Properties

Label 1.64.a
Level 1
Weight 64
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 64 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{64}(\Gamma_0(1))\).

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

Trace form

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

Decomposition of \(S_{64}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.64.a.a \(5\) \(25.136\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(507315096\) \(95\!\cdots\!52\) \(-5\!\cdots\!30\) \(37\!\cdots\!56\) \(+\) \(q+(101463019-\beta _{1})q^{2}+(190649070219572+\cdots)q^{3}+\cdots\)