Properties

Label 9.34
Level 9
Weight 34
Dimension 77
Nonzero newspaces 2
Newform subspaces 6
Sturm bound 204
Trace bound 1

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 9 = 3^{2} \)
Weight: \( k \) = \( 34 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 6 \)
Sturm bound: \(204\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(\Gamma_1(9))\).

Total New Old
Modular forms 103 82 21
Cusp forms 95 77 18
Eisenstein series 8 5 3

Trace form

\( 77q + 9393q^{2} - 37919883q^{3} - 79510812205q^{4} + 562376777997q^{5} + 9277861410423q^{6} - 73813756686755q^{7} + 1974168301674q^{8} - 172172452129677q^{9} + O(q^{10}) \) \( 77q + 9393q^{2} - 37919883q^{3} - 79510812205q^{4} + 562376777997q^{5} + 9277861410423q^{6} - 73813756686755q^{7} + 1974168301674q^{8} - 172172452129677q^{9} + 41721279678300144q^{10} + 500201438224553934q^{11} - 986757437556451452q^{12} - 3164411118476099363q^{13} + 13379432434625477496q^{14} + 12974004890753206563q^{15} - 554844693892610440945q^{16} + 171455940044707179402q^{17} + 1729477431108814841460q^{18} - 3262056535332736653482q^{19} + 7535694048511834871940q^{20} - 9490450594209272296035q^{21} - 21715546252625160626361q^{22} + 4346368740239250351855q^{23} - 178161906319508858117643q^{24} + 26146108231296681977402q^{25} - 1360917044896159668296940q^{26} + 2050788489893235319637880q^{27} - 3450255376430851973952740q^{28} + 3209059800168609213912075q^{29} - 513955868306454019253016q^{30} + 2956045483950087912255481q^{31} + 27967453347241011711084255q^{32} - 13734637216730002698127992q^{33} - 47597236991044817084720811q^{34} - 30120775130325033604956234q^{35} + 126982770270445041740139123q^{36} + 37031383499313216557806714q^{37} - 71281476444273939087841293q^{38} - 38516100433597113351809145q^{39} - 143233643701219795986302688q^{40} + 1479209709307450625604463854q^{41} - 3432018866094445938345455886q^{42} + 186402934397297097874520176q^{43} - 7640884517807614109060087382q^{44} + 12779943324704411645074933953q^{45} - 8741870359047683928311813880q^{46} + 12375573682736859766296657369q^{47} + 9438402430726406174048949987q^{48} + 2551916201084999857638755004q^{49} - 22764783637712630551103530671q^{50} + 48012302270207928799089357417q^{51} - 617857720362236933753824118q^{52} + 166467389022971093849058756468q^{53} - 221167773867578424128496243207q^{54} - 99716965449331090443648050634q^{55} + 94878094258823477039837549070q^{56} + 210382634390061939744669224385q^{57} - 314583362958031994670914285868q^{58} + 372635298425098260308655710490q^{59} + 434743444459352124712210917348q^{60} - 673266375389701032557048166605q^{61} - 167287281342733266754890428700q^{62} + 529404169082455483103216885355q^{63} - 162508834863972468433881766462q^{64} + 5044486466795014544082781174791q^{65} - 86121183129723235486032106374q^{66} - 2594001946424971471992483941156q^{67} + 16622237965215565838549127548511q^{68} - 4311767350161924686539872219081q^{69} - 16438784359422094987646010328734q^{70} + 18675408558135253016522341997136q^{71} + 1300396021230803448731992818363q^{72} - 17199957135460673045185283362148q^{73} + 69375669813332713224181765660620q^{74} - 19378645061993627357209133303067q^{75} - 30576244126699549565283547752515q^{76} + 39664318377890944618837454005365q^{77} - 24712894178647665299134589255562q^{78} - 18360400019863852122793150482833q^{79} + 248323457614864701539014318826688q^{80} - 53589837559472354567374958554569q^{81} - 113054175369682352090831143402026q^{82} + 47362575757889063494986064446795q^{83} + 36212360455031369124196429555602q^{84} - 40867640260262454723033197919762q^{85} + 81688476044563756194658169819217q^{86} + 394932005632584997767831262589847q^{87} - 104876935613847067684286447478645q^{88} + 30102104054672032180548164180544q^{89} - 253601539714448049591062895859092q^{90} + 657490724925203159128893554148446q^{91} - 1593665077204811199306496050206286q^{92} - 415629377369235831879113092397817q^{93} + 400548608765495960491335588977328q^{94} - 418907245469649572454394032922476q^{95} - 1680379483219649555464514789051616q^{96} + 1361293757484519443367209527995952q^{97} - 6423155448794234931777780115458720q^{98} + 2786860892426519033037266123581713q^{99} + O(q^{100}) \)

Decomposition of \(S_{34}^{\mathrm{new}}(\Gamma_1(9))\)

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
9.34.a \(\chi_{9}(1, \cdot)\) 9.34.a.a 1 1
9.34.a.b 2
9.34.a.c 3
9.34.a.d 3
9.34.a.e 4
9.34.c \(\chi_{9}(4, \cdot)\) 9.34.c.a 64 2

Decomposition of \(S_{34}^{\mathrm{old}}(\Gamma_1(9))\) into lower level spaces

\( S_{34}^{\mathrm{old}}(\Gamma_1(9)) \cong \) \(S_{34}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)