Properties

Label 1.96.a
Level 1
Weight 96
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 8
Newforms 1
Sturm bound 8
Trace bound 0

Related objects

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 96 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{96}(\Gamma_0(1))\).

Total New Old
Modular forms 9 9 0
Cusp forms 8 8 0
Eisenstein series 1 1 0

Trace form

\(8q \) \(\mathstrut -\mathstrut 5835659138280q^{2} \) \(\mathstrut -\mathstrut 9565982513916703570080q^{3} \) \(\mathstrut +\mathstrut 208956598309707350371623569984q^{4} \) \(\mathstrut +\mathstrut 1941568507475850402526904141070960q^{5} \) \(\mathstrut +\mathstrut 10651800775920653731297343298528492576q^{6} \) \(\mathstrut +\mathstrut 31232311735415758067806325356531573912000q^{7} \) \(\mathstrut -\mathstrut 14761127603920085098561309094124598702287360q^{8} \) \(\mathstrut +\mathstrut 9274438133561954597944854467482391143953072936q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut -\mathstrut 5835659138280q^{2} \) \(\mathstrut -\mathstrut 9565982513916703570080q^{3} \) \(\mathstrut +\mathstrut 208956598309707350371623569984q^{4} \) \(\mathstrut +\mathstrut 1941568507475850402526904141070960q^{5} \) \(\mathstrut +\mathstrut 10651800775920653731297343298528492576q^{6} \) \(\mathstrut +\mathstrut 31232311735415758067806325356531573912000q^{7} \) \(\mathstrut -\mathstrut 14761127603920085098561309094124598702287360q^{8} \) \(\mathstrut +\mathstrut 9274438133561954597944854467482391143953072936q^{9} \) \(\mathstrut -\mathstrut 355384205613899841010372205704985147108657534640q^{10} \) \(\mathstrut +\mathstrut 53080108095821756826858489331993621982645992125216q^{11} \) \(\mathstrut +\mathstrut 1065031032961827853079380844579017283696993846403840q^{12} \) \(\mathstrut +\mathstrut 117293508281179239843264964380833942161194396039342640q^{13} \) \(\mathstrut +\mathstrut 8850886815767090581799564344683737269936151852930265408q^{14} \) \(\mathstrut +\mathstrut 187812376414067333691564154745798290909917959215041625920q^{15} \) \(\mathstrut +\mathstrut 9517116971431211282501221161054789131283343644054948220928q^{16} \) \(\mathstrut -\mathstrut 13655041265063090981829171372625119189425374473948274915440q^{17} \) \(\mathstrut -\mathstrut 1790266901749030205580776247252673430153004351197542602854280q^{18} \) \(\mathstrut -\mathstrut 5232175975370167369536369873888207394303637759872553281713440q^{19} \) \(\mathstrut +\mathstrut 136065209104116992530471413843386338746929879497239386344644480q^{20} \) \(\mathstrut +\mathstrut 1346571177849118208545064341536207444072396945735327627682503936q^{21} \) \(\mathstrut -\mathstrut 20365500099170357171519767897869972385636855003458825137197491360q^{22} \) \(\mathstrut -\mathstrut 7129054072165937484825035531327773489156117409617881426435061440q^{23} \) \(\mathstrut +\mathstrut 288860682603965362857322541557744811472884721216169744526242990080q^{24} \) \(\mathstrut +\mathstrut 8177806376085721196783759852983887433280593317172609841487587996600q^{25} \) \(\mathstrut -\mathstrut 69072273179717436642550386629266724895941590936463282023015399323504q^{26} \) \(\mathstrut +\mathstrut 64049503386294800673569522679695786753122795388715525750679249767360q^{27} \) \(\mathstrut +\mathstrut 303354815522537415860404332264897505740906926923909508834765584637440q^{28} \) \(\mathstrut +\mathstrut 7715272198415359380593902919630157934289467091855373333108685675435440q^{29} \) \(\mathstrut -\mathstrut 62913685170287068298704199843316213881225133796680396150164526710345280q^{30} \) \(\mathstrut +\mathstrut 48520677903801540370519073843711920597057994260920479636592334181199616q^{31} \) \(\mathstrut +\mathstrut 911347110324473008775326747695560179887781374647708612161794209209221120q^{32} \) \(\mathstrut -\mathstrut 1535322742350198888271103254480947687741587903792512354063710702943493760q^{33} \) \(\mathstrut -\mathstrut 16409772766982648656985219134942803587399227958333745923026675404562961232q^{34} \) \(\mathstrut +\mathstrut 58800416933815614414155173269063056087887600285328689246425433374756677760q^{35} \) \(\mathstrut +\mathstrut 51665208441213434468989869710710146210173003797753332160946711226240568128q^{36} \) \(\mathstrut -\mathstrut 181116344963557296256979160619337453378797091102974834966000994855965247120q^{37} \) \(\mathstrut -\mathstrut 1676466315180766681626408275142200947978975839695306622930354052184199692640q^{38} \) \(\mathstrut +\mathstrut 465478714369259758144024065308323445042256641733578800363164365799686202432q^{39} \) \(\mathstrut +\mathstrut 39028182173606372825635252450401491624189758401191157685601991729209269171200q^{40} \) \(\mathstrut -\mathstrut 87541390126560450267544465567119030351560808726320656469732601708266148308784q^{41} \) \(\mathstrut -\mathstrut 157435820560022140348706044721413472652300880194209574021901207450891596867840q^{42} \) \(\mathstrut +\mathstrut 360093033489081253538156425248276463103949347025569853491672117723107522861600q^{43} \) \(\mathstrut +\mathstrut 1942224484251042670482996667732829207493398934442399145050649033803969221005568q^{44} \) \(\mathstrut -\mathstrut 1611554371538604569657837598986488298494511731253236200388961579880024486332880q^{45} \) \(\mathstrut -\mathstrut 19332434944442851407749457669991401004991143268030327859543986888040547882373184q^{46} \) \(\mathstrut +\mathstrut 38672453335683563852366980570346257355794761888911368752480783496161211070336640q^{47} \) \(\mathstrut +\mathstrut 93863838769591236482712272126012963144755254935077324856132076191099747033333760q^{48} \) \(\mathstrut +\mathstrut 265668043093542548841947390620517395072194945166225827717144824590425137465244744q^{49} \) \(\mathstrut -\mathstrut 1423963459280866882678609595824694565889878038511273700600414891648711070234429400q^{50} \) \(\mathstrut +\mathstrut 2434476695354895883532253554814552047229450451049452072207263289482820720406821056q^{51} \) \(\mathstrut +\mathstrut 15678746704556392183126484026214298441253990030076674973212546269606119207477104000q^{52} \) \(\mathstrut -\mathstrut 2922690482809426126710991861168746969788895886261814706776237561500358605037675280q^{53} \) \(\mathstrut +\mathstrut 44393564079821957628952458152403809172972567715888333832276777433089826621820157760q^{54} \) \(\mathstrut +\mathstrut 77963865832782922646862204005771036172886494149999882551809226033579503680996905920q^{55} \) \(\mathstrut +\mathstrut 723822110434297992891221750986765045769194525611914833690699475848521019635777392640q^{56} \) \(\mathstrut +\mathstrut 1459603943948321457517074656112276013643674313689343212415092604638087582879924782720q^{57} \) \(\mathstrut +\mathstrut 2398120500739528001867383787619453843290390222445601081527493426426916763954522209040q^{58} \) \(\mathstrut +\mathstrut 2444569112045817337560949868287606200158569651761097862873350630901953709318185022880q^{59} \) \(\mathstrut +\mathstrut 41015921945833187827435663222575462810347191746192004435818365735996703011205515880960q^{60} \) \(\mathstrut +\mathstrut 26252719580888049069066995575288184611473664654647035829209505915961690057602967485616q^{61} \) \(\mathstrut +\mathstrut 109318411457586083204284032417457169492313955459811319765445849679642744506848521207040q^{62} \) \(\mathstrut +\mathstrut 170984018880767416687602973051010439420211230624233991381305273834268390445660056281280q^{63} \) \(\mathstrut +\mathstrut 407545659960425058121678577897271227683793728749313452587765989597513138495845491277824q^{64} \) \(\mathstrut +\mathstrut 711217468942010938456527729098183388378886665557115838437689631605619958224435834575520q^{65} \) \(\mathstrut +\mathstrut 1747938075646007071584137716302374690644541046339320226994976444199784352790302021223552q^{66} \) \(\mathstrut -\mathstrut 646475642994207391400653355260241732956721934256209274545597969100350739031184431188640q^{67} \) \(\mathstrut +\mathstrut 91675839067201266020688320385568861573762045194469769590554263557238860857176520405120q^{68} \) \(\mathstrut -\mathstrut 1671348258106164448387617904756675195481964064504427142194954632911883632406377850960128q^{69} \) \(\mathstrut -\mathstrut 15589682350948763132524633727148211085350313303119537319661619119948806738470696493235840q^{70} \) \(\mathstrut -\mathstrut 14595295080721751466823982356267079020901744922845645857244436108167397828048945561374784q^{71} \) \(\mathstrut -\mathstrut 168731956650076191328348463912100975176233311308158667034794509156143705616303905637470720q^{72} \) \(\mathstrut -\mathstrut 167722859263497180232486905674536831998056258335586734743256934373976249561602911979579440q^{73} \) \(\mathstrut -\mathstrut 209312489678791718598684146630297797595302804804578868479635191055424978871400486510408112q^{74} \) \(\mathstrut -\mathstrut 319918492419260578418623942107150301135641877679303067145274604119881385565549842206216800q^{75} \) \(\mathstrut -\mathstrut 959273209575432254809587692424149415253949631691365417587931662952012091653615772375589120q^{76} \) \(\mathstrut -\mathstrut 358973379150050060834656745211596557040941835816686113329022190288009228708654757892460800q^{77} \) \(\mathstrut +\mathstrut 590425535394410417923583601115147442109710886806797004396557673983317347484688655751672000q^{78} \) \(\mathstrut +\mathstrut 4672642903096907209502768293890247708239627672362847349478671278970829923925879535283527040q^{79} \) \(\mathstrut +\mathstrut 18415268594255335517079731605762998550074832241200743044677945286622776635630921688252866560q^{80} \) \(\mathstrut +\mathstrut 12509737552066767544095911653095580991572013599361129872125476231341584536182121238921405768q^{81} \) \(\mathstrut +\mathstrut 32657845092209493410036294321958173121440540177602229019397776717126981442788576405027965040q^{82} \) \(\mathstrut +\mathstrut 34387792212015780744754986808561666458900302762495709021597904850967930099747337487085254880q^{83} \) \(\mathstrut +\mathstrut 173836457542583880184373241725060178629119564679421678850358203433258194499103546320231344128q^{84} \) \(\mathstrut +\mathstrut 58585978711733607272815047107060888289878133655773893600270763487144112403111490135244590560q^{85} \) \(\mathstrut -\mathstrut 153511472921832187435283964804212642635464712353485304877046031498544471884447149897205104544q^{86} \) \(\mathstrut -\mathstrut 544464219458114578116693663783217812912359092004929393234553696235186032730900539616052969920q^{87} \) \(\mathstrut -\mathstrut 1202425497404423912185881933157195269872332267934742515736241252480851349730675866727622174720q^{88} \) \(\mathstrut -\mathstrut 342673661311688548077760584785109887358595471462214186557789870415877447806348084055852796080q^{89} \) \(\mathstrut -\mathstrut 3514062299884453064121468346218192535289244482618329972865712072788945397515179474700715316080q^{90} \) \(\mathstrut -\mathstrut 3490211360016960529246147249335483533013067701963330513611222538458526220206688421639066690944q^{91} \) \(\mathstrut -\mathstrut 12008074146638359830472895966704879561255070000267734630900014099911412498586265442549753546240q^{92} \) \(\mathstrut +\mathstrut 197667690727810326296814984504358164807428856713575716952413727748092885643497784281407575040q^{93} \) \(\mathstrut +\mathstrut 15433462798640093333378242254437202047220637579307237556798289796157532672617883642933732299648q^{94} \) \(\mathstrut +\mathstrut 15321400721190643816477985005690604983976540891819618748501840926190750159388834713154020724800q^{95} \) \(\mathstrut +\mathstrut 97555071644510782149318139986276901553221426854121546320985366392022081200430710682001871077376q^{96} \) \(\mathstrut +\mathstrut 10072532354157458294768094296505188523874048354320514397914144859011793551098974691865811668240q^{97} \) \(\mathstrut +\mathstrut 146363464831387371243245039459581022362075942196915081212239417921551560440470151788055390975960q^{98} \) \(\mathstrut +\mathstrut 307096415144337525387251975813943414746365371627429389615225939474864146107991251707726185786272q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{96}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.96.a.a \(8\) \(57.154\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-5\!\cdots\!80\) \(-9\!\cdots\!80\) \(19\!\cdots\!60\) \(31\!\cdots\!00\) \(+\) \(q+(-729457392285+\beta _{1})q^{2}+\cdots\)