Properties

Label 1.70
Level 1
Weight 70
Dimension 5
Nonzero newspaces 1
Newforms 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 70 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{70}(\Gamma_1(1))\).

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

Trace form

\(5q \) \(\mathstrut -\mathstrut 18005734368q^{2} \) \(\mathstrut -\mathstrut 4858082326815804q^{3} \) \(\mathstrut +\mathstrut 1258222332330311336960q^{4} \) \(\mathstrut -\mathstrut 1863826173406730009099250q^{5} \) \(\mathstrut +\mathstrut 656206758200548766362988160q^{6} \) \(\mathstrut +\mathstrut 76799665171164846436246213192q^{7} \) \(\mathstrut -\mathstrut 45904305194055745607709713203200q^{8} \) \(\mathstrut -\mathstrut 317098314648431447640165640938735q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut -\mathstrut 18005734368q^{2} \) \(\mathstrut -\mathstrut 4858082326815804q^{3} \) \(\mathstrut +\mathstrut 1258222332330311336960q^{4} \) \(\mathstrut -\mathstrut 1863826173406730009099250q^{5} \) \(\mathstrut +\mathstrut 656206758200548766362988160q^{6} \) \(\mathstrut +\mathstrut 76799665171164846436246213192q^{7} \) \(\mathstrut -\mathstrut 45904305194055745607709713203200q^{8} \) \(\mathstrut -\mathstrut 317098314648431447640165640938735q^{9} \) \(\mathstrut +\mathstrut 44330196388334747724288536990904000q^{10} \) \(\mathstrut -\mathstrut 60667038452283127772973811588820340q^{11} \) \(\mathstrut -\mathstrut 11483075252723727688688753994339790848q^{12} \) \(\mathstrut +\mathstrut 241757308976474000869098277194908009686q^{13} \) \(\mathstrut +\mathstrut 354251192093531665156722201608564593920q^{14} \) \(\mathstrut -\mathstrut 22070061029664005246083216762166031993000q^{15} \) \(\mathstrut +\mathstrut 959158246463054504693505368032717942292480q^{16} \) \(\mathstrut -\mathstrut 3406116484103989032025799295223462139713638q^{17} \) \(\mathstrut +\mathstrut 24028760578245796491398335690330074428977056q^{18} \) \(\mathstrut +\mathstrut 50409644862695734347948203723209710229820500q^{19} \) \(\mathstrut -\mathstrut 1423124021474831957749573329409407107348736000q^{20} \) \(\mathstrut +\mathstrut 3013464004165585730133470747616333350946636960q^{21} \) \(\mathstrut -\mathstrut 11532803895526133094453480299474752792963837056q^{22} \) \(\mathstrut +\mathstrut 49597077165419749499080141147449313474867772376q^{23} \) \(\mathstrut -\mathstrut 3758573903021835292505270073849755869023436800q^{24} \) \(\mathstrut +\mathstrut 464109230075747674561453215791202707168413296875q^{25} \) \(\mathstrut -\mathstrut 16366243363702391437841515238911258759405955787840q^{26} \) \(\mathstrut -\mathstrut 4656668144254073384201536267744600116223141335000q^{27} \) \(\mathstrut -\mathstrut 145657936238300983941227399236934030905596038045696q^{28} \) \(\mathstrut -\mathstrut 623609331535478016897341347681349171717970694417050q^{29} \) \(\mathstrut -\mathstrut 3363430262026080628144709187077082169492181498016000q^{30} \) \(\mathstrut -\mathstrut 7773979811443490840377264327630961134705736859811040q^{31} \) \(\mathstrut -\mathstrut 59446525385187765185716890552455969166501734680363008q^{32} \) \(\mathstrut -\mathstrut 114056291760419605293140369499335251414708842916007568q^{33} \) \(\mathstrut -\mathstrut 257146382902997900108453969123952433606251002004626880q^{34} \) \(\mathstrut -\mathstrut 746713702965644817139124842748848714607056852166946000q^{35} \) \(\mathstrut -\mathstrut 2051949564713522439077005513759167028086223411246648320q^{36} \) \(\mathstrut +\mathstrut 1173349927804932358065167442366744839628119054724224302q^{37} \) \(\mathstrut +\mathstrut 118225357325580676139934406348110667239400005459024000q^{38} \) \(\mathstrut +\mathstrut 14057637047001351842470294363781888979755467326981836280q^{39} \) \(\mathstrut +\mathstrut 113448309945374158392264311043353386142011790732943360000q^{40} \) \(\mathstrut +\mathstrut 126046983235211396249316718220813524712126370275682679410q^{41} \) \(\mathstrut +\mathstrut 293618058653079520265272756273690037096976372387400909824q^{42} \) \(\mathstrut +\mathstrut 182990795236310295463906097926157021228111368794869386156q^{43} \) \(\mathstrut -\mathstrut 207861964397629572369029141530074424104092312018072801280q^{44} \) \(\mathstrut -\mathstrut 1643209216033810606361059101690783215624601629799145190250q^{45} \) \(\mathstrut -\mathstrut 10254004636983168196931301388746633342901210187441053098240q^{46} \) \(\mathstrut -\mathstrut 10227620449924872974485942387482033943920758356350760046928q^{47} \) \(\mathstrut -\mathstrut 32395077603800850016659260748043884333789001078303069569024q^{48} \) \(\mathstrut -\mathstrut 18333133463047872956569862100374253860638045246565546349315q^{49} \) \(\mathstrut +\mathstrut 36528582075561740316450944849185458926809558787823115500000q^{50} \) \(\mathstrut +\mathstrut 118668467511484226348705374365583184000267089107653013314760q^{51} \) \(\mathstrut +\mathstrut 942523544779067327174672695236090488789159958525129397368832q^{52} \) \(\mathstrut +\mathstrut 632699876044410239466855544904774161379655010323706866957246q^{53} \) \(\mathstrut +\mathstrut 180558070990413352422035814551902697653880540863671629472000q^{54} \) \(\mathstrut +\mathstrut 908306905388987301982805388456202130484984202488366374469000q^{55} \) \(\mathstrut -\mathstrut 3333324356971334653614007426143869616663160772285360681779200q^{56} \) \(\mathstrut -\mathstrut 10204523476105540193819201045109650965597050176490899356681200q^{57} \) \(\mathstrut -\mathstrut 21357003692165570079369319070573084097392679296022668457345600q^{58} \) \(\mathstrut -\mathstrut 33658105593968338077893783802509858432791301363490818469557700q^{59} \) \(\mathstrut +\mathstrut 4120988224178099264267892216282931461935581678787045796864000q^{60} \) \(\mathstrut +\mathstrut 26493274349159915694337742892910871952893265772033046389592710q^{61} \) \(\mathstrut +\mathstrut 44671386079622887685677726725261963790680651281391262992405504q^{62} \) \(\mathstrut +\mathstrut 328016742630707922691415372382087941549150107260006661759940136q^{63} \) \(\mathstrut +\mathstrut 1145396334142953198321101499067029773326674384142624569121832960q^{64} \) \(\mathstrut +\mathstrut 32395374544526764253115310833548550857549161202925434554654500q^{65} \) \(\mathstrut -\mathstrut 338570852359916448113902185281844117937336911423509879777978880q^{66} \) \(\mathstrut -\mathstrut 1263671747756647516553966063420040358632142902313472768464353788q^{67} \) \(\mathstrut -\mathstrut 4242259843001640357556603344412218995999623052710587648746797056q^{68} \) \(\mathstrut -\mathstrut 6814317814451425604632002110369996993863432815743912687188684320q^{69} \) \(\mathstrut -\mathstrut 12017797477418109745097884516334700669100677302053986880978752000q^{70} \) \(\mathstrut -\mathstrut 11362995327515584413483941817933086342825689164345402588802686840q^{71} \) \(\mathstrut +\mathstrut 33340305480431860824635017027459448788044465030309454443456921600q^{72} \) \(\mathstrut +\mathstrut 33966190478000707541728805214544524983949148170634721693934875026q^{73} \) \(\mathstrut +\mathstrut 33287841323757960873231466351855256670579388646335713232882057920q^{74} \) \(\mathstrut +\mathstrut 133279503236831559979066107911998455423803652698542098545072437500q^{75} \) \(\mathstrut +\mathstrut 183360103953987098564098859807800968353232769985153900286854041600q^{76} \) \(\mathstrut -\mathstrut 68777883874935499089374017393044391085266332314302726754935189536q^{77} \) \(\mathstrut -\mathstrut 57072566318401512231072936702879380800620122459787990692269387008q^{78} \) \(\mathstrut -\mathstrut 368980120609165108452324012570275063461532695000205866878292977200q^{79} \) \(\mathstrut -\mathstrut 2297307515344457444954054326919281387940022207684288488149352448000q^{80} \) \(\mathstrut -\mathstrut 1101671322957552996191157562976784281568686466036132881049220065795q^{81} \) \(\mathstrut -\mathstrut 931502706981052883685780503022082242955330053475976826093455630016q^{82} \) \(\mathstrut +\mathstrut 1154866061089842220595327582106550433201200060522873707675675258516q^{83} \) \(\mathstrut +\mathstrut 2982792317318014581404535874546389828859810656181796104246410117120q^{84} \) \(\mathstrut +\mathstrut 7495188972487466607434575375594377348887576076812903274045952741500q^{85} \) \(\mathstrut +\mathstrut 18898926811527982953627013747012343020261345543532646428747294271360q^{86} \) \(\mathstrut +\mathstrut 12567354207673775260644045622671132292173268168085315900596903577400q^{87} \) \(\mathstrut +\mathstrut 15163923620712287826914767806325902037685216056349718267565463961600q^{88} \) \(\mathstrut -\mathstrut 18794883963687081977506023684762454245562992435196209807107213565150q^{89} \) \(\mathstrut -\mathstrut 85191607767474905371023384802405560846731062106202026396755774248000q^{90} \) \(\mathstrut -\mathstrut 80964793679514484977485771721533938042559852862777758867826841866640q^{91} \) \(\mathstrut -\mathstrut 21013231692212615201045059193164259260053682303043508524037104345088q^{92} \) \(\mathstrut -\mathstrut 112906043990099714252090302813260364787306717550744493130306572821888q^{93} \) \(\mathstrut -\mathstrut 320329342040387206482715898781454186419182431678416100998048980820480q^{94} \) \(\mathstrut +\mathstrut 150021391313508674306348088796351704171326160875536630528081545795000q^{95} \) \(\mathstrut +\mathstrut 782790419970794266899143250915194035456012168622622133055202797813760q^{96} \) \(\mathstrut +\mathstrut 368226872658277176269129285066418598650754906087385239386955040860522q^{97} \) \(\mathstrut +\mathstrut 1783735577381778172290937711296356094085482547558896852990197505179424q^{98} \) \(\mathstrut +\mathstrut 586262466890180722819447934223042169763434625676688596008715148885980q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{70}^{\mathrm{new}}(\Gamma_1(1))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1.70.a \(\chi_{1}(1, \cdot)\) 1.70.a.a 5 1