Properties

Label 2.74.a
Level 2
Weight 74
Character orbit a
Rep. character \(\chi_{2}(1,\cdot)\)
Character field \(\Q\)
Dimension 7
Newforms 2
Sturm bound 18
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 74 \)
Character orbit: \([\chi]\) = 2.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(18\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{74}(\Gamma_0(2))\).

Total New Old
Modular forms 19 7 12
Cusp forms 17 7 10
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators.

\(2\)Dim.
\(+\)\(3\)
\(-\)\(4\)

Trace form

\(7q \) \(\mathstrut +\mathstrut 68719476736q^{2} \) \(\mathstrut +\mathstrut 1027124703510204q^{3} \) \(\mathstrut +\mathstrut 33056565380087516495872q^{4} \) \(\mathstrut -\mathstrut 40558853897019556618457910q^{5} \) \(\mathstrut +\mathstrut 41857413074783112692842364928q^{6} \) \(\mathstrut +\mathstrut 1319013575200782974071512211448q^{7} \) \(\mathstrut +\mathstrut 324518553658426726783156020576256q^{8} \) \(\mathstrut +\mathstrut 197377606713669685301132051646756411q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(7q \) \(\mathstrut +\mathstrut 68719476736q^{2} \) \(\mathstrut +\mathstrut 1027124703510204q^{3} \) \(\mathstrut +\mathstrut 33056565380087516495872q^{4} \) \(\mathstrut -\mathstrut 40558853897019556618457910q^{5} \) \(\mathstrut +\mathstrut 41857413074783112692842364928q^{6} \) \(\mathstrut +\mathstrut 1319013575200782974071512211448q^{7} \) \(\mathstrut +\mathstrut 324518553658426726783156020576256q^{8} \) \(\mathstrut +\mathstrut 197377606713669685301132051646756411q^{9} \) \(\mathstrut +\mathstrut 1708704931234681219841889137212784640q^{10} \) \(\mathstrut -\mathstrut 27600640793130220835781688640423160396q^{11} \) \(\mathstrut +\mathstrut 4850459273584009196858899998896553984q^{12} \) \(\mathstrut +\mathstrut 16382312624706684550801940331533298616514q^{13} \) \(\mathstrut +\mathstrut 409136272750615877298547410438906536001536q^{14} \) \(\mathstrut -\mathstrut 405584036700872141132474996756634202511640q^{15} \) \(\mathstrut +\mathstrut 156105216389714361990750027908538530541862912q^{16} \) \(\mathstrut -\mathstrut 1066999187182198043388511037865747532008417282q^{17} \) \(\mathstrut +\mathstrut 3255842558478021353341847588179331692256821248q^{18} \) \(\mathstrut +\mathstrut 53935121388410443644614146326771216282991503020q^{19} \) \(\mathstrut -\mathstrut 191533772226892047038045311404722620279931535360q^{20} \) \(\mathstrut +\mathstrut 2849533425198940897609224165597780267210940964064q^{21} \) \(\mathstrut +\mathstrut 9150072434788992021693852445701475242905343885312q^{22} \) \(\mathstrut +\mathstrut 11487021927231577132753977745688995443452136273384q^{23} \) \(\mathstrut +\mathstrut 197666044563985429738489049912218491753452575653888q^{24} \) \(\mathstrut +\mathstrut 4442341753390189342611612360612615751804313224567225q^{25} \) \(\mathstrut -\mathstrut 939464668009392503125801142449113923737510721093632q^{26} \) \(\mathstrut +\mathstrut 20892584344354699149244907986957825120077530692347480q^{27} \) \(\mathstrut +\mathstrut 6228865497978237779384994213988670550246569497591808q^{28} \) \(\mathstrut -\mathstrut 242659031370254704226112349973038557876808498312734030q^{29} \) \(\mathstrut -\mathstrut 1048349114291221124294475848520501250019442670845296640q^{30} \) \(\mathstrut +\mathstrut 4754620827269862681198675317057706435180399687073524704q^{31} \) \(\mathstrut +\mathstrut 1532495540865888858358347027150309183618739122183602176q^{32} \) \(\mathstrut +\mathstrut 79761089777578567682110917335748475775550335479302834768q^{33} \) \(\mathstrut +\mathstrut 204488278882446941187474408379912421395940926602866589696q^{34} \) \(\mathstrut +\mathstrut 1376295186694272619908786072829995978621818296087679962320q^{35} \) \(\mathstrut +\mathstrut 932089394413660384054868395110595432490074489749353005056q^{36} \) \(\mathstrut +\mathstrut 6897014531797115945750823550982798156661639192166851483818q^{37} \) \(\mathstrut +\mathstrut 9412804191936413646891909754675577992402077739949049774080q^{38} \) \(\mathstrut +\mathstrut 31375857019095066098997026182603358399649004449542485849032q^{39} \) \(\mathstrut +\mathstrut 8069130896376740533603203935689390719884189644076026429440q^{40} \) \(\mathstrut +\mathstrut 207561036577549239977618711632076555016582409617518912741094q^{41} \) \(\mathstrut -\mathstrut 104694486954058443037028594421282234244035423158989737689088q^{42} \) \(\mathstrut -\mathstrut 669515376121954138996540636248178131700536910793579100133996q^{43} \) \(\mathstrut -\mathstrut 130340340987202815896841738532383521291484781898447103983616q^{44} \) \(\mathstrut -\mathstrut 11325235544690847000804714518542546119529809765856199775650430q^{45} \) \(\mathstrut -\mathstrut 10055187030076398392878405673493410750203033255974000931110912q^{46} \) \(\mathstrut -\mathstrut 39353768626244150141187396234568307076650970187101967232623152q^{47} \) \(\mathstrut +\mathstrut 22905646300097371733925919643989710940845052141613680164864q^{48} \) \(\mathstrut +\mathstrut 129493632285583023439988456210141822988159886108545342585511119q^{49} \) \(\mathstrut +\mathstrut 170350141534045943234869791869403118604747023091471721535897600q^{50} \) \(\mathstrut +\mathstrut 976530651006378911356405853843811633989428798214510502430152504q^{51} \) \(\mathstrut +\mathstrut 77363284050807091967402032577698632221310401846446098684575744q^{52} \) \(\mathstrut +\mathstrut 1476036265911713078264026743636826897017112209944569985002104474q^{53} \) \(\mathstrut +\mathstrut 225136682955043068034732808337908589915161904277953973950873600q^{54} \) \(\mathstrut -\mathstrut 9172316756840955451381907105110761413428399399663556429421224520q^{55} \) \(\mathstrut +\mathstrut 1932091421363721765158679284673494912285910202569978892104237056q^{56} \) \(\mathstrut -\mathstrut 19246343545762558322604740763123478340316280134768466377718019280q^{57} \) \(\mathstrut -\mathstrut 39513537017273788236988247971454006076366280736916740878054195200q^{58} \) \(\mathstrut -\mathstrut 74921937563676145846070393075894640398784399890648016828516609660q^{59} \) \(\mathstrut -\mathstrut 1915316460903170675719989706391312359075569008799417707727421440q^{60} \) \(\mathstrut +\mathstrut 222903490578238099115364191117178893194949750880947971935694990994q^{61} \) \(\mathstrut +\mathstrut 195504071699382183303554505973484078352271385303884221638122668032q^{62} \) \(\mathstrut +\mathstrut 678865034144871199370209925607341661497036129209431559643530266264q^{63} \) \(\mathstrut +\mathstrut 737186041679900306885426193785693026232265667803843778780176842752q^{64} \) \(\mathstrut +\mathstrut 6840147896488363686507276668005205679632480056088891731592702691660q^{65} \) \(\mathstrut +\mathstrut 3069860275698184453678654113958670789622501761274434325754744406016q^{66} \) \(\mathstrut -\mathstrut 7587584248381195618707457069538120550412828037866999031232038314372q^{67} \) \(\mathstrut -\mathstrut 5038761198798366803334407150633833722506784674618586571275629494272q^{68} \) \(\mathstrut -\mathstrut 21242639944698603837144967984504325973796588470663724540063832232288q^{69} \) \(\mathstrut -\mathstrut 35236659370606449042543653930245981331402869469140142926019092807680q^{70} \) \(\mathstrut -\mathstrut 54190860046980946062970823072982786833668067514475229703471473178696q^{71} \) \(\mathstrut +\mathstrut 15375281771657160870229969994716837558235628710503758158730633412608q^{72} \) \(\mathstrut +\mathstrut 302204276459526144519916965475340033188079342798263447893361558739654q^{73} \) \(\mathstrut +\mathstrut 460788297382010659258858143952886782081979620906639511666754999812096q^{74} \) \(\mathstrut +\mathstrut 1321988182453308808957469062463764651479002141783122360382572395384900q^{75} \) \(\mathstrut +\mathstrut 254701409494135202491619664917666445418981268382573756093980129361920q^{76} \) \(\mathstrut +\mathstrut 1136290782245844952967529647847166832148473964718146517215659790189216q^{77} \) \(\mathstrut -\mathstrut 599357099842967606540357177425328183707393143418058291814117182275584q^{78} \) \(\mathstrut -\mathstrut 2063644198299887356015584664968287745082399564774871245601417500935760q^{79} \) \(\mathstrut -\mathstrut 904492666301863930243089081419238237195853008895807926928396580290560q^{80} \) \(\mathstrut -\mathstrut 16891815155353385788713120786633925888175683542107829174659509500480753q^{81} \) \(\mathstrut -\mathstrut 6446672193337464673511795801397809916038289746403453740221072542793728q^{82} \) \(\mathstrut +\mathstrut 20637316524023922777695817093166723059825032985062213786640521552119404q^{83} \) \(\mathstrut +\mathstrut 13456541138976215781259821921857622832470000144438510839450677536620544q^{84} \) \(\mathstrut +\mathstrut 17020911204842079191578418414879669130697869935588821344636303582004020q^{85} \) \(\mathstrut +\mathstrut 19124031929912910639273030116541437792145765208839809191835113952903168q^{86} \) \(\mathstrut -\mathstrut 11898630724605207728038010903252775519339509401543700937344046348372600q^{87} \) \(\mathstrut +\mathstrut 43209995381876983363698417646408761043080555936919912203426521155633152q^{88} \) \(\mathstrut +\mathstrut 207336285159197918258375121859361162714964365933301696623144396043125430q^{89} \) \(\mathstrut -\mathstrut 317728036129547092571635979865630963286270874163859138802031801957089280q^{90} \) \(\mathstrut -\mathstrut 534340988981832565293850366847600554295341775746604779176000263013148016q^{91} \) \(\mathstrut +\mathstrut 54245927337147076542352991515708572016052829493901493648502741757067264q^{92} \) \(\mathstrut -\mathstrut 2106624457661050548013889439781993705135349795614255107465567210376551552q^{93} \) \(\mathstrut -\mathstrut 984126126936657408329473443273688080352037863578757473463124749675659264q^{94} \) \(\mathstrut -\mathstrut 4667409163598269693325856603058210361118245346808039972183000921107828600q^{95} \) \(\mathstrut +\mathstrut 933451503650382427298696882819844350924165111346864003082343036693250048q^{96} \) \(\mathstrut +\mathstrut 5896832155048876985101920414621646427655604788621115351504190027391728558q^{97} \) \(\mathstrut -\mathstrut 2124579222479382129816851660207925419012878646227427237621783845675204608q^{98} \) \(\mathstrut +\mathstrut 31261167116176375892644199050595144491934483437936698088824988018572848292q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{74}^{\mathrm{new}}(\Gamma_0(2))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
2.74.a.a \(3\) \(67.497\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-206158430208\) \(-3\!\cdots\!72\) \(-3\!\cdots\!50\) \(-2\!\cdots\!64\) \(+\) \(q-2^{36}q^{2}+(-101346400339911324+\cdots)q^{3}+\cdots\)
2.74.a.b \(4\) \(67.497\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(274877906944\) \(30\!\cdots\!76\) \(-7\!\cdots\!60\) \(36\!\cdots\!12\) \(-\) \(q+2^{36}q^{2}+(76266581430811044+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{74}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces

\( S_{74}^{\mathrm{old}}(\Gamma_0(2)) \cong \) \(S_{74}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)