Properties

Label 3.42
Level 3
Weight 42
Dimension 7
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 28
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 42 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(28\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{42}(\Gamma_1(3))\).

Total New Old
Modular forms 15 7 8
Cusp forms 13 7 6
Eisenstein series 2 0 2

Trace form

\( 7 q - 359202 q^{2} + 3486784401 q^{3} + 3098681410132 q^{4} + 157187509968306 q^{5} + 765551409514758 q^{6} + 105654053587518368 q^{7} + 8547659196809395080 q^{8} + 85103658213398501607 q^{9} + O(q^{10}) \) \( 7 q - 359202 q^{2} + 3486784401 q^{3} + 3098681410132 q^{4} + 157187509968306 q^{5} + 765551409514758 q^{6} + 105654053587518368 q^{7} + 8547659196809395080 q^{8} + 85103658213398501607 q^{9} + 1029435805124780542164 q^{10} + 2887214225248717473660 q^{11} + 26524714300400374748532 q^{12} + 35871439840874147686034 q^{13} + 814121134383105838377552 q^{14} + 278546714684548950421854 q^{15} - 11421429587339909471968496 q^{16} - 49221515452774894676004402 q^{17} - 4367057748224166939176802 q^{18} + 458239816960683610422662276 q^{19} + 1317078708802896919455800184 q^{20} + 679429495183093137017433504 q^{21} - 10835653338027404099619293304 q^{22} - 20060723551274129388995858616 q^{23} + 13987560939606541875202583688 q^{24} + 112741912197127321489742871001 q^{25} + 59951728496322544602361807524 q^{26} + 42391158275216203514294433201 q^{27} + 84612644924529015441375525536 q^{28} - 1977654451176175768473033328278 q^{29} + 1471653955084285604978002090116 q^{30} + 2800527890869229757891015241496 q^{31} + 10451255461999993483707442222368 q^{32} - 5012576606051926011540924758748 q^{33} + 42009179670420411943699963793244 q^{34} + 54061742342062084106633253973440 q^{35} + 37672731948583633247947804011732 q^{36} - 242065375197179473114939693545142 q^{37} + 314930001138451392992297251383480 q^{38} - 186750060884734904297998103261250 q^{39} + 1734682904709656035688674311540528 q^{40} + 1919772488651818449733020167096406 q^{41} + 602440311893806808992036727951184 q^{42} + 2632359378218766285475830966693884 q^{43} - 19937525714249582008307420905778832 q^{44} + 1911033160536840537417125208581106 q^{45} - 36254649124121789242053962151968304 q^{46} + 55633854121325526194894129703603648 q^{47} - 1753714286036360588361388333995504 q^{48} + 138035826290957567679458976119440143 q^{49} - 187990375985029453423588111219375326 q^{50} - 94985755416285397758254198036972574 q^{51} - 617218879754977585961579952999168232 q^{52} + 130398746597587280084701480383481074 q^{53} + 9307317928589919211191457164745158 q^{54} + 1391092265182485973540701545396386056 q^{55} + 1372448310706724961467332343944230720 q^{56} + 228194964739280558656530161545568220 q^{57} + 1118358566329856274942833707260398820 q^{58} - 6391974776969397351480135095996322756 q^{59} + 884963814320884755837398974113114936 q^{60} - 3312712827218201776253073157251557422 q^{61} + 14374498612437137001029858555251499616 q^{62} + 1284506637910321854753178081255716768 q^{63} + 16591897231730805285648730656448281664 q^{64} - 7033288095370619074610943489877063332 q^{65} - 6306358621743532720405111555196485848 q^{66} - 40405345193781585575277868138739047612 q^{67} - 55757692275676972944877351967679897624 q^{68} - 37414675978671770942781643564589712648 q^{69} - 28830724918545442617573855638025077280 q^{70} + 65352753330602401579129433901404850744 q^{71} + 103919580972839873560231523607439699080 q^{72} - 38087455622379499723731802436503585786 q^{73} - 285201647615202678069885610769237365068 q^{74} + 425247987466981253017161984441433632399 q^{75} + 591482750285183039994389345638940386064 q^{76} - 121632284063118375562702456886125352064 q^{77} - 647972920533404340562713236608161798828 q^{78} + 303763181148476262286751933509169683880 q^{79} - 883861409260176376420569508380870292896 q^{80} + 1034661805900421463212582471444683083207 q^{81} + 506031307509525931610314373513550403116 q^{82} + 338569766654854122754573119661314323844 q^{83} + 4477946200719041862634183758838962173088 q^{84} + 5867714862762767359034463946267521425892 q^{85} - 10044657135880119837887847414531534010680 q^{86} - 329652723836651682867696900815988461850 q^{87} - 1871964150689809834871464807801300340640 q^{88} - 42501185633754390669462796933591813434474 q^{89} + 12515536130282004128514779324929526465364 q^{90} + 10902563805559929629531821715171473391296 q^{91} - 54939669480377726604465653835946284263712 q^{92} + 54954157779576051546191591009674393431912 q^{93} + 133210973073415598318228698663050409590240 q^{94} - 76709837386263260643038774052059049311496 q^{95} + 100557259542361618704666346381235459514144 q^{96} - 15729678699391001866619231092467803918962 q^{97} - 336568502755298601082628274470658413757714 q^{98} + 35101784659204143757639477722503212881660 q^{99} + O(q^{100}) \)

Decomposition of \(S_{42}^{\mathrm{new}}(\Gamma_1(3))\)

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
3.42.a \(\chi_{3}(1, \cdot)\) 3.42.a.a 3 1
3.42.a.b 4

Decomposition of \(S_{42}^{\mathrm{old}}(\Gamma_1(3))\) into lower level spaces

\( S_{42}^{\mathrm{old}}(\Gamma_1(3)) \cong \) \(S_{42}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)