Properties

Label 1.72.a
Level 1
Weight 72
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 1
Sturm bound 6
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 72 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{72}(\Gamma_0(1))\).

Total New Old
Modular forms 7 7 0
Cusp forms 6 6 0
Eisenstein series 1 1 0

Trace form

\(6q \) \(\mathstrut +\mathstrut 66157336440q^{2} \) \(\mathstrut +\mathstrut 89896952777770440q^{3} \) \(\mathstrut +\mathstrut 8215211164782426312768q^{4} \) \(\mathstrut -\mathstrut 4278141122384906054186220q^{5} \) \(\mathstrut -\mathstrut 3844185387092474097708129888q^{6} \) \(\mathstrut +\mathstrut 339238077991027352510892027600q^{7} \) \(\mathstrut +\mathstrut 261748255411117464004338054151680q^{8} \) \(\mathstrut +\mathstrut 28987747971890967878679507858381342q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut +\mathstrut 66157336440q^{2} \) \(\mathstrut +\mathstrut 89896952777770440q^{3} \) \(\mathstrut +\mathstrut 8215211164782426312768q^{4} \) \(\mathstrut -\mathstrut 4278141122384906054186220q^{5} \) \(\mathstrut -\mathstrut 3844185387092474097708129888q^{6} \) \(\mathstrut +\mathstrut 339238077991027352510892027600q^{7} \) \(\mathstrut +\mathstrut 261748255411117464004338054151680q^{8} \) \(\mathstrut +\mathstrut 28987747971890967878679507858381342q^{9} \) \(\mathstrut -\mathstrut 263398563778288244573047848548292720q^{10} \) \(\mathstrut -\mathstrut 7282201071395957974463753532023511528q^{11} \) \(\mathstrut +\mathstrut 541210468937914072607016891134121050880q^{12} \) \(\mathstrut +\mathstrut 1979976617302538140528908237391294561380q^{13} \) \(\mathstrut -\mathstrut 128017496622836040959531046300766482377664q^{14} \) \(\mathstrut +\mathstrut 1384527570467769328220186624774837086552560q^{15} \) \(\mathstrut +\mathstrut 3676888394993384085040045713048320116002816q^{16} \) \(\mathstrut +\mathstrut 31832108800317870559262101483836997103387820q^{17} \) \(\mathstrut +\mathstrut 976142520820390022814071543254815896584170840q^{18} \) \(\mathstrut -\mathstrut 2134599176603329812909260431734119625520534680q^{19} \) \(\mathstrut -\mathstrut 1002259534476043660011780426984126177063212160q^{20} \) \(\mathstrut +\mathstrut 84959027471295034369736212294538752678486836672q^{21} \) \(\mathstrut -\mathstrut 1485722316536652800011319935933937121116600101920q^{22} \) \(\mathstrut +\mathstrut 964854402645396933763118399083810192495520292720q^{23} \) \(\mathstrut +\mathstrut 26174405694167952285079299527486641934970354984960q^{24} \) \(\mathstrut -\mathstrut 19281402740175290596320190755488341912491573055350q^{25} \) \(\mathstrut -\mathstrut 25489031065287762421766150549142637053582510650928q^{26} \) \(\mathstrut +\mathstrut 512562833403212721097503677963237444718074155383120q^{27} \) \(\mathstrut +\mathstrut 1359669743900832828937216228217468952624925402529280q^{28} \) \(\mathstrut -\mathstrut 1317039720567844349957114876746978985654238312884220q^{29} \) \(\mathstrut +\mathstrut 143339222293502384515474601773595895115677772364794560q^{30} \) \(\mathstrut +\mathstrut 207186478465068422331238247449690908034655530755715392q^{31} \) \(\mathstrut +\mathstrut 1088184206695308121738071837188209251978669942775971840q^{32} \) \(\mathstrut +\mathstrut 3691362947608430538982225244260639132989887834164526880q^{33} \) \(\mathstrut +\mathstrut 14816033950170870833607759912486854048128229988725590896q^{34} \) \(\mathstrut +\mathstrut 23051745539129054008487744498480782457434321413678307680q^{35} \) \(\mathstrut +\mathstrut 170434058245258338832832617243164934895140508181403488576q^{36} \) \(\mathstrut +\mathstrut 204469200012514149249942417779481789241448706895708248660q^{37} \) \(\mathstrut +\mathstrut 214562893987288214244615314981415065648734184296060185120q^{38} \) \(\mathstrut -\mathstrut 59592640589388524102808790877963748287382610795162303056q^{39} \) \(\mathstrut +\mathstrut 68960371201928160764899098042432251971214776224924902400q^{40} \) \(\mathstrut -\mathstrut 2919734046508252424588883022005626663089526220940467621348q^{41} \) \(\mathstrut -\mathstrut 30671294643397208367759780874400134513517016912238240615680q^{42} \) \(\mathstrut -\mathstrut 20040916369245642405547102129405243305810023246036805945000q^{43} \) \(\mathstrut -\mathstrut 97782453551268367387376497569051770607699386454832461475584q^{44} \) \(\mathstrut -\mathstrut 125260483937857526052956293044059264550801286160703506832540q^{45} \) \(\mathstrut -\mathstrut 153046715682271793176047221192835149722125813975592551106368q^{46} \) \(\mathstrut +\mathstrut 808817457363531455346008899794487365168024913483463537549280q^{47} \) \(\mathstrut +\mathstrut 2609198603968928396969404046103782910615054495128256557137920q^{48} \) \(\mathstrut +\mathstrut 2781254770563189488685819613146286428997272420256410557714358q^{49} \) \(\mathstrut +\mathstrut 7006022579700627712942214090063761901402175546735980199443400q^{50} \) \(\mathstrut +\mathstrut 5207384206251438333593957907132920357364678014965573534558992q^{51} \) \(\mathstrut -\mathstrut 14725121811173026783809130229242035456081751221768853161600q^{52} \) \(\mathstrut -\mathstrut 25679718795007592157741622782050324347181366369160532409346060q^{53} \) \(\mathstrut -\mathstrut 137149233644558648010083562893383635363635093434709473900255680q^{54} \) \(\mathstrut -\mathstrut 117204222076916896957422109693993993787887100230247369516318640q^{55} \) \(\mathstrut -\mathstrut 399675884388383438003206851384376896886023450279264479189790720q^{56} \) \(\mathstrut -\mathstrut 782227658930786946913543064710323069676066812613811573724368160q^{57} \) \(\mathstrut +\mathstrut 448079701387471532953636422287948168832061908600051366602252880q^{58} \) \(\mathstrut +\mathstrut 2574973077571448260016144269589718601018514468483198670599207160q^{59} \) \(\mathstrut +\mathstrut 8123589807705373813616392838803767380183688475255335181392775680q^{60} \) \(\mathstrut +\mathstrut 475826432092865634978052553570578668506543772710052231981685572q^{61} \) \(\mathstrut +\mathstrut 11448364903088694797640723309684276673600813166292613065633204480q^{62} \) \(\mathstrut +\mathstrut 12651716130374230363535487627387763606235866258941468391309842960q^{63} \) \(\mathstrut -\mathstrut 24713081846841456807546154884737687683145557071081015591709704192q^{64} \) \(\mathstrut -\mathstrut 64361385967902296711263719440079272798609683319753125480723589640q^{65} \) \(\mathstrut -\mathstrut 190230440842560220491451696290153136784050133308916444591791337856q^{66} \) \(\mathstrut -\mathstrut 144659082341179727176864823539854352180542085255822335340299697080q^{67} \) \(\mathstrut +\mathstrut 103906765022280475409201312234853190364811728527577591423200525440q^{68} \) \(\mathstrut -\mathstrut 324178142584238303283610175482820308872990835336256741226468985536q^{69} \) \(\mathstrut +\mathstrut 149058995123458688341122966890772635236709780299529720693195383680q^{70} \) \(\mathstrut +\mathstrut 1235687217541473731844866277247085329953553172066626000767894890832q^{71} \) \(\mathstrut +\mathstrut 4756831008242737873947724915842925231281989210351278910206749980160q^{72} \) \(\mathstrut +\mathstrut 2367941808342149806657639366589641208779949871411828605636295901020q^{73} \) \(\mathstrut +\mathstrut 9011435259578808279041169928582984111943617430403441524175408617616q^{74} \) \(\mathstrut -\mathstrut 13222323962608659927909870888644111847952601354444631362060975848200q^{75} \) \(\mathstrut -\mathstrut 18582782951953033569252470264774735316811316464954475202007848157440q^{76} \) \(\mathstrut -\mathstrut 1325886884597236605670798015501090754589875143123368772240211064000q^{77} \) \(\mathstrut -\mathstrut 82734460874562257213604869472472902109931833071258216779579101108800q^{78} \) \(\mathstrut -\mathstrut 60094699780856590551494040309517729660578378792856107127665085175520q^{79} \) \(\mathstrut +\mathstrut 44547588558087884776699653673631630698194001426805365604181595054080q^{80} \) \(\mathstrut +\mathstrut 90431879106172356691623372809945513347962349100492777817548343419766q^{81} \) \(\mathstrut +\mathstrut 131880025121092502946065745838775597252029739409272681579129156984880q^{82} \) \(\mathstrut +\mathstrut 478198003543301822300844025982176525658793260101595969531167537027560q^{83} \) \(\mathstrut +\mathstrut 357830150741096835660154046759297297209098846217256694071293018761216q^{84} \) \(\mathstrut +\mathstrut 211578728369556023050184481668102823215907914559259741440636420213480q^{85} \) \(\mathstrut +\mathstrut 1059998024210927691622156922996285506825265712550377293381092088317152q^{86} \) \(\mathstrut +\mathstrut 37277468187846628282172211514267021090427372083464347850766486010160q^{87} \) \(\mathstrut -\mathstrut 4443462717687788793413327377388585733175808835000327093394681148835840q^{88} \) \(\mathstrut -\mathstrut 4779569984649315840943802647699331383415548856834721435179426845446660q^{89} \) \(\mathstrut -\mathstrut 8627488862261215164556279664276659138357576658847574866996794738453040q^{90} \) \(\mathstrut -\mathstrut 78452933928526481195247745840882105733919101509887292910721637755168q^{91} \) \(\mathstrut -\mathstrut 3933588954885781964901938276884159688714299191002877628906051305530880q^{92} \) \(\mathstrut +\mathstrut 7624909019792303887861325379837512501943653991471804221089819053530880q^{93} \) \(\mathstrut +\mathstrut 31015980122032090056194424797719170840226576067548731364883132813755776q^{94} \) \(\mathstrut +\mathstrut 8322227458201878249902498709514623471463205177085801654971437001319600q^{95} \) \(\mathstrut +\mathstrut 166002069551604543422134778398052912195595330234015359484477454750973952q^{96} \) \(\mathstrut +\mathstrut 90247623387797693983114581554183210926698820590955654168827969225413580q^{97} \) \(\mathstrut -\mathstrut 169139078685664146344588160185862842690193055977419515754924822957831880q^{98} \) \(\mathstrut -\mathstrut 148347266170563325638880362653524309583634182291703142145633675457993096q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{72}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.72.a.a \(6\) \(31.925\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(66157336440\) \(89\!\cdots\!40\) \(-4\!\cdots\!20\) \(33\!\cdots\!00\) \(+\) \(q+(11026222740-\beta _{1})q^{2}+(14982825462961740+\cdots)q^{3}+\cdots\)