Properties

Label 21.22
Level 21
Weight 22
Dimension 238
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 704
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 22 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(704\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(21))\).

Total New Old
Modular forms 348 250 98
Cusp forms 324 238 86
Eisenstein series 24 12 12

Trace form

\( 238q + 900q^{2} - 118101q^{3} - 16118510q^{4} + 76218024q^{5} + 152346420q^{6} - 3098621510q^{7} + 15241380678q^{8} - 53921586885q^{9} + O(q^{10}) \) \( 238q + 900q^{2} - 118101q^{3} - 16118510q^{4} + 76218024q^{5} + 152346420q^{6} - 3098621510q^{7} + 15241380678q^{8} - 53921586885q^{9} - 134729193264q^{10} + 125657451936q^{11} - 756005654856q^{12} + 721102493012q^{13} - 5819777842344q^{14} + 2893365613818q^{15} - 16508267041550q^{16} + 13610147776764q^{17} + 42870061049058q^{18} + 1010380128830q^{19} + 534236385714948q^{20} - 249147873121983q^{21} + 362122271916240q^{22} + 59898258294744q^{23} + 369538929361512q^{24} - 3240545190819866q^{25} + 6737731156498026q^{26} + 823564528378596q^{27} + 383898408235786q^{28} - 8764564581446760q^{29} - 10826544614345442q^{30} - 529033783211662q^{31} + 22186563534663486q^{32} + 1843531852737771q^{33} + 16247807371841316q^{34} - 65849970948802908q^{35} + 296039849652303738q^{36} + 114173328954630278q^{37} + 102996010233564390q^{38} - 21457817203617276q^{39} - 289152376317120552q^{40} + 355123856942771376q^{41} + 16412151037795686q^{42} - 268256376232381264q^{43} + 955630435745965272q^{44} - 119390576013127269q^{45} - 3035254292311331196q^{46} + 428504088269151576q^{47} + 3996807154278690528q^{48} - 655805928315826058q^{49} - 10624941084273540750q^{50} + 5395364710291216827q^{51} + 10356188702993623064q^{52} - 1545197862683255340q^{53} + 1199014176171159522q^{54} + 6510951705923451012q^{55} + 313084118118039090q^{56} - 8131179066174385398q^{57} - 32560667367137697912q^{58} - 3871866642654202320q^{59} + 70988734239235610364q^{60} - 6509903505830523070q^{61} - 74703506043303185244q^{62} - 2996532256136908341q^{63} + 44947829508283181350q^{64} + 53542072485477176328q^{65} - 159908530010191419438q^{66} - 48429710834533249114q^{67} + 200948235689093189808q^{68} + 30060958255147015128q^{69} + 143374086320680057104q^{70} + 23084822182511549172q^{71} + 76294714697079406326q^{72} - 51423110484087128566q^{73} + 56936362414423143462q^{74} + 234903276227970022296q^{75} + 545497889942222828168q^{76} - 179451555430342303260q^{77} - 384639845567223457872q^{78} + 444401504213983317986q^{79} + 542814660888579083304q^{80} + 370879550237637273231q^{81} - 1123481457876471002712q^{82} + 838560663274778749320q^{83} - 859703449500793233780q^{84} - 789831419452422734100q^{85} + 1457624029268334455478q^{86} + 249678338931294046560q^{87} - 2799808346193340722900q^{88} - 885281642841164060472q^{89} + 490574510921652512472q^{90} + 2077056699050506382180q^{91} + 4605973418720508064608q^{92} - 4562897820555679010133q^{93} - 7802465919484180402920q^{94} + 2965271210004390894912q^{95} + 9678048862628447274852q^{96} - 2243853989622187529500q^{97} - 2003820677280203207514q^{98} - 6575148330127815651390q^{99} + O(q^{100}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.22.a \(\chi_{21}(1, \cdot)\) 21.22.a.a 4 1
21.22.a.b 5
21.22.a.c 5
21.22.a.d 6
21.22.c \(\chi_{21}(20, \cdot)\) 21.22.c.a 2 1
21.22.c.b 52
21.22.e \(\chi_{21}(4, \cdot)\) 21.22.e.a 26 2
21.22.e.b 30
21.22.g \(\chi_{21}(5, \cdot)\) 21.22.g.a 108 2

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)