Properties

Label 5.34
Level 5
Weight 34
Dimension 27
Nonzero newspaces 2
Newforms 3
Sturm bound 68
Trace bound 1

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 34 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 3 \)
Sturm bound: \(68\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(\Gamma_1(5))\).

Total New Old
Modular forms 35 29 6
Cusp forms 31 27 4
Eisenstein series 4 2 2

Trace form

\( 27q + 177822q^{2} + 11525186q^{3} - 42189369860q^{4} - 79580269655q^{5} + 30542599711984q^{6} - 46338728939658q^{7} + 3225430753821000q^{8} + 608196999164035q^{9} + O(q^{10}) \) \( 27q + 177822q^{2} + 11525186q^{3} - 42189369860q^{4} - 79580269655q^{5} + 30542599711984q^{6} - 46338728939658q^{7} + 3225430753821000q^{8} + 608196999164035q^{9} - 4437026337863130q^{10} + 82933685420380464q^{11} + 60971626392900112q^{12} + 994105514137102766q^{13} - 5825703674266765320q^{14} + 15565211823061495190q^{15} + 108502886852597908272q^{16} - 174344791525389819618q^{17} + 1211227884109649084006q^{18} - 319268182263749031500q^{19} + 9902115666414432029260q^{20} - 969352898687748668676q^{21} - 11286990651079412083096q^{22} + 62333637911030794355346q^{23} - 96754544634174936811200q^{24} + 525586859697933313945275q^{25} - 763688373213708589577196q^{26} + 338636629821008839676300q^{27} - 3115868286788324128981536q^{28} + 2589170838390072666220050q^{29} - 8401524253319651368045760q^{30} + 14294454993317336554440884q^{31} + 26005215441519452400962592q^{32} + 1642692718077028889156752q^{33} - 59864954906301147337517220q^{34} + 47743922478956884198205570q^{35} + 138949919267432416198775132q^{36} + 133921119169281602784846862q^{37} + 505006684026590239645411800q^{38} - 1156496302953533714081342380q^{39} + 1412640112003235269661521000q^{40} + 83014531328023081800539994q^{41} - 1167391858000793668973715936q^{42} - 92495886232735084451898694q^{43} + 1015823960819284587567520080q^{44} + 5816671302252555784265648065q^{45} + 4649642035879614636004777624q^{46} - 3894170809960417686673993698q^{47} + 17220199818666666799165381696q^{48} - 51933192711478455237661742185q^{49} + 68272975570593191581962495150q^{50} - 9896380093591513993606349996q^{51} - 41590127827476399212699255528q^{52} + 156563227269110886940338961686q^{53} - 535298114572873500168933692000q^{54} + 275746779012179048540792817040q^{55} - 37823843974586650250646146400q^{56} - 33607110592102782383869594600q^{57} - 231402277243182521036482067900q^{58} - 125818156535129186399787798300q^{59} - 187526971769175485198182310480q^{60} + 397669164845347789111392089614q^{61} + 536014589511457033791035265024q^{62} - 1563787994007206511931699103034q^{63} + 4171803923197192407870131355840q^{64} - 1735693050700995548226920111110q^{65} - 1257528395426119346283590893312q^{66} - 400301447551034298034555574418q^{67} + 5041910916091392617758749111144q^{68} + 4448405177260991092012092808020q^{69} - 8743844275985256043534159232280q^{70} + 2861607596995409938042920375324q^{71} - 7231385689119979182171909639000q^{72} - 15386476146017658598833492512554q^{73} + 59996387687591921630478775688580q^{74} - 27457747296832479297115956221950q^{75} - 2009615051304788708608859109200q^{76} + 46058584922060308397847985058544q^{77} - 45152184871995014141159045031728q^{78} - 42901447999817402969817336197800q^{79} + 48364820937617153806986665687920q^{80} + 71805733931942069149185606065167q^{81} - 128752451332055475378604069526516q^{82} + 45475167144980311320038954371626q^{83} - 463514621056497118057888636002720q^{84} + 242229429718872448582253244962970q^{85} - 82143262548433711611840015673536q^{86} - 38030330953052174525222225679700q^{87} + 691679161832993789415604141212000q^{88} - 1213802628144671896320132691862850q^{89} + 835416512578241296876715302772990q^{90} + 498007030017271378342854467654844q^{91} - 1116484363668251966439651529251168q^{92} - 483217130549593702040631640697688q^{93} + 2207322059838506448009398603798280q^{94} - 839310835810001871851209023866500q^{95} + 1430940986977911141531844228999424q^{96} + 1701361424317563414831140787172102q^{97} - 1984116428580865663437978238924146q^{98} + 3302698738788004481175707842585520q^{99} + O(q^{100}) \)

Decomposition of \(S_{34}^{\mathrm{new}}(\Gamma_1(5))\)

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
5.34.a \(\chi_{5}(1, \cdot)\) 5.34.a.a 5 1
5.34.a.b 6
5.34.b \(\chi_{5}(4, \cdot)\) 5.34.b.a 16 1

Decomposition of \(S_{34}^{\mathrm{old}}(\Gamma_1(5))\) into lower level spaces

\( S_{34}^{\mathrm{old}}(\Gamma_1(5)) \cong \) \(S_{34}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)