( T + \)\(83\!\cdots\!13\)\( T^{2} - \)\(29\!\cdots\!00\)\( T^{3} + \)\(46\!\cdots\!38\)\( T^{4} - \)\(10\!\cdots\!88\)\( T^{5} + \)\(15\!\cdots\!94\)\( T^{6} - \)\(31\!\cdots\!00\)\( T^{7} + \)\(29\!\cdots\!61\)\( T^{8} - \)\(27\!\cdots\!86\)\( T^{9} + \)\(39\!\cdots\!93\)\( T^{10} \)
$19$ \( 1 + \)\(78\!\cdots\!00\)\( T + \)\(14\!\cdots\!95\)\( T^{2} + \)\(11\!\cdots\!00\)\( T^{3} + \)\(94\!\cdots\!10\)\( T^{4} + \)\(61\!\cdots\!00\)\( T^{5} + \)\(34\!\cdots\!90\)\( T^{6} + \)\(15\!\cdots\!00\)\( T^{7} + \)\(70\!\cdots\!05\)\( T^{8} + \)\(13\!\cdots\!00\)\( T^{9} + \)\(64\!\cdots\!99\)\( T^{10} \)
$23$ \( 1 - \)\(15\!\cdots\!72\)\( T + \)\(26\!\cdots\!67\)\( T^{2} - \)\(19\!\cdots\!00\)\( T^{3} + \)\(18\!\cdots\!78\)\( T^{4} - \)\(98\!\cdots\!16\)\( T^{5} + \)\(11\!\cdots\!26\)\( T^{6} - \)\(72\!\cdots\!00\)\( T^{7} + \)\(61\!\cdots\!21\)\( T^{8} - \)\(22\!\cdots\!12\)\( T^{9} + \)\(87\!\cdots\!07\)\( T^{10} \)
$29$ \( 1 - \)\(50\!\cdots\!50\)\( T + \)\(16\!\cdots\!45\)\( T^{2} - \)\(35\!\cdots\!00\)\( T^{3} + \)\(59\!\cdots\!10\)\( T^{4} - \)\(78\!\cdots\!00\)\( T^{5} + \)\(80\!\cdots\!90\)\( T^{6} - \)\(64\!\cdots\!00\)\( T^{7} + \)\(39\!\cdots\!05\)\( T^{8} - \)\(16\!\cdots\!50\)\( T^{9} + \)\(45\!\cdots\!49\)\( T^{10} \)
$31$ \( 1 - \)\(15\!\cdots\!60\)\( T + \)\(36\!\cdots\!95\)\( T^{2} - \)\(39\!\cdots\!20\)\( T^{3} + \)\(60\!\cdots\!10\)\( T^{4} - \)\(50\!\cdots\!52\)\( T^{5} + \)\(54\!\cdots\!10\)\( T^{6} - \)\(32\!\cdots\!20\)\( T^{7} + \)\(27\!\cdots\!45\)\( T^{8} - \)\(10\!\cdots\!60\)\( T^{9} + \)\(60\!\cdots\!51\)\( T^{10} \)
$37$ \( 1 + \)\(17\!\cdots\!34\)\( T + \)\(27\!\cdots\!53\)\( T^{2} + \)\(37\!\cdots\!00\)\( T^{3} + \)\(32\!\cdots\!18\)\( T^{4} + \)\(33\!\cdots\!12\)\( T^{5} + \)\(20\!\cdots\!54\)\( T^{6} + \)\(14\!\cdots\!00\)\( T^{7} + \)\(67\!\cdots\!81\)\( T^{8} + \)\(26\!\cdots\!54\)\( T^{9} + \)\(96\!\cdots\!93\)\( T^{10} \)
$41$ \( 1 - \)\(15\!\cdots\!10\)\( T + \)\(26\!\cdots\!45\)\( T^{2} - \)\(25\!\cdots\!20\)\( T^{3} + \)\(23\!\cdots\!10\)\( T^{4} - \)\(15\!\cdots\!52\)\( T^{5} + \)\(95\!\cdots\!10\)\( T^{6} - \)\(40\!\cdots\!20\)\( T^{7} + \)\(17\!\cdots\!45\)\( T^{8} - \)\(41\!\cdots\!10\)\( T^{9} + \)\(10\!\cdots\!01\)\( T^{10} \)
$43$ \( 1 + \)\(29\!\cdots\!08\)\( T + \)\(36\!\cdots\!07\)\( T^{2} + \)\(88\!\cdots\!00\)\( T^{3} + \)\(55\!\cdots\!98\)\( T^{4} + \)\(10\!\cdots\!84\)\( T^{5} + \)\(45\!\cdots\!86\)\( T^{6} + \)\(57\!\cdots\!00\)\( T^{7} + \)\(19\!\cdots\!01\)\( T^{8} + \)\(12\!\cdots\!08\)\( T^{9} + \)\(34\!\cdots\!07\)\( T^{10} \)
$47$ \( 1 + \)\(48\!\cdots\!64\)\( T + \)\(11\!\cdots\!23\)\( T^{2} + \)\(41\!\cdots\!00\)\( T^{3} + \)\(49\!\cdots\!58\)\( T^{4} + \)\(13\!\cdots\!12\)\( T^{5} + \)\(10\!\cdots\!34\)\( T^{6} + \)\(19\!\cdots\!00\)\( T^{7} + \)\(11\!\cdots\!41\)\( T^{8} + \)\(11\!\cdots\!24\)\( T^{9} + \)\(51\!\cdots\!43\)\( T^{10} \)
$53$ \( 1 + \)\(69\!\cdots\!98\)\( T + \)\(12\!\cdots\!77\)\( T^{2} + \)\(24\!\cdots\!00\)\( T^{3} + \)\(72\!\cdots\!58\)\( T^{4} - \)\(39\!\cdots\!16\)\( T^{5} + \)\(30\!\cdots\!66\)\( T^{6} + \)\(45\!\cdots\!00\)\( T^{7} + \)\(10\!\cdots\!41\)\( T^{8} + \)\(22\!\cdots\!18\)\( T^{9} + \)\(14\!\cdots\!57\)\( T^{10} \)
$59$ \( 1 - \)\(10\!\cdots\!00\)\( T + \)\(18\!\cdots\!95\)\( T^{2} - \)\(13\!\cdots\!00\)\( T^{3} + \)\(12\!\cdots\!10\)\( T^{4} - \)\(67\!\cdots\!00\)\( T^{5} + \)\(47\!\cdots\!90\)\( T^{6} - \)\(17\!\cdots\!00\)\( T^{7} + \)\(88\!\cdots\!05\)\( T^{8} - \)\(18\!\cdots\!00\)\( T^{9} + \)\(65\!\cdots\!99\)\( T^{10} \)
$61$ \( 1 - \)\(39\!\cdots\!10\)\( T + \)\(97\!\cdots\!45\)\( T^{2} - \)\(13\!\cdots\!20\)\( T^{3} + \)\(17\!\cdots\!10\)\( T^{4} - \)\(19\!\cdots\!52\)\( T^{5} + \)\(52\!\cdots\!10\)\( T^{6} - \)\(11\!\cdots\!20\)\( T^{7} + \)\(25\!\cdots\!45\)\( T^{8} - \)\(31\!\cdots\!10\)\( T^{9} + \)\(23\!\cdots\!01\)\( T^{10} \)
$67$ \( 1 + \)\(47\!\cdots\!24\)\( T + \)\(56\!\cdots\!63\)\( T^{2} + \)\(19\!\cdots\!00\)\( T^{3} + \)\(12\!\cdots\!38\)\( T^{4} + \)\(31\!\cdots\!12\)\( T^{5} + \)\(13\!\cdots\!94\)\( T^{6} + \)\(23\!\cdots\!00\)\( T^{7} + \)\(76\!\cdots\!61\)\( T^{8} + \)\(70\!\cdots\!64\)\( T^{9} + \)\(16\!\cdots\!43\)\( T^{10} \)
$71$ \( 1 - \)\(50\!\cdots\!60\)\( T + \)\(23\!\cdots\!95\)\( T^{2} - \)\(62\!\cdots\!20\)\( T^{3} + \)\(16\!\cdots\!10\)\( T^{4} - \)\(32\!\cdots\!52\)\( T^{5} + \)\(72\!\cdots\!10\)\( T^{6} - \)\(11\!\cdots\!20\)\( T^{7} + \)\(18\!\cdots\!45\)\( T^{8} - \)\(16\!\cdots\!60\)\( T^{9} + \)\(14\!\cdots\!51\)\( T^{10} \)
$73$ \( 1 + \)\(29\!\cdots\!78\)\( T + \)\(69\!\cdots\!17\)\( T^{2} + \)\(36\!\cdots\!00\)\( T^{3} + \)\(23\!\cdots\!78\)\( T^{4} + \)\(13\!\cdots\!84\)\( T^{5} + \)\(57\!\cdots\!26\)\( T^{6} + \)\(21\!\cdots\!00\)\( T^{7} + \)\(10\!\cdots\!21\)\( T^{8} + \)\(10\!\cdots\!38\)\( T^{9} + \)\(88\!\cdots\!57\)\( T^{10} \)
$79$ \( 1 - \)\(58\!\cdots\!00\)\( T + \)\(13\!\cdots\!95\)\( T^{2} - \)\(81\!\cdots\!00\)\( T^{3} + \)\(81\!\cdots\!10\)\( T^{4} - \)\(43\!\cdots\!00\)\( T^{5} + \)\(29\!\cdots\!90\)\( T^{6} - \)\(10\!\cdots\!00\)\( T^{7} + \)\(60\!\cdots\!05\)\( T^{8} - \)\(93\!\cdots\!00\)\( T^{9} + \)\(56\!\cdots\!99\)\( T^{10} \)
$83$ \( 1 - \)\(27\!\cdots\!32\)\( T + \)\(25\!\cdots\!87\)\( T^{2} - \)\(58\!\cdots\!00\)\( T^{3} + \)\(33\!\cdots\!38\)\( T^{4} - \)\(58\!\cdots\!16\)\( T^{5} + \)\(26\!\cdots\!06\)\( T^{6} - \)\(37\!\cdots\!00\)\( T^{7} + \)\(13\!\cdots\!61\)\( T^{8} - \)\(11\!\cdots\!52\)\( T^{9} + \)\(32\!\cdots\!07\)\( T^{10} \)
$89$ \( 1 - \)\(32\!\cdots\!50\)\( T + \)\(78\!\cdots\!45\)\( T^{2} - \)\(14\!\cdots\!00\)\( T^{3} + \)\(71\!\cdots\!10\)\( T^{4} - \)\(11\!\cdots\!00\)\( T^{5} + \)\(46\!\cdots\!90\)\( T^{6} - \)\(59\!\cdots\!00\)\( T^{7} + \)\(21\!\cdots\!05\)\( T^{8} - \)\(57\!\cdots\!50\)\( T^{9} + \)\(11\!\cdots\!49\)\( T^{10} \)
$97$ \( 1 + \)\(17\!\cdots\!14\)\( T + \)\(52\!\cdots\!73\)\( T^{2} + \)\(12\!\cdots\!00\)\( T^{3} + \)\(12\!\cdots\!58\)\( T^{4} + \)\(29\!\cdots\!12\)\( T^{5} + \)\(18\!\cdots\!34\)\( T^{6} + \)\(26\!\cdots\!00\)\( T^{7} + \)\(16\!\cdots\!41\)\( T^{8} + \)\(79\!\cdots\!74\)\( T^{9} + \)\(68\!\cdots\!93\)\( T^{10} \)
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