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Properties

Label 21.38
Level 21
Weight 38
Dimension 424
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 1216
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 38 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(1216\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{38}(\Gamma_1(21))\).

Total New Old
Modular forms 604 436 168
Cusp forms 580 424 156
Eisenstein series 24 12 12

Trace form

\( 424 q - 253308 q^{2} - 387420492 q^{3} - 819395298798 q^{4} + 16405192640994 q^{5} + 29414513206836 q^{6} + 7709692545799506 q^{7} - 106262215447402554 q^{8} - 2304114964190819034 q^{9} + O(q^{10}) \) \( 424 q - 253308 q^{2} - 387420492 q^{3} - 819395298798 q^{4} + 16405192640994 q^{5} + 29414513206836 q^{6} + 7709692545799506 q^{7} - 106262215447402554 q^{8} - 2304114964190819034 q^{9} + 11107176974892140496 q^{10} - 14141368910019656262 q^{11} + 343803181650974302200 q^{12} + 1989563433046326592810 q^{13} + 3537237273628652107992 q^{14} - 29965715037757284943932 q^{15} - 184953856268756440982798 q^{16} + 83924719080482145711984 q^{17} + 178621448786624073392226 q^{18} - 603140222950794358414538 q^{19} + 11199703021611003138719748 q^{20} + 1701365891952807599618748 q^{21} - 86319491663645126713208496 q^{22} - 37284212150403723913409976 q^{23} + 20320974728111997872342568 q^{24} - 97307297587202619627910046 q^{25} - 615143096865642706209101334 q^{26} + 116299474006080119380780338 q^{27} - 8589080867184403623359860214 q^{28} - 2832215703385804197048646032 q^{29} + 3051969261373461494376961758 q^{30} + 11265802033258072342028796214 q^{31} + 11021306615867177717292859326 q^{32} + 8207650503548498706851820114 q^{33} + 106092683084861272147855225380 q^{34} - 342725022140455979381432933958 q^{35} + 1998645268180488254270487167226 q^{36} - 968297825851096765567682376636 q^{37} + 1276661190333762252108951008358 q^{38} - 2109520036211331247401466915638 q^{39} + 7366307549355907768435184821848 q^{40} - 4981619105706364971794743679508 q^{41} + 10861052406981067564985896159014 q^{42} - 7940800952125390174642385991408 q^{43} + 4963359699308558850677674632408 q^{44} + 9497683645085322763033904961066 q^{45} + 37805144892432088842135889589124 q^{46} - 39094106116962379680352929218106 q^{47} + 22340585187343969377284237128416 q^{48} - 68885746519898674141363266381950 q^{49} + 201414277780327626348081050689650 q^{50} - 71772645333234070114982361524088 q^{51} - 359354206293600684992560583526632 q^{52} + 759276305091467855097007551219132 q^{53} + 24878918642952887165696555019042 q^{54} + 2067069694006854454381795174632552 q^{55} - 1724528132089494752261606829386958 q^{56} + 31308233265261719115729211647108 q^{57} + 3817899820277187635143681806835848 q^{58} - 2388315297611705810917086704203812 q^{59} + 1851710537591020952830656996708924 q^{60} + 3061210793100483554053861313300458 q^{61} - 7230406676138059822469807559146076 q^{62} + 7049713614404365876880037341781942 q^{63} - 34143887528598081378904589925638106 q^{64} + 5061975253797907001998659646389138 q^{65} + 6298321271101022337152831776759698 q^{66} - 42818022191093026450323493966766854 q^{67} + 2702312177720394160972131068768304 q^{68} + 21601053793536635868957965277877032 q^{69} - 165078717970799045573518694032575216 q^{70} - 39824074485613072689801660439760724 q^{71} - 83184507089554178120408935287176394 q^{72} - 197367874368108033582307376089220576 q^{73} + 158847352824091208906173904719477542 q^{74} - 236213831540549761787652653894856414 q^{75} - 682816007417561579118838341030297464 q^{76} + 525136032986354358658660575652205256 q^{77} - 478863742020816299573190369249237456 q^{78} - 109842467745829837566274817640358498 q^{79} + 1793863191148057924151418274579524264 q^{80} - 628278995504965974527101357111176414 q^{81} - 1240680897520658692073717839878555864 q^{82} + 2369110859034950700099106447850411628 q^{83} - 2794840271525591013248284718729218164 q^{84} - 1547707217126723738356749373720862160 q^{85} + 5636827820970813738517034632228729398 q^{86} - 3532137062458561048043814936270002796 q^{87} + 421572491071377430576115760136450860 q^{88} - 2162013701869330630277587875637355760 q^{89} - 1404117035801492777742394571834824488 q^{90} - 3834385124737938208375734732685712504 q^{91} + 10927239052802000546666707278775276128 q^{92} - 5117970879279094868858622518695184064 q^{93} - 6655511879404897994851001639461848168 q^{94} + 11782511127761400453604351381484599602 q^{95} - 7729135155316926582112967806289418012 q^{96} + 1595103510151629185016645310948907644 q^{97} + 20283921381894580175531879354088224934 q^{98} - 4175970997151411067560924753712330588 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{38}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.38.a \(\chi_{21}(1, \cdot)\) 21.38.a.a 8 1
21.38.a.b 9
21.38.a.c 9
21.38.a.d 10
21.38.c \(\chi_{21}(20, \cdot)\) 21.38.c.a 96 1
21.38.e \(\chi_{21}(4, \cdot)\) 21.38.e.a 48 2
21.38.e.b 50
21.38.g \(\chi_{21}(5, \cdot)\) 21.38.g.a 2 2
21.38.g.b 192

Decomposition of \(S_{38}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{38}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{38}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{38}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{38}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)