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

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

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

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