Properties

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

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 43 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
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

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