Properties

Label 2.50
Level 2
Weight 50
Dimension 5
Nonzero newspaces 1
Newforms 2
Sturm bound 12
Trace bound 0

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 50 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{50}(\Gamma_1(2))\).

Total New Old
Modular forms 13 5 8
Cusp forms 11 5 6
Eisenstein series 2 0 2

Trace form

\(5q \) \(\mathstrut +\mathstrut 16777216q^{2} \) \(\mathstrut +\mathstrut 264847461204q^{3} \) \(\mathstrut +\mathstrut 1407374883553280q^{4} \) \(\mathstrut -\mathstrut 18638485219296930q^{5} \) \(\mathstrut -\mathstrut 4987106140807495680q^{6} \) \(\mathstrut -\mathstrut 557868444516202015832q^{7} \) \(\mathstrut +\mathstrut 4722366482869645213696q^{8} \) \(\mathstrut +\mathstrut 280721402774176601867265q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut +\mathstrut 16777216q^{2} \) \(\mathstrut +\mathstrut 264847461204q^{3} \) \(\mathstrut +\mathstrut 1407374883553280q^{4} \) \(\mathstrut -\mathstrut 18638485219296930q^{5} \) \(\mathstrut -\mathstrut 4987106140807495680q^{6} \) \(\mathstrut -\mathstrut 557868444516202015832q^{7} \) \(\mathstrut +\mathstrut 4722366482869645213696q^{8} \) \(\mathstrut +\mathstrut 280721402774176601867265q^{9} \) \(\mathstrut -\mathstrut 3103576043133487420538880q^{10} \) \(\mathstrut -\mathstrut 28365608284701363831431940q^{11} \) \(\mathstrut +\mathstrut 74547932974272268493389824q^{12} \) \(\mathstrut +\mathstrut 1271483866889126024941566214q^{13} \) \(\mathstrut +\mathstrut 5149096806336651063449354240q^{14} \) \(\mathstrut +\mathstrut 214847871537777285741720697080q^{15} \) \(\mathstrut +\mathstrut 396140812571321687967719751680q^{16} \) \(\mathstrut +\mathstrut 5152941537749680842191457808218q^{17} \) \(\mathstrut +\mathstrut 8357477209072966959936703561728q^{18} \) \(\mathstrut +\mathstrut 46341407445428881648983974068900q^{19} \) \(\mathstrut -\mathstrut 5246267193023509460628359086080q^{20} \) \(\mathstrut -\mathstrut 559284133080226526186327023974240q^{21} \) \(\mathstrut -\mathstrut 391822908885270015944302880882688q^{22} \) \(\mathstrut -\mathstrut 7831329242647530058437600484227336q^{23} \) \(\mathstrut -\mathstrut 1403745584837359368749795329966080q^{24} \) \(\mathstrut +\mathstrut 47629982895347058295233852912669275q^{25} \) \(\mathstrut +\mathstrut 77489996734861184268108829105848320q^{26} \) \(\mathstrut +\mathstrut 206445919322502956875507659031005000q^{27} \) \(\mathstrut -\mathstrut 157026007427807851323569879795105792q^{28} \) \(\mathstrut -\mathstrut 247527321733942898985506970467111850q^{29} \) \(\mathstrut -\mathstrut 656919347782328483126789725193502720q^{30} \) \(\mathstrut -\mathstrut 4690501690750749324289013431841855840q^{31} \) \(\mathstrut +\mathstrut 1329227995784915872903807060280344576q^{32} \) \(\mathstrut +\mathstrut 54050705662548577707614642759829170928q^{33} \) \(\mathstrut +\mathstrut 44771168724957977082517808188584099840q^{34} \) \(\mathstrut +\mathstrut 146807633005118450883143794431190245360q^{35} \) \(\mathstrut +\mathstrut 79016050308044041640235218237223075840q^{36} \) \(\mathstrut -\mathstrut 141224859266832750691437704043300925442q^{37} \) \(\mathstrut -\mathstrut 287911479833086098582315297230647459840q^{38} \) \(\mathstrut -\mathstrut 1483694045958777701643328472443999407720q^{39} \) \(\mathstrut -\mathstrut 873578994460748273001554791397358305280q^{40} \) \(\mathstrut +\mathstrut 5837281266020750863591249937583403824210q^{41} \) \(\mathstrut +\mathstrut 5696800652343028796496744041099613437952q^{42} \) \(\mathstrut +\mathstrut 5426330416373199601603436204868309699484q^{43} \) \(\mathstrut -\mathstrut 7984208931319907272792305772123536752640q^{44} \) \(\mathstrut -\mathstrut 86925253652175935161144662252858764431290q^{45} \) \(\mathstrut -\mathstrut 34812502120267569161491740843751589806080q^{46} \) \(\mathstrut -\mathstrut 230419494120900556639230369093924230606352q^{47} \) \(\mathstrut +\mathstrut 20983377697760831247406890107482662764544q^{48} \) \(\mathstrut +\mathstrut 410460682658525880199903254150977318928285q^{49} \) \(\mathstrut +\mathstrut 524670684231693022835584659437082011238400q^{50} \) \(\mathstrut +\mathstrut 1840814094647166636543757567809498045302760q^{51} \) \(\mathstrut +\mathstrut 357890891820591581439361495868934543376384q^{52} \) \(\mathstrut -\mathstrut 3255741187077740704432998366691597498508466q^{53} \) \(\mathstrut +\mathstrut 3117137442451018211300844150422584374067200q^{54} \) \(\mathstrut -\mathstrut 7413119005014717463507128836848112026350360q^{55} \) \(\mathstrut +\mathstrut 1449341903644522046008760560066162526781440q^{56} \) \(\mathstrut -\mathstrut 10972460577016464801645288735793062528386160q^{57} \) \(\mathstrut +\mathstrut 35603587276128039447232465468509208612700160q^{58} \) \(\mathstrut -\mathstrut 31299442004599717113735073038141116234855700q^{59} \) \(\mathstrut +\mathstrut 60474299637429873593046630185364533784084480q^{60} \) \(\mathstrut -\mathstrut 66894309067789985792204509754926988828519690q^{61} \) \(\mathstrut +\mathstrut 159721137676069834981339855431435216886956032q^{62} \) \(\mathstrut -\mathstrut 554022586770393686777096994052605277017064056q^{63} \) \(\mathstrut +\mathstrut 111503725992653115707678591363241807529902080q^{64} \) \(\mathstrut -\mathstrut 1052628489073426957113152396992241527143651420q^{65} \) \(\mathstrut +\mathstrut 1928998656113819566256453087528516456168816640q^{66} \) \(\mathstrut -\mathstrut 20885003468135713186598920647668702204221292q^{67} \) \(\mathstrut +\mathstrut 1450424099329463330514537562561586792924971008q^{68} \) \(\mathstrut -\mathstrut 1257559858360555896437195834297656389818725920q^{69} \) \(\mathstrut +\mathstrut 7618037059227102853981604103256516677347573760q^{70} \) \(\mathstrut -\mathstrut 6594142656484316264086959029054209943412047640q^{71} \) \(\mathstrut +\mathstrut 2352420702783651680787935004437281324891373568q^{72} \) \(\mathstrut -\mathstrut 19756885769059370139676576183477802818928731406q^{73} \) \(\mathstrut +\mathstrut 12750362298794385505728320817555046789063639040q^{74} \) \(\mathstrut -\mathstrut 27905622673610296942656094011894237718545426900q^{75} \) \(\mathstrut +\mathstrut 13043946581441115021393311842568604922308198400q^{76} \) \(\mathstrut +\mathstrut 12602774717208971429421128542194190666655134176q^{77} \) \(\mathstrut +\mathstrut 37001104240479571914234863709295328137781968896q^{78} \) \(\mathstrut +\mathstrut 19096525780528455865201933661363886028057286800q^{79} \) \(\mathstrut -\mathstrut 1476692935974170951191455457926057088757268480q^{80} \) \(\mathstrut -\mathstrut 70934640664141770240050219142683596980815080995q^{81} \) \(\mathstrut -\mathstrut 136289723431352802248020881663065807260628287488q^{82} \) \(\mathstrut +\mathstrut 126217178168945828921481068490657733955840008164q^{83} \) \(\mathstrut -\mathstrut 157424488333396192411121232794771046167677501440q^{84} \) \(\mathstrut +\mathstrut 417930567475700218907549622522904206857671893660q^{85} \) \(\mathstrut -\mathstrut 680892727632315740413194786983907995215703572480q^{86} \) \(\mathstrut +\mathstrut 1321368679037303347007178017036700024540174119640q^{87} \) \(\mathstrut -\mathstrut 110288344153182865628212719184099971732055523328q^{88} \) \(\mathstrut +\mathstrut 1559139292710419737771563637847468513168982096450q^{89} \) \(\mathstrut -\mathstrut 2394128797123032286624071503358166980557946224640q^{90} \) \(\mathstrut +\mathstrut 795244717410814649701589752966368909666334406960q^{91} \) \(\mathstrut -\mathstrut 2204323216187692813920925315004509188862997692416q^{92} \) \(\mathstrut -\mathstrut 2186942403209429777679591366091800352812220382592q^{93} \) \(\mathstrut -\mathstrut 3468326649069504737796404475680414179263051202560q^{94} \) \(\mathstrut +\mathstrut 308019764153508454748351919334293296300623632600q^{95} \) \(\mathstrut -\mathstrut 395119255799781914560402250065368998826454548480q^{96} \) \(\mathstrut +\mathstrut 5206218436371069170636818419182500514721889141738q^{97} \) \(\mathstrut +\mathstrut 5650488057759347948652183551009121211852806684672q^{98} \) \(\mathstrut +\mathstrut 9268770207435901369155123842136775797278733317580q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{50}^{\mathrm{new}}(\Gamma_1(2))\)

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
2.50.a \(\chi_{2}(1, \cdot)\) 2.50.a.a 2 1
2.50.a.b 3

Decomposition of \(S_{50}^{\mathrm{old}}(\Gamma_1(2))\) into lower level spaces

\( S_{50}^{\mathrm{old}}(\Gamma_1(2)) \cong \) \(S_{50}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)