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Properties

Label 3.34
Level 3
Weight 34
Dimension 6
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 22
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 34 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(22\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(\Gamma_1(3))\).

Total New Old
Modular forms 12 6 6
Cusp forms 10 6 4
Eisenstein series 2 0 2

Trace form

\( 6 q + 177822 q^{2} + 13482087828 q^{4} - 209226212244 q^{5} - 4107432024378 q^{6} + 86874432908088 q^{7} + 2960501398298568 q^{8} + 11118121133111046 q^{9} + O(q^{10}) \) \( 6 q + 177822 q^{2} + 13482087828 q^{4} - 209226212244 q^{5} - 4107432024378 q^{6} + 86874432908088 q^{7} + 2960501398298568 q^{8} + 11118121133111046 q^{9} - 62509461110728236 q^{10} - 449006118086241936 q^{11} - 675705385624963212 q^{12} + 2645460304339642212 q^{13} - 623424763998893808 q^{14} + 13419809246242181304 q^{15} + 7934564529906055440 q^{16} - 258653397384591512580 q^{17} + 329507756022012070302 q^{18} + 2328317563074002616432 q^{19} - 2832186239254640505096 q^{20} + 2813233869418186771704 q^{21} - 36961884613614549287160 q^{22} + 17355959020293329080944 q^{23} - 28075187719107417563064 q^{24} + 309760212790824676319706 q^{25} + 240939296120424419983332 q^{26} - 3179954796066109814583264 q^{28} - 87520055623899111320436 q^{29} + 2168520208582488630910596 q^{30} + 9404979446089190524964376 q^{31} - 1377800974112414254997472 q^{32} + 10415525222258975937185496 q^{33} - 70047252666116601527703204 q^{34} + 42741570963318342266667600 q^{35} + 24982580933157666841491348 q^{36} - 24398623144056563705950332 q^{37} + 138515143387720884389889336 q^{38} + 51026072063587382678815728 q^{39} - 666603972770909171495825232 q^{40} - 82495185163465057480504404 q^{41} + 788179982212326927140369424 q^{42} + 689701393818295549314642768 q^{43} - 174033782712048399977072016 q^{44} - 387700395325132247736141204 q^{45} + 3471243809650395496715385936 q^{46} - 6836926096450491478798863024 q^{47} - 4574194001448167622481425648 q^{48} + 2153650856362724309507673750 q^{49} - 7402582325439675829830417246 q^{50} + 9674788827085671124615387248 q^{51} + 42398780957106823522699650840 q^{52} - 3852173940864945775224631236 q^{53} - 7611154465509021146142179898 q^{54} + 115421563110144076811045862336 q^{55} - 390089298585719034008857160640 q^{56} + 126232097217675503608179371016 q^{57} - 72582753964845845996239927068 q^{58} - 117982592922362455434893493312 q^{59} + 696925242983005702549805489976 q^{60} + 398824389169005399434159376180 q^{61} - 500551338110073204948731499744 q^{62} + 160980078073741816283402590008 q^{63} + 582951333761644192897747140672 q^{64} - 4825025736195151172098980215352 q^{65} + 3801619691249157714568461812136 q^{66} + 984965068868360104472930212800 q^{67} - 6650821662680525716356005131416 q^{68} + 6100220380573604686558690163232 q^{69} + 14479638597204604630826115408480 q^{70} - 19813073594379731833841112469968 q^{71} + 5485868860171351827118834463688 q^{72} + 15416367676240187982354626307324 q^{73} - 52680237352801562465269545820428 q^{74} + 23093952125795679596533694675424 q^{75} + 29988221603153600309366590357008 q^{76} - 17485051106419525012295737625184 q^{77} + 34043746928968522497668334156180 q^{78} + 49260232851840949380842264008440 q^{79} - 148847362062960976344714747351456 q^{80} + 20602102921755074907947094535686 q^{81} + 44575651200347810159192872953516 q^{82} - 146226750147659319601601214665424 q^{83} + 140529829321164494053048180550688 q^{84} + 31684625191014759932677029007992 q^{85} + 119550971068579657891314147831624 q^{86} + 104703420491450418708009240541992 q^{87} - 151795518860587545649068868831392 q^{88} - 19279840944590570783081053457028 q^{89} - 115831293432428446551652219282476 q^{90} - 391502509912830777018467946307824 q^{91} + 386075363713040990861985630295008 q^{92} - 553807765870392878194908982534488 q^{93} - 214603113669067969123982552129952 q^{94} + 1749705275522762958515615329497984 q^{95} - 1264214847656649287350127672987616 q^{96} - 60064883721192870252886280710740 q^{97} + 2994672129981768309774723023624238 q^{98} - 832017401731800053096906385004176 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{34}^{\mathrm{new}}(\Gamma_1(3))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3.34.a \(\chi_{3}(1, \cdot)\) 3.34.a.a 3 1
3.34.a.b 3

Decomposition of \(S_{34}^{\mathrm{old}}(\Gamma_1(3))\) into lower level spaces

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