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Properties

Label 21.42
Level 21
Weight 42
Dimension 472
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 1344
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 42 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(1344\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{42}(\Gamma_1(21))\).

Total New Old
Modular forms 668 484 184
Cusp forms 644 472 172
Eisenstein series 24 12 12

Trace form

\( 472 q + 718404 q^{2} - 3486784404 q^{3} - 14993455842478 q^{4} - 892092856709826 q^{5} + 20405847821348340 q^{6} - 67432334790123646 q^{7} - 13168342325180432922 q^{8} - 175158327575316027372 q^{9} + O(q^{10}) \) \( 472 q + 718404 q^{2} - 3486784404 q^{3} - 14993455842478 q^{4} - 892092856709826 q^{5} + 20405847821348340 q^{6} - 67432334790123646 q^{7} - 13168342325180432922 q^{8} - 175158327575316027372 q^{9} - 3256229785860142334064 q^{10} - 2844193265849679927222 q^{11} + 16983983835365691364296 q^{12} + 77639615282369940040686 q^{13} + 615049787615954223621432 q^{14} + 568839105204258782173068 q^{15} - 8412551055041705798431118 q^{16} + 79640182496145302053622256 q^{17} + 338193960565619529583519554 q^{18} - 976418054552394035973574554 q^{19} + 1388713614151254911368218948 q^{20} + 906461634448757274444833178 q^{21} - 1839072122920111292867407248 q^{22} + 56016025329771206915482776456 q^{23} + 49570896759040612507575199896 q^{24} - 399940149779651630221979887466 q^{25} - 211346891421793778452072684086 q^{26} + 84782316550432407028588866402 q^{27} - 877318507090783654447779017270 q^{28} + 6203485601881479521735380409544 q^{29} - 1001679559178691063999292667442 q^{30} - 22459336389707680000657932837978 q^{31} + 46287983317029718446029691345630 q^{32} - 103291039280106326041050759600996 q^{33} + 76307973959674733191981569610980 q^{34} - 44888544518415650075376467365158 q^{35} + 2122215527878466478245643169139802 q^{36} - 348041807780520262953433173581336 q^{37} + 857120361275364382926570932973894 q^{38} - 2020032943945634675650604168739678 q^{39} - 7771226730012167935447011537804552 q^{40} - 3074537912331819032172307306874628 q^{41} + 8200458198496565696958123413186838 q^{42} - 25032250756530467145909511545168368 q^{43} + 20418012959925889258030834836268248 q^{44} - 73420862388188560340098297513465944 q^{45} + 169110512806175917280327047852780740 q^{46} + 1864071524243903836442431613894718 q^{47} + 96243229747638155607552737841523680 q^{48} + 207662337804513821069843517351217726 q^{49} + 520332571795671832530314719396979250 q^{50} + 13683181298218790253949375803719208 q^{51} + 244098502908887017653639111050857176 q^{52} + 544174507740676064643620407289087940 q^{53} - 3050235216049747721945128130951142030 q^{54} + 2730254216123373462877463520599538312 q^{55} - 3619248903192923611845967061182711182 q^{56} + 5971167340611976933800484856387896224 q^{57} - 7691575510002285708584862613894332216 q^{58} + 5604859147930130777828690594276099196 q^{59} + 15790136764171810174491537829352199564 q^{60} - 41941498222876441798667401760948871198 q^{61} + 78516573781910706696918959242655822820 q^{62} - 20376111533697271797962024696150774406 q^{63} - 110170606870769966556690389106445873690 q^{64} - 49385690393280787173481452803781460722 q^{65} + 103506739256113804526362280345464638210 q^{66} - 58071727464022333615593574115860645030 q^{67} + 8898985943991279024825704554284925200 q^{68} + 218442121134526486020635475537312855720 q^{69} - 771440923404053463230435912560340941296 q^{70} + 375795723431792105542281980316020689068 q^{71} - 438526973910294395073534146324529576762 q^{72} - 519219545673019142664536039979758023764 q^{73} + 2308530676366719395528266450050022075110 q^{74} - 1630574933573011299313946710718795769654 q^{75} + 692639912375489589299214425487485390856 q^{76} - 54193082201301279762498604839230508384 q^{77} - 1470726975784066290692580613762316053296 q^{78} + 3922153251571704786661788128145173590814 q^{79} - 1396542332899829765009350196975190605496 q^{80} + 2993798529898558883231635891734672578472 q^{81} + 6187070611647396410391954053701279168392 q^{82} - 12710313240909900659335765984172646664404 q^{83} + 29853202769629555181204314682298140868300 q^{84} - 18852030232311868313304373313256696043800 q^{85} - 5851039304126968480976279721068796767466 q^{86} + 32165383187683105554594350412370543614084 q^{87} - 55711958090292354711723940450977728001108 q^{88} + 103405552566682066125618650353945939331016 q^{89} - 10441873709695693695829558649859052930728 q^{90} + 36423273159760157398081342647916436165928 q^{91} - 83081316634689330424555852758972218585568 q^{92} - 18805578574500863510360696745264855295206 q^{93} + 4340659536150507814229703204459336503352 q^{94} + 10643467934431309815552909197627870323962 q^{95} - 193603224424932418189449640112362083236796 q^{96} + 202606558644421197914502102690723770295588 q^{97} - 158728519535650237574359445650520544460890 q^{98} - 460601477606288905237937306011536617482188 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{42}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.42.a \(\chi_{21}(1, \cdot)\) 21.42.a.a 9 1
21.42.a.b 10
21.42.a.c 10
21.42.a.d 11
21.42.c \(\chi_{21}(20, \cdot)\) 21.42.c.a 108 1
21.42.e \(\chi_{21}(4, \cdot)\) 21.42.e.a 54 2
21.42.e.b 56
21.42.g \(\chi_{21}(5, \cdot)\) 21.42.g.a 2 2
21.42.g.b 212

Decomposition of \(S_{42}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{42}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{42}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{42}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{42}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)