Properties

Label 1.92.a
Level 1
Weight 92
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 7
Newforms 1
Sturm bound 7
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 92 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{92}(\Gamma_0(1))\).

Total New Old
Modular forms 8 8 0
Cusp forms 7 7 0
Eisenstein series 1 1 0

Trace form

\(7q \) \(\mathstrut +\mathstrut 3841716838056q^{2} \) \(\mathstrut +\mathstrut 6226865993447967511332q^{3} \) \(\mathstrut +\mathstrut 5671662926176418572725837376q^{4} \) \(\mathstrut +\mathstrut 23504964778584408375486754830930q^{5} \) \(\mathstrut +\mathstrut 451174906579592943363587112684473184q^{6} \) \(\mathstrut -\mathstrut 171085178649369081126501604564827872344q^{7} \) \(\mathstrut -\mathstrut 10385570201002723586914837423420014159360q^{8} \) \(\mathstrut +\mathstrut 38080901154162874719072934775718033448005459q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(7q \) \(\mathstrut +\mathstrut 3841716838056q^{2} \) \(\mathstrut +\mathstrut 6226865993447967511332q^{3} \) \(\mathstrut +\mathstrut 5671662926176418572725837376q^{4} \) \(\mathstrut +\mathstrut 23504964778584408375486754830930q^{5} \) \(\mathstrut +\mathstrut 451174906579592943363587112684473184q^{6} \) \(\mathstrut -\mathstrut 171085178649369081126501604564827872344q^{7} \) \(\mathstrut -\mathstrut 10385570201002723586914837423420014159360q^{8} \) \(\mathstrut +\mathstrut 38080901154162874719072934775718033448005459q^{9} \) \(\mathstrut +\mathstrut 4697789292978379445837627874024155681811061680q^{10} \) \(\mathstrut -\mathstrut 240582832892068760628122732280591830839146659316q^{11} \) \(\mathstrut +\mathstrut 15234465137330235186821811325942149339051634358016q^{12} \) \(\mathstrut +\mathstrut 712268684544237976989939315593627958143865337752122q^{13} \) \(\mathstrut +\mathstrut 17766212926078897376844163559794320416860400218986432q^{14} \) \(\mathstrut +\mathstrut 818092333276881407770547708857297926161740517153634360q^{15} \) \(\mathstrut -\mathstrut 5543121629719415776419174196841312964977690510556459008q^{16} \) \(\mathstrut -\mathstrut 116788563921119361626790446343979264424208809345044156194q^{17} \) \(\mathstrut +\mathstrut 2532221674884609223972217344567154578664327889292374599112q^{18} \) \(\mathstrut +\mathstrut 24914430965691713272160835064548829827762713320225549023860q^{19} \) \(\mathstrut +\mathstrut 213622308691313951002559876190359340784045827397766986247040q^{20} \) \(\mathstrut -\mathstrut 2997932825643989744485469587195205163128865044067155102498976q^{21} \) \(\mathstrut +\mathstrut 2770354076929612113872013355190927517116944942304065995485472q^{22} \) \(\mathstrut +\mathstrut 28060217473226028795108958325793316282935533444516172471797112q^{23} \) \(\mathstrut -\mathstrut 676645515624503740032420639044230674317241134651601877083678720q^{24} \) \(\mathstrut +\mathstrut 3263569264491109562693810546136813966434457662326151208223443025q^{25} \) \(\mathstrut +\mathstrut 14647231349517882504358224484901087010163561052132416579801164144q^{26} \) \(\mathstrut +\mathstrut 88534490857595263563477937784200716693877558838426769810977256360q^{27} \) \(\mathstrut -\mathstrut 1267961512722154560010156489449223630509765593702989988702255606272q^{28} \) \(\mathstrut -\mathstrut 1998207010601468906936357688217559269263973686319086789407593851510q^{29} \) \(\mathstrut +\mathstrut 46684773092381185628041557878825569520483461165868165669687502423360q^{30} \) \(\mathstrut -\mathstrut 59925208170796133190382607870079728441723654705660441096474565882976q^{31} \) \(\mathstrut -\mathstrut 349236116256080438032682462092197690284580228848172295706337753268224q^{32} \) \(\mathstrut +\mathstrut 48956964959741209887245659130472098420831296585540373363667238885584q^{33} \) \(\mathstrut +\mathstrut 4422724362741906584267050702673869603971959112955389299199109971390672q^{34} \) \(\mathstrut -\mathstrut 13368721150607890395306302586915792313883425318712829768566063087971920q^{35} \) \(\mathstrut +\mathstrut 48271193532350417136817688340793844028122089698778111115225583548795712q^{36} \) \(\mathstrut -\mathstrut 193385642725694230212647842547384176779300890377457537180445039472551694q^{37} \) \(\mathstrut +\mathstrut 648885030040198126856514202904430175712235671732708835862375911231617760q^{38} \) \(\mathstrut -\mathstrut 1888050736392299353100554804844814233146715239003942457135725287045138792q^{39} \) \(\mathstrut +\mathstrut 612437306889339293021693643280174203404468934648721750255585003111910400q^{40} \) \(\mathstrut +\mathstrut 27467963396808209903058935820529109024708043852794661490538346949004391894q^{41} \) \(\mathstrut +\mathstrut 2490746600045939910899268282231591851463383036227202908840686832900714752q^{42} \) \(\mathstrut -\mathstrut 305936680392367608196854535263961824203961856383604167638158912234512481108q^{43} \) \(\mathstrut +\mathstrut 205463536657254300042685770932278214832998693823974867822888457185152941312q^{44} \) \(\mathstrut +\mathstrut 4760687647415457141753353234910279174019798332678698076640623508070611166010q^{45} \) \(\mathstrut -\mathstrut 1366266407223913965782607380535324534407310537728351887747959292074575330496q^{46} \) \(\mathstrut +\mathstrut 6016385666666683617266527127107702489089132053603324831460234388201640236656q^{47} \) \(\mathstrut +\mathstrut 34119609737617524136090987754275812795178080643639536100065326182318914650112q^{48} \) \(\mathstrut +\mathstrut 147622366871958729066285529870014845360644877218444002326443275466876372382751q^{49} \) \(\mathstrut +\mathstrut 987686706148773430200902630527966650567454297252982416951455545242325575637400q^{50} \) \(\mathstrut +\mathstrut 742769239785716829162529676417470760468992847219971127251563531253033686474504q^{51} \) \(\mathstrut +\mathstrut 4318717132385281312358095915519383012120671308396466785048290702799702098686336q^{52} \) \(\mathstrut +\mathstrut 13308120064559469621843967381370895719631000840255977547855692839275328956239682q^{53} \) \(\mathstrut +\mathstrut 49855304363851366001446865238806860151072717129384273575810932439561849626548160q^{54} \) \(\mathstrut +\mathstrut 71294075726222567616681402637553088151526343199773263267028104308906720840973160q^{55} \) \(\mathstrut +\mathstrut 221193813355805774602587289215941353561793271848452643887988504737893638457815040q^{56} \) \(\mathstrut +\mathstrut 528504764627515846582196025944068103123296527378022647769732650016063847427593520q^{57} \) \(\mathstrut +\mathstrut 1238229446269131105368662021237658933365297194812595452448484778585094416520960240q^{58} \) \(\mathstrut +\mathstrut 1315161090691534242045211041321797641427216505845115765078938874240054573263728380q^{59} \) \(\mathstrut +\mathstrut 4823153254365391976824193526392851616116082049689724166967862952927612944155374080q^{60} \) \(\mathstrut +\mathstrut 5062201896875711919454365982321524134556244374094873318866473906778984033476168234q^{61} \) \(\mathstrut +\mathstrut 5944009317613068040880423794674923373270855087786172352031955991395153732464744192q^{62} \) \(\mathstrut -\mathstrut 3636043453736261219929075304472074905914693023981615502769720183430994506848383288q^{63} \) \(\mathstrut -\mathstrut 51461933507510968227229909173673546488880558907251327588128558485838721977163710464q^{64} \) \(\mathstrut -\mathstrut 77004978625744224526600511688707953799859895672813324064129546096894713766789516340q^{65} \) \(\mathstrut -\mathstrut 308541964188130582740963794759741868505184177678097911786772179394411954828298046592q^{66} \) \(\mathstrut -\mathstrut 375865111304983135837477510931607479316175718244865448118159181323617876690058988444q^{67} \) \(\mathstrut -\mathstrut 1534213067668968494728693973596412463295117507399423353249302546218581933051381708672q^{68} \) \(\mathstrut -\mathstrut 2173315533882618835358431426746324715455060324131802571545777868624263537306736200672q^{69} \) \(\mathstrut -\mathstrut 2678915571128698388724922631831368101885281292954514535801987008907571514431164929920q^{70} \) \(\mathstrut +\mathstrut 965663858399224787677892593054987300813257337626219343051035389437608903566853136104q^{71} \) \(\mathstrut +\mathstrut 4759225550598725097796726774244526164682601876181738961172151381039656425240893268480q^{72} \) \(\mathstrut +\mathstrut 9530120766269923537811918138494095655717782977571711295781136472585782479177982847862q^{73} \) \(\mathstrut +\mathstrut 19110889051618327071497328002063508382221976511726809975089825510120232325728977189552q^{74} \) \(\mathstrut +\mathstrut 125021668038726866132333086418803849235968631984043287433627055625310081344612351442300q^{75} \) \(\mathstrut +\mathstrut 201417481997189328603388340686282158978023686930352491852420967420198850453092214874880q^{76} \) \(\mathstrut +\mathstrut 203838117981454989170200594078013407199331583446926407393231313568448855161412400016672q^{77} \) \(\mathstrut +\mathstrut 348422592585817152583346169273764440235290509078131053609004533439300203952600764751424q^{78} \) \(\mathstrut -\mathstrut 5875385290546216656185911308903463222289330212802402962421344496345859662855253387760q^{79} \) \(\mathstrut -\mathstrut 704730665751803958915921202265388401277484106681191434954636540435925847481999762923520q^{80} \) \(\mathstrut -\mathstrut 645876221088024404019866830164659790161069128158743050337018784266949283332298558348353q^{81} \) \(\mathstrut -\mathstrut 5377119810649520829232661929626958820402325732939303335851648698643252753720266284836848q^{82} \) \(\mathstrut -\mathstrut 7188939673179725085045886441204184334512306517239973817301478804674514872311469770345548q^{83} \) \(\mathstrut -\mathstrut 17037797188065238374634346038194001797920522141104843305926325070074414892172026480416768q^{84} \) \(\mathstrut -\mathstrut 18949626274852488910142757348951127712395103983201418376580212098044613619651779587066620q^{85} \) \(\mathstrut -\mathstrut 13930550649009692825744367374854352346751992408208092118301786049776748630048877827166176q^{86} \) \(\mathstrut +\mathstrut 14997220283992832178383660427617039138145206474606482931148662045188858037160846958683480q^{87} \) \(\mathstrut +\mathstrut 35205946317573638735966560050796709996519491901124319190557129002743085716478822258247680q^{88} \) \(\mathstrut +\mathstrut 58910603928414585742462774445274283779895728554450265497847918725594089228346625287686470q^{89} \) \(\mathstrut +\mathstrut 596817611113547745433166439395807555701671900247626319346669516201533941956589878026043760q^{90} \) \(\mathstrut +\mathstrut 431556051755722691175733360455273666621786312136528121760420810812400911428233396155619184q^{91} \) \(\mathstrut +\mathstrut 649582018326251344367774515135408104477035917640264872918599325106081734967368208117408256q^{92} \) \(\mathstrut +\mathstrut 176140526645345381525949017432055243763067046580068760248910898954659817267839614775511424q^{93} \) \(\mathstrut +\mathstrut 528728237301347142597743478920778358077668394817645608650770473672424789094546213047704192q^{94} \) \(\mathstrut +\mathstrut 460150241832447303916160340674008161933312298406246509746195633852627501820464219531336600q^{95} \) \(\mathstrut -\mathstrut 5308520687978816513495454896751155260796827272022533467944875093089923121365143311537012736q^{96} \) \(\mathstrut -\mathstrut 7025964934206676021621272614488614108607978598995771668040441707563730547939229623877790994q^{97} \) \(\mathstrut -\mathstrut 20729666350145773779493369529709111649648862211758783582357755821769845548186544170995584792q^{98} \) \(\mathstrut -\mathstrut 23913014682919445875702212438204672119308558146529134638425833150071457007907375951005388292q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{92}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.92.a.a \(7\) \(52.442\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(38\!\cdots\!56\) \(62\!\cdots\!32\) \(23\!\cdots\!30\) \(-1\!\cdots\!44\) \(+\) \(q+(548816691151+\beta _{1})q^{2}+\cdots\)