Properties

Label 1.74.a
Level 1
Weight 74
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 74 \)
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 \(M_{74}(\Gamma_0(1))\).

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

Trace form

\(5q \) \(\mathstrut -\mathstrut 92089333488q^{2} \) \(\mathstrut -\mathstrut 129195798226305804q^{3} \) \(\mathstrut +\mathstrut 891110479259563516160q^{4} \) \(\mathstrut +\mathstrut 23099529720469471562826750q^{5} \) \(\mathstrut -\mathstrut 3335695451789843173883221440q^{6} \) \(\mathstrut -\mathstrut 4356178487147579439806268090008q^{7} \) \(\mathstrut -\mathstrut 382321348565178801062509850849280q^{8} \) \(\mathstrut +\mathstrut 32335028924861937033188022998788065q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut -\mathstrut 92089333488q^{2} \) \(\mathstrut -\mathstrut 129195798226305804q^{3} \) \(\mathstrut +\mathstrut 891110479259563516160q^{4} \) \(\mathstrut +\mathstrut 23099529720469471562826750q^{5} \) \(\mathstrut -\mathstrut 3335695451789843173883221440q^{6} \) \(\mathstrut -\mathstrut 4356178487147579439806268090008q^{7} \) \(\mathstrut -\mathstrut 382321348565178801062509850849280q^{8} \) \(\mathstrut +\mathstrut 32335028924861937033188022998788065q^{9} \) \(\mathstrut -\mathstrut 1082726120403847340426026649690244000q^{10} \) \(\mathstrut +\mathstrut 50083756421782317855880849016778496860q^{11} \) \(\mathstrut +\mathstrut 1389386159501111619787899997887234696192q^{12} \) \(\mathstrut +\mathstrut 4753748397471720291047553799357192278886q^{13} \) \(\mathstrut +\mathstrut 263363595637460329420141722180437171694720q^{14} \) \(\mathstrut -\mathstrut 5053973124818591694478703469878924549517000q^{15} \) \(\mathstrut +\mathstrut 57509595349357883169785087518099233197588480q^{16} \) \(\mathstrut +\mathstrut 663279725175909884624200257401822351394256602q^{17} \) \(\mathstrut +\mathstrut 6936746909593304334038759770389897835631806416q^{18} \) \(\mathstrut +\mathstrut 31387402430958534058855312636541530201995765700q^{19} \) \(\mathstrut +\mathstrut 68535205735011202400715856751699460073169856000q^{20} \) \(\mathstrut +\mathstrut 873650260100519441483759434874628458149545804960q^{21} \) \(\mathstrut -\mathstrut 9492394168845783423791120540922405517833204177216q^{22} \) \(\mathstrut -\mathstrut 41173446223173693726617088414497261153026772718024q^{23} \) \(\mathstrut +\mathstrut 16216566841440134675070566439222517257116824780800q^{24} \) \(\mathstrut +\mathstrut 321010940201155914585034686800814006311220324546875q^{25} \) \(\mathstrut +\mathstrut 4496438035379975943261998606627087983483848085006560q^{26} \) \(\mathstrut -\mathstrut 12482045195529499122248281309176768796522105943881080q^{27} \) \(\mathstrut -\mathstrut 37814301174111882879202704910382387341459683517577216q^{28} \) \(\mathstrut -\mathstrut 217397685843681573854388291537651452827057882148450250q^{29} \) \(\mathstrut -\mathstrut 809277931163833776121134244746469476931174350662544000q^{30} \) \(\mathstrut -\mathstrut 3959918978904396097569386510196715694840286709585401440q^{31} \) \(\mathstrut -\mathstrut 9479144378484593489541015426974249650207814007382867968q^{32} \) \(\mathstrut -\mathstrut 73769578315518021607552488579011739564089308117835328528q^{33} \) \(\mathstrut -\mathstrut 324638192385754362369074018224584035205208569018875155680q^{34} \) \(\mathstrut -\mathstrut 1051811671165262926972759981500117019527196204743409914000q^{35} \) \(\mathstrut -\mathstrut 3440544904928519792841567448764696150680442862608580965120q^{36} \) \(\mathstrut -\mathstrut 6710426612911460903226679780416929578822322356442579950178q^{37} \) \(\mathstrut -\mathstrut 20075776649866586500887218371135359952534984707306414947520q^{38} \) \(\mathstrut -\mathstrut 53266590853912928667191550341591883996636524676049287303720q^{39} \) \(\mathstrut -\mathstrut 87443314425210154156114784714128373503740284779633935360000q^{40} \) \(\mathstrut -\mathstrut 89999556000464227434562342749528590851939245788450434103790q^{41} \) \(\mathstrut +\mathstrut 151860645080061390785566939100205618848419219581171296592384q^{42} \) \(\mathstrut +\mathstrut 1171421579861687300375905115748875459141635816468653452284156q^{43} \) \(\mathstrut +\mathstrut 3620387401482413711753562750789250834104238410455247119723520q^{44} \) \(\mathstrut +\mathstrut 8637496301209289669216900677161766462676265859857821184867750q^{45} \) \(\mathstrut +\mathstrut 13122337792181100518478081314861771936057558300377044573644160q^{46} \) \(\mathstrut +\mathstrut 26407117391117866585989236437476333636637017745173062895096432q^{47} \) \(\mathstrut -\mathstrut 305063509192507618357183882504465545852009436962512246145024q^{48} \) \(\mathstrut -\mathstrut 47859785088079990485612756297590896342589260563105328803969315q^{49} \) \(\mathstrut -\mathstrut 198341627273982740927873511630518057650356858808871192258250000q^{50} \) \(\mathstrut -\mathstrut 666572032421535161197734372534298884381369595464382997470670040q^{51} \) \(\mathstrut -\mathstrut 1819820853930882517149424007699825989256997486995920851867734528q^{52} \) \(\mathstrut -\mathstrut 2253672757277210109476755074185818948452790752453662372858468754q^{53} \) \(\mathstrut -\mathstrut 981929879310881011928466994898412465282666955980051795540412800q^{54} \) \(\mathstrut +\mathstrut 5272301841223840031246441919708126997046467528986443289345081000q^{55} \) \(\mathstrut +\mathstrut 17369101267271748189623122493455314696373137673860233497989120000q^{56} \) \(\mathstrut +\mathstrut 39672259194438733138452388186436605652387179030172301666478212240q^{57} \) \(\mathstrut +\mathstrut 63080485469034924979732075223792805715626817023343777138220605920q^{58} \) \(\mathstrut +\mathstrut 49827032054541030737892137385762950528020446432538215007741437900q^{59} \) \(\mathstrut +\mathstrut 91369267546356596727702377377074204109693912478731602288473856000q^{60} \) \(\mathstrut -\mathstrut 200207946356755779993110124671040230418699916707275462827300034090q^{61} \) \(\mathstrut -\mathstrut 456512716932753516995161459627410738703514050956609499700325060096q^{62} \) \(\mathstrut -\mathstrut 1444699606935245693297879065147738830138012519879166909023399465144q^{63} \) \(\mathstrut -\mathstrut 2671988611100492125931167910213768824231319631401339943695669002240q^{64} \) \(\mathstrut -\mathstrut 2221078323698894670419341126197735507928898751783246157619800369500q^{65} \) \(\mathstrut -\mathstrut 797490624045567852983392967901985951789407586519264116965780839680q^{66} \) \(\mathstrut +\mathstrut 1726934463658866670044856129309631728944059099751189118466533017652q^{67} \) \(\mathstrut +\mathstrut 25844159932565717701710366021885253281928511625890180327915132834304q^{68} \) \(\mathstrut +\mathstrut 43307862567803975621848996603714756131647359083362619530437754803680q^{69} \) \(\mathstrut +\mathstrut 60019715162941233136874683443010604187189046779871920798680662752000q^{70} \) \(\mathstrut +\mathstrut 29528228383509762365399718501357560736875772117852859701209862331560q^{71} \) \(\mathstrut +\mathstrut 5937319857025079492793067138582418624443592391466592842045028290560q^{72} \) \(\mathstrut -\mathstrut 237248424072934328617284197336037660641948064767277176027665176375374q^{73} \) \(\mathstrut -\mathstrut 385668396032745357868624366253781435784895053179379214963132226802080q^{74} \) \(\mathstrut -\mathstrut 785444151134296088966742788487546108897483082972592363003091781312500q^{75} \) \(\mathstrut -\mathstrut 402469771116557587325960702574461860644965601604695023105081798528000q^{76} \) \(\mathstrut -\mathstrut 1160921420345569675442649510235573702285949327395662717704239852301856q^{77} \) \(\mathstrut +\mathstrut 339124438335685564147183055565832879915531514801135920231578753382272q^{78} \) \(\mathstrut +\mathstrut 1210019475236668608258558597507004925943189831192425236151129201347600q^{79} \) \(\mathstrut +\mathstrut 7695510793835037324754830224890315360926193938062866122926593916928000q^{80} \) \(\mathstrut +\mathstrut 12895807280425851869767179003361520763349212513521199742652083367867805q^{81} \) \(\mathstrut +\mathstrut 19869905655996015892436375229312420723635630923691072274009372051144864q^{82} \) \(\mathstrut +\mathstrut 10633758535693793129462935403233565634399957806616398467042339222483716q^{83} \) \(\mathstrut -\mathstrut 17104473919241589848125111473450344991721950406193981672669373028884480q^{84} \) \(\mathstrut -\mathstrut 28641392301460491393930553180957463692521548910270676165772874742366500q^{85} \) \(\mathstrut -\mathstrut 130748824105220136322401247193488038601024385677355691179590030869522240q^{86} \) \(\mathstrut -\mathstrut 158256246334086183408933559981662943488738078279070353132629771124728040q^{87} \) \(\mathstrut -\mathstrut 221808067516055560593893382793377773024661552295403957235825845052456960q^{88} \) \(\mathstrut -\mathstrut 44230399340933247556508628049428956972940692248797881370004235332026750q^{89} \) \(\mathstrut +\mathstrut 205005728265438963974181523583877066710560749255482389735945594174668000q^{90} \) \(\mathstrut +\mathstrut 503963419362898329804217905595235878617892804641236823955454638331741360q^{91} \) \(\mathstrut +\mathstrut 1056276182251025158869277711594662138415929570173882076378175681365399552q^{92} \) \(\mathstrut +\mathstrut 2087551224100544830404247844376209582022159740935531745376318713047458432q^{93} \) \(\mathstrut +\mathstrut 1211599009021421323842808603980852406277919665987296133682388929757489920q^{94} \) \(\mathstrut +\mathstrut 1134809355692277446299742482002998127744674957590385906379174039024255000q^{95} \) \(\mathstrut -\mathstrut 1239624362529508037215561089866383709629049658259836228855181445997527040q^{96} \) \(\mathstrut -\mathstrut 4705643796144250410051227741367571092615369303801441364082016351450032918q^{97} \) \(\mathstrut -\mathstrut 7645702282951838206479981702299956043322685777549671658293752892775157616q^{98} \) \(\mathstrut -\mathstrut 15823110517274977002648456256699492623727665140588002701017544901953092820q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{74}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.74.a.a \(5\) \(33.748\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-92089333488\) \(-1\!\cdots\!04\) \(23\!\cdots\!50\) \(-4\!\cdots\!08\) \(+\) \(q+(-18417866698-\beta _{1})q^{2}+\cdots\)