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Properties

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

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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

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

Display 100 coefficients 10 coefficients

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 available 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

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