Properties

Label 3.43
Level 3
Weight 43
Dimension 13
Nonzero newspaces 1
Newforms 2
Sturm bound 28
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 43 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 2 \)
Sturm bound: \(28\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{43}(\Gamma_1(3))\).

Total New Old
Modular forms 15 15 0
Cusp forms 13 13 0
Eisenstein series 2 2 0

Trace form

\(13q \) \(\mathstrut +\mathstrut 6526851993q^{3} \) \(\mathstrut -\mathstrut 30601457050784q^{4} \) \(\mathstrut -\mathstrut 47900661722006688q^{6} \) \(\mathstrut +\mathstrut 104431479090834554q^{7} \) \(\mathstrut +\mathstrut 98939492749372360149q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut +\mathstrut 6526851993q^{3} \) \(\mathstrut -\mathstrut 30601457050784q^{4} \) \(\mathstrut -\mathstrut 47900661722006688q^{6} \) \(\mathstrut +\mathstrut 104431479090834554q^{7} \) \(\mathstrut +\mathstrut 98939492749372360149q^{9} \) \(\mathstrut -\mathstrut 1558337248111507093440q^{10} \) \(\mathstrut +\mathstrut 3371257617792639413472q^{12} \) \(\mathstrut -\mathstrut 253012333644251341412734q^{13} \) \(\mathstrut -\mathstrut 448128019361693763840960q^{15} \) \(\mathstrut +\mathstrut 49532793987439104163820032q^{16} \) \(\mathstrut +\mathstrut 467763252053696004788775360q^{18} \) \(\mathstrut +\mathstrut 1576909774199427781769570258q^{19} \) \(\mathstrut +\mathstrut 7572989610421557604517258514q^{21} \) \(\mathstrut -\mathstrut 4314702866032998614435578560q^{22} \) \(\mathstrut +\mathstrut 213252820822149659960046027264q^{24} \) \(\mathstrut -\mathstrut 1248191749023087121437353235035q^{25} \) \(\mathstrut +\mathstrut 3535242569745007589266902603777q^{27} \) \(\mathstrut -\mathstrut 11929994979570989528218827713344q^{28} \) \(\mathstrut +\mathstrut 62452866934923176992747679887680q^{30} \) \(\mathstrut -\mathstrut 42510819487048676995695358862134q^{31} \) \(\mathstrut +\mathstrut 43265764437015443353441835054400q^{33} \) \(\mathstrut -\mathstrut 263315485295738664634172504653056q^{34} \) \(\mathstrut -\mathstrut 1923971593950224017148630445513120q^{36} \) \(\mathstrut +\mathstrut 1526196720239071204471967871249074q^{37} \) \(\mathstrut -\mathstrut 7248612364199215982418683252126214q^{39} \) \(\mathstrut +\mathstrut 14264689156939495925288444850785280q^{40} \) \(\mathstrut -\mathstrut 2831182046378653470535212831685440q^{42} \) \(\mathstrut -\mathstrut 41240191555200066457703837814401374q^{43} \) \(\mathstrut +\mathstrut 171247471703495918987972144910848640q^{45} \) \(\mathstrut -\mathstrut 368252835390302858087002506036095616q^{46} \) \(\mathstrut +\mathstrut 190719216730956732645885104049043968q^{48} \) \(\mathstrut +\mathstrut 212869305691518808215922573851245175q^{49} \) \(\mathstrut -\mathstrut 26481340521925644924949289315966208q^{51} \) \(\mathstrut +\mathstrut 4621003571934453098144523281061984704q^{52} \) \(\mathstrut -\mathstrut 7762950205729260582930120693521404128q^{54} \) \(\mathstrut +\mathstrut 7333373720922934220673629457367543680q^{55} \) \(\mathstrut -\mathstrut 5917433808744215242767209354239887606q^{57} \) \(\mathstrut -\mathstrut 40828097874719028971304350423217887040q^{58} \) \(\mathstrut +\mathstrut 67409911106604936995672440638418037760q^{60} \) \(\mathstrut -\mathstrut 30214456684741097447409854535489547294q^{61} \) \(\mathstrut +\mathstrut 116836120779656750125400090217501760266q^{63} \) \(\mathstrut -\mathstrut 56388048458203571721647092899163381760q^{64} \) \(\mathstrut -\mathstrut 410927857618739095889759252898209949120q^{66} \) \(\mathstrut +\mathstrut 240564925468816186556265888196697026994q^{67} \) \(\mathstrut -\mathstrut 900977595682723671847728174824987261568q^{69} \) \(\mathstrut +\mathstrut 1299257312773585175235999395827621799040q^{70} \) \(\mathstrut -\mathstrut 1002862304292335428089280868557297904640q^{72} \) \(\mathstrut +\mathstrut 3596840906002472576188859342548993298666q^{73} \) \(\mathstrut +\mathstrut 7913245428648450142303694817241331316945q^{75} \) \(\mathstrut -\mathstrut 11577637952750293583108597010602259595840q^{76} \) \(\mathstrut -\mathstrut 1154864387471236146792590220220273542720q^{78} \) \(\mathstrut -\mathstrut 2394298619153593223068126360634187742102q^{79} \) \(\mathstrut -\mathstrut 17962382915172057496073817662807569190307q^{81} \) \(\mathstrut +\mathstrut 12117774709574398821091222390193736370560q^{82} \) \(\mathstrut -\mathstrut 122230594401868819650764739876303888650304q^{84} \) \(\mathstrut +\mathstrut 179892388106464049414097141341403281134080q^{85} \) \(\mathstrut -\mathstrut 108737363241821037303405571455850394882880q^{87} \) \(\mathstrut +\mathstrut 262137413065538961600854476553505008040960q^{88} \) \(\mathstrut -\mathstrut 246742532847586844558695609281104739341760q^{90} \) \(\mathstrut +\mathstrut 33297383399835377811307712929369792008388q^{91} \) \(\mathstrut -\mathstrut 265172693180256540460917211677794463781854q^{93} \) \(\mathstrut +\mathstrut 711306705503600048406114202903471029729024q^{94} \) \(\mathstrut -\mathstrut 1719405066055622809595776412409802129711104q^{96} \) \(\mathstrut +\mathstrut 1316788779790214809459143375755232261157274q^{97} \) \(\mathstrut -\mathstrut 4562402641239113129658705054315657608741760q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{43}^{\mathrm{new}}(\Gamma_1(3))\)

We only show spaces with odd 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
3.43.b \(\chi_{3}(2, \cdot)\) 3.43.b.a 1 1
3.43.b.b 12