Properties

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

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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

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

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