Properties

Label 5.18
Level 5
Weight 18
Dimension 13
Nonzero newspaces 2
Newforms 3
Sturm bound 36
Trace bound 1

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 18 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 3 \)
Sturm bound: \(36\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(5))\).

Total New Old
Modular forms 19 15 4
Cusp forms 15 13 2
Eisenstein series 4 2 2

Trace form

\( 13q + 798q^{2} + 4964q^{3} - 492036q^{4} + 769825q^{5} - 11051024q^{6} - 20681392q^{7} + 68510280q^{8} + 164317921q^{9} + O(q^{10}) \) \( 13q + 798q^{2} + 4964q^{3} - 492036q^{4} + 769825q^{5} - 11051024q^{6} - 20681392q^{7} + 68510280q^{8} + 164317921q^{9} + 110038950q^{10} + 1199688636q^{11} - 847383152q^{12} + 3777271134q^{13} - 32010052872q^{14} + 41163413900q^{15} + 20293830448q^{16} + 17882253978q^{17} - 59413475866q^{18} - 43605787580q^{19} - 68350766900q^{20} + 76405071336q^{21} - 743329560344q^{22} + 88453643904q^{23} + 1936485840960q^{24} - 1026309981875q^{25} + 2575040578836q^{26} + 1134753193880q^{27} - 2958913603744q^{28} - 10796895392970q^{29} + 4983668382400q^{30} + 15420395020656q^{31} - 13601229092832q^{32} + 12219974135008q^{33} - 48161060501412q^{34} + 13769667024200q^{35} + 86634462479708q^{36} + 7200734791318q^{37} - 73963660327080q^{38} - 9258976853848q^{39} - 185688704047000q^{40} + 38578004609466q^{41} + 368236786390176q^{42} + 39049006404444q^{43} - 339765495510192q^{44} - 269751914800475q^{45} + 790842920396696q^{46} + 560714665635288q^{47} - 542741018933696q^{48} - 1218913804071971q^{49} - 1161501165191250q^{50} + 1947505095378856q^{51} + 1823362047940888q^{52} - 435506791917786q^{53} - 6188766368624480q^{54} - 932126128320100q^{55} + 7181380877246880q^{56} + 6130627916698160q^{57} - 979293205423420q^{58} - 6327116089246740q^{59} - 8716980151854800q^{60} + 11351273048633086q^{61} + 5500522387896576q^{62} - 7978269996483936q^{63} - 10745489618904896q^{64} - 9234774224307850q^{65} + 29241789843932672q^{66} + 3291302147555828q^{67} - 1888622336311704q^{68} - 26713051642023528q^{69} - 4172770469947800q^{70} + 21332963745768696q^{71} + 22930402491977640q^{72} - 1147634674990446q^{73} - 42193099731066492q^{74} + 4596682005942500q^{75} + 13568611470896560q^{76} + 10970815186652976q^{77} - 22136761293403952q^{78} + 9803915383194480q^{79} - 7273010228358800q^{80} - 45141141511949027q^{81} - 14844458017154164q^{82} + 66630532639512324q^{83} + 194156710350899808q^{84} - 2699603060681550q^{85} - 200718600924494784q^{86} - 93965064890397160q^{87} + 32201422365176160q^{88} + 122884189975315890q^{89} + 118003186880417150q^{90} - 257056564975511504q^{91} - 153380249446363872q^{92} - 7723516209480432q^{93} + 394726324209160968q^{94} + 189896646638064500q^{95} - 532624779226403584q^{96} - 229317165133259462q^{97} + 96345875569324686q^{98} + 145455505623766412q^{99} + O(q^{100}) \)

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(5))\)

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
5.18.a \(\chi_{5}(1, \cdot)\) 5.18.a.a 2 1
5.18.a.b 3
5.18.b \(\chi_{5}(4, \cdot)\) 5.18.b.a 8 1

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(5))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(5)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)