Properties

Label 1.108.a
Level 1
Weight 108
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 9
Newforms 1
Sturm bound 9
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 108 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{108}(\Gamma_0(1))\).

Total New Old
Modular forms 10 10 0
Cusp forms 9 9 0
Eisenstein series 1 1 0

Trace form

\(9q \) \(\mathstrut +\mathstrut 5465779613435496q^{2} \) \(\mathstrut +\mathstrut 15983866788128062714366812q^{3} \) \(\mathstrut +\mathstrut 641838178072986908923140040636992q^{4} \) \(\mathstrut +\mathstrut 24730262360170403173006735448079708750q^{5} \) \(\mathstrut -\mathstrut 120659696701040014765473752948751733206432q^{6} \) \(\mathstrut -\mathstrut 935936272579440558945885185297012359442693544q^{7} \) \(\mathstrut -\mathstrut 1000549071290096181876510601182828415482105239040q^{8} \) \(\mathstrut +\mathstrut 3695400441386851970702053152997489358579707799946813q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 5465779613435496q^{2} \) \(\mathstrut +\mathstrut 15983866788128062714366812q^{3} \) \(\mathstrut +\mathstrut 641838178072986908923140040636992q^{4} \) \(\mathstrut +\mathstrut 24730262360170403173006735448079708750q^{5} \) \(\mathstrut -\mathstrut 120659696701040014765473752948751733206432q^{6} \) \(\mathstrut -\mathstrut 935936272579440558945885185297012359442693544q^{7} \) \(\mathstrut -\mathstrut 1000549071290096181876510601182828415482105239040q^{8} \) \(\mathstrut +\mathstrut 3695400441386851970702053152997489358579707799946813q^{9} \) \(\mathstrut -\mathstrut 1051865624814321749095840304599907252969934693398466000q^{10} \) \(\mathstrut +\mathstrut 75371386674400378520973626363253224857093312063724664948q^{11} \) \(\mathstrut -\mathstrut 7994600333787230851514661173029738426135745580020653426944q^{12} \) \(\mathstrut +\mathstrut 386688410581830829569835770029121092890073212075170355706982q^{13} \) \(\mathstrut -\mathstrut 7425120169660057221925189838061614099801999208262592119204416q^{14} \) \(\mathstrut +\mathstrut 1114849595057357604173216029035423209082636701646415622289453000q^{15} \) \(\mathstrut +\mathstrut 29408614076374287218252370499930154042728180304312580290885259264q^{16} \) \(\mathstrut +\mathstrut 557190110555184717584150469172018747011155217501263013200292053826q^{17} \) \(\mathstrut +\mathstrut 23686310065847344603267400477778156225688961326793890396260803764872q^{18} \) \(\mathstrut +\mathstrut 858726527367010511176780653766124295103204700130810063275302960078860q^{19} \) \(\mathstrut +\mathstrut 13293825016749054587175558577837356326662860013460552585283415249200000q^{20} \) \(\mathstrut +\mathstrut 98208620574357072907810930779441373553105765539483211558155794396236448q^{21} \) \(\mathstrut -\mathstrut 2120482037145318757833662337561674615184814159100624269907546121294686688q^{22} \) \(\mathstrut -\mathstrut 10034721240753129475726648205629192527604953514063764213610508652545603448q^{23} \) \(\mathstrut -\mathstrut 2941281585435310612767332425157841570788095859273373502643916660565125120q^{24} \) \(\mathstrut +\mathstrut 2090668146509277585662418878235593338432069837730236508072952837108480609375q^{25} \) \(\mathstrut +\mathstrut 297618678938898468541825094241452097503242676900281081118135240117081112048q^{26} \) \(\mathstrut +\mathstrut 12010637132277372007849219431146961646841705965134800444369356096651346807640q^{27} \) \(\mathstrut -\mathstrut 772836919356016231875276488741314175452898152873144799220188421863529684675072q^{28} \) \(\mathstrut +\mathstrut 3591314969861592690040264647853795847194812597017039069680951706167032656423190q^{29} \) \(\mathstrut +\mathstrut 1723952423459255307102435810928767115448833503290363214135969710252703496200000q^{30} \) \(\mathstrut +\mathstrut 80089747856260124585510286878769275145759211608657844798932602922226546761434208q^{31} \) \(\mathstrut -\mathstrut 1446206593191149472500309116447393072011146060673364310104554905463216959190564864q^{32} \) \(\mathstrut +\mathstrut 3945091609919542459300423121384432970721444207912781947382890849249898482566767664q^{33} \) \(\mathstrut +\mathstrut 11119656315304296004606294411853238631199272487238804497227126821893639468830096464q^{34} \) \(\mathstrut +\mathstrut 49067962462953733482940013097788952961901858200557588372758479947688558453676754000q^{35} \) \(\mathstrut -\mathstrut 471823079431745456450508655131148234440317478341437039102283657625130709182178187456q^{36} \) \(\mathstrut -\mathstrut 211704323021230989692835910298149365559694037564054725936839839132550744753936919634q^{37} \) \(\mathstrut +\mathstrut 8222885444046313840674570479741432975521521666418514540085950022601909450574547779040q^{38} \) \(\mathstrut +\mathstrut 12361178896398609619161562511793017908827480821637222996756699411815138902405469354856q^{39} \) \(\mathstrut -\mathstrut 46215645594071398383759344185895857310354869228136299740138569713991972194487637120000q^{40} \) \(\mathstrut -\mathstrut 152723040798290839871602016171161581257438821965138798374317736485575056512069694567862q^{41} \) \(\mathstrut +\mathstrut 1126972287891090202493176150041627427283154361091115578522922093800965746370272835782912q^{42} \) \(\mathstrut +\mathstrut 588069515895858848125340008029591292900452115124091837264351724714905019444084944743892q^{43} \) \(\mathstrut -\mathstrut 6139643207231705808426527030461811499402203060055049552369302116418471883341886274962176q^{44} \) \(\mathstrut -\mathstrut 31911427383192526363701563735501578120849438309590564668521639113629216238459194946116250q^{45} \) \(\mathstrut -\mathstrut 18263182784420532146882371818610257236316553965008962373113458516888555657572617999188672q^{46} \) \(\mathstrut +\mathstrut 411127412634686500562199358253262979305374320422388983156864942033640143172424484152539536q^{47} \) \(\mathstrut +\mathstrut 143930370214090114738516122425367964462847873560413052946256979092891611198246163544522752q^{48} \) \(\mathstrut -\mathstrut 4997644842464582200845249613678276624838382931152181846690817178995051025280570789312693263q^{49} \) \(\mathstrut -\mathstrut 327953810706856692980141167207241667907351028782006717494410015078645777795786692667625000q^{50} \) \(\mathstrut +\mathstrut 42691516908125956684809245526355840553570893389914391645941980034335859681366662250925257208q^{51} \) \(\mathstrut +\mathstrut 59364881289634100249284358230824565528876555321811374467351490113119501371198417490401094016q^{52} \) \(\mathstrut -\mathstrut 53335374129204409504769785775612138052491162110126476217063770562215392060493506708504818338q^{53} \) \(\mathstrut -\mathstrut 1554605781923117836337527850943594545571965959146902578434980467357667330247224121116945547840q^{54} \) \(\mathstrut +\mathstrut 1474216898342963983363455770095216024051493885851745466905891181181387017915931645476666255000q^{55} \) \(\mathstrut +\mathstrut 7453692229427932770491342947786818133880887558034867118652861854414844393630476278780284170240q^{56} \) \(\mathstrut -\mathstrut 9382173343921294589567308072318971089362548602163794938031557584052656917238640814769133635120q^{57} \) \(\mathstrut -\mathstrut 14675317362256339836240584983997175224307357531571668080947702647986363061369632064127758276240q^{58} \) \(\mathstrut -\mathstrut 17201443369933521380448054479438020840215748691907958949057650623559478137031846309102734186620q^{59} \) \(\mathstrut +\mathstrut 119942427235571024011403351926139340364016919293031353278124824892037701815579444998816654144000q^{60} \) \(\mathstrut +\mathstrut 996825825169496808828278558344476432289838610202339535134269176536499940712988317319113083438198q^{61} \) \(\mathstrut -\mathstrut 1806664642208894952880819938644089164868010113998872083788864908221482430118942433714202980872448q^{62} \) \(\mathstrut -\mathstrut 525131716387364530569619107989883435883820178537003544594931993029001820968120281192738395294408q^{63} \) \(\mathstrut +\mathstrut 8859800242100397923173345055025991374254635563298611761326132852774863587391298255452246238298112q^{64} \) \(\mathstrut +\mathstrut 3354685369129755322181059460881157417967535549386685974710181837734684369198862379954288278640500q^{65} \) \(\mathstrut +\mathstrut 57953332747637118130796913061247956114095776689582635716826448321044474448975464944502438440474496q^{66} \) \(\mathstrut +\mathstrut 67272594646508937763531278535250984988721264552212406692490519409868542593541008988303512955099676q^{67} \) \(\mathstrut -\mathstrut 5271355091203561642375555737902479878900668615857946963901492781607485228195805621489749763440512q^{68} \) \(\mathstrut +\mathstrut 1211310643069343900708768635208063407543461033111793008132153244460934861341593025873966799465486816q^{69} \) \(\mathstrut +\mathstrut 3012778566653438568685732696962102874663629250451589330912197198332559170935750394136926553795280000q^{70} \) \(\mathstrut +\mathstrut 557606230265736297562017362716168472788611890356025926095319973789617215901574196175404049892853528q^{71} \) \(\mathstrut +\mathstrut 16960010475120540092713267652235654327415255109531175122804202418279614126703951005828887393908830720q^{72} \) \(\mathstrut +\mathstrut 13389828619022747318968894782762272535480348540089259518080823938522165418472525950139881426529375402q^{73} \) \(\mathstrut +\mathstrut 72532783100036668116960948230568216484424073462645933664305672446671831241015488437308573521198008624q^{74} \) \(\mathstrut +\mathstrut 181746227987304022931719943233189267636401541776890365701313509214346868335764760358972397994607562500q^{75} \) \(\mathstrut +\mathstrut 369203366658532984115827909838760339113448992029578983924004973867253851696995490992782273693567066880q^{76} \) \(\mathstrut +\mathstrut 388491114360440288787870394325327319503105866790556270795138762844335429572119358188629406545039198432q^{77} \) \(\mathstrut +\mathstrut 1684225666426130585491319943814839912966891568955799622030995821490516792520001316121300784238905446464q^{78} \) \(\mathstrut +\mathstrut 1767099872706468468805139692411742252367926917059947532799767578463589430448822266501638541217663494640q^{79} \) \(\mathstrut +\mathstrut 6734051899360870505834986379536968461908477509814468240268598557190207937484585956747946194493844480000q^{80} \) \(\mathstrut +\mathstrut 8587274871353378729934471647154494323432295856816917259751843692725713832863430007711361770205995287889q^{81} \) \(\mathstrut +\mathstrut 8604324829509629266993327118230721908083540408244010940656031675054140623869235247377840945490064899472q^{82} \) \(\mathstrut +\mathstrut 10573584024255166860785482858544789933175527426032260694531283318949407366175819470225352840720947271372q^{83} \) \(\mathstrut +\mathstrut 29398865778509538549966771421066766907861809604721299372151512034272864117018289488710440505099182516224q^{84} \) \(\mathstrut +\mathstrut 28217101873426464307527276596170727373321741101882319418731811087750656251683841267824081156479505981500q^{85} \) \(\mathstrut -\mathstrut 5660340715902714082316421136856625160042953949488572010019823412763437338500312808862231168781884748512q^{86} \) \(\mathstrut -\mathstrut 238801934255165782785740400186129085029676437910074769136670805304976544209174607407124977464878965608280q^{87} \) \(\mathstrut -\mathstrut 649669481755409892912473717222108679378769149016402953512733477402495574055782427323588758822348679034880q^{88} \) \(\mathstrut -\mathstrut 887044331989597087426634052611019082958734414422732136340380168408138968025139915003605988823387508725030q^{89} \) \(\mathstrut -\mathstrut 2358060024132454293950038004387227695091155243819311445899211024200212376406755931436993187026324923882000q^{90} \) \(\mathstrut -\mathstrut 2028610692814038362284016228595385975371756633777610476239575578728190535138139517202725484712408010671472q^{91} \) \(\mathstrut -\mathstrut 9605953523619230804079170889956757296920712871591046684448269611692869761363895640295324681873778639117824q^{92} \) \(\mathstrut -\mathstrut 10277229372847627124269654885108201819576328825280371977906378287406641199658335902623697673880879481373056q^{93} \) \(\mathstrut -\mathstrut 13250229074063549042347396359745980974584115253516850536254551366146505318484654226001161612613989202932096q^{94} \) \(\mathstrut +\mathstrut 1932498314000384011251898358613786886453409028619258552182745516014729315280931175089689966876445460945000q^{95} \) \(\mathstrut +\mathstrut 8188689385662642160607934226103033776391463701323345460407294147322816918802843383187307295905239187980288q^{96} \) \(\mathstrut +\mathstrut 18319527847032942156630290559559475585838161401404427251154943474039162663641018432069269659324962153774386q^{97} \) \(\mathstrut +\mathstrut 91489091329550984599525415507771543780042234198589939082127267861983786873859650920519076378970080872245928q^{98} \) \(\mathstrut +\mathstrut 211118154688143874137117803870035099572707397285369760168480766428388700807018832202269547436760962791157636q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{108}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.108.a.a \(9\) \(72.504\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(54\!\cdots\!96\) \(15\!\cdots\!12\) \(24\!\cdots\!50\) \(-9\!\cdots\!44\) \(+\) \(q+(607308845937277-\beta _{1})q^{2}+\cdots\)