Properties

Label 3.34.a
Level 3
Weight 34
Character orbit a
Rep. character \(\chi_{3}(1,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 2
Sturm bound 11
Trace bound 2

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 34 \)
Character orbit: \([\chi]\) = 3.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(11\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(\Gamma_0(3))\).

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

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators.

\(3\)Dim.
\(+\)\(3\)
\(-\)\(3\)

Trace form

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

Decomposition of \(S_{34}^{\mathrm{new}}(\Gamma_0(3))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3
3.34.a.a \(3\) \(20.695\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(41202\) \(129140163\) \(51261823890\) \(76\!\cdots\!56\) \(-\) \(q+(13734-\beta _{1})q^{2}+3^{16}q^{3}+(-369155924+\cdots)q^{4}+\cdots\)
3.34.a.b \(3\) \(20.695\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(136620\) \(-129140163\) \(-260488036134\) \(10\!\cdots\!32\) \(+\) \(q+(45540-\beta _{1})q^{2}-3^{16}q^{3}+(4863185200+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{34}^{\mathrm{old}}(\Gamma_0(3))\) into lower level spaces

\( S_{34}^{\mathrm{old}}(\Gamma_0(3)) \cong \) \(S_{34}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)