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Properties

Label 21.36
Level 21
Weight 36
Dimension 404
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 1152
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 36 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(1152\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{36}(\Gamma_1(21))\).

Total New Old
Modular forms 572 416 156
Cusp forms 548 404 144
Eisenstein series 24 12 12

Trace form

\( 404 q + 296484 q^{2} + 129140160 q^{3} - 316702339086 q^{4} - 2686732537674 q^{5} - 108383206320684 q^{6} - 1052835676625502 q^{7} - 5051858741359242 q^{8} - 306692628325091772 q^{9} + O(q^{10}) \) \( 404 q + 296484 q^{2} + 129140160 q^{3} - 316702339086 q^{4} - 2686732537674 q^{5} - 108383206320684 q^{6} - 1052835676625502 q^{7} - 5051858741359242 q^{8} - 306692628325091772 q^{9} + 1828324334688607728 q^{10} - 2344712011957246350 q^{11} - 26999313755036255184 q^{12} - 206034490184487965890 q^{13} + 179377290715504319208 q^{14} + 2884177835246027657412 q^{15} - 1574303949339359667406 q^{16} - 22735129273923192527712 q^{17} + 33125860128695203315314 q^{18} + 71032050180110347451846 q^{19} - 876295319887300863112476 q^{20} - 697830828710445668021910 q^{21} - 1329546815903247099738240 q^{22} - 1640798786316705697942968 q^{23} - 5540288460260480081201520 q^{24} - 23760782580082735040917366 q^{25} + 27994482747925221153216570 q^{26} - 4307387926151115532621494 q^{27} + 209707336935580722504389930 q^{28} - 135003909314428616763260256 q^{29} - 338148301818723240114240570 q^{30} - 215366295193944432887612266 q^{31} - 892374621359690431949600658 q^{32} + 690699688162421084107600248 q^{33} + 2742723770740556738038210884 q^{34} - 262370081025934965717495006 q^{35} + 23747447291707547572037156106 q^{36} + 26884966685857413556477858344 q^{37} - 34905695087394987572881927626 q^{38} + 31133298648833405005474130322 q^{39} - 8663345404925242479849056184 q^{40} + 92998323118134035081159313732 q^{41} - 100652511033041165316560238642 q^{42} - 51945706624360378840017490080 q^{43} + 70404412189131041527219243224 q^{44} + 88995667408553213661457495116 q^{45} - 790686181729602707956138102044 q^{46} + 470851765572856484521866604038 q^{47} - 105347117347045916431306241952 q^{48} + 3655347264678733063853192223866 q^{49} - 3631429564522046984924522967918 q^{50} + 1503515692494054527379573797604 q^{51} + 2490820189883538886315705389368 q^{52} - 2491693815695509893930933688284 q^{53} + 18845897147144734288338449823258 q^{54} - 18573285682555590070099742810040 q^{55} - 10071814208714088577858712643822 q^{56} + 20916392593946981607307478643552 q^{57} - 64792959360152084713937616935832 q^{58} + 5340908444267732884239889735020 q^{59} - 1797998631522689115281633728140 q^{60} - 67001839606467732228857374501030 q^{61} + 29116196136291334202546142600708 q^{62} - 151141360550596695857940694782618 q^{63} - 253060292500634856407903930325690 q^{64} + 179439497088309383422872710657454 q^{65} - 521293266565789701624603911872902 q^{66} + 312574020758264160845565587023738 q^{67} - 1245994728506844723938942752345728 q^{68} - 97999856910323501756658432597000 q^{69} + 879269801015741351399811272337936 q^{70} - 1240298123577107076531923477597556 q^{71} + 1007710556181935157943638178409550 q^{72} + 2038605938358768303624272884396244 q^{73} + 651980139831944431612048809600966 q^{74} + 197008342842348390075861321780546 q^{75} - 2107443885689808209777358839387704 q^{76} - 243017095570244123782816605304488 q^{77} - 3143344256804316351571393762929888 q^{78} + 13520318330321810037208340460295294 q^{79} - 19920852914465434670296965411374184 q^{80} - 11209397468179031979728904500509440 q^{81} + 65007689512544067091013816272286904 q^{82} - 30743412384474762567050274656179236 q^{83} + 47908674677225445980341186098797484 q^{84} - 39468317877133412755561153894131192 q^{85} - 36474857491163091639748801556835066 q^{86} + 25938109459132406837769319562424204 q^{87} + 69112317635651550039582954291769068 q^{88} - 29954242061432012969954407022012160 q^{89} + 21257599515473799835662329142358680 q^{90} + 8102221969251286668565038473797880 q^{91} + 288381564956478924924647814384717696 q^{92} - 17598027177688187675325190146998946 q^{93} - 243017232211925631710446127017789176 q^{94} + 252678775261989083281481143913538834 q^{95} + 93315169238841660113439796719811188 q^{96} - 488638469631715984086060526748622412 q^{97} - 112470499710673575568924440804265818 q^{98} + 176772810413054613367598936436193644 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{36}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.36.a \(\chi_{21}(1, \cdot)\) 21.36.a.a 8 1
21.36.a.b 9
21.36.a.c 9
21.36.a.d 10
21.36.c \(\chi_{21}(20, \cdot)\) 21.36.c.a 92 1
21.36.e \(\chi_{21}(4, \cdot)\) 21.36.e.a 46 2
21.36.e.b 48
21.36.g \(\chi_{21}(5, \cdot)\) 21.36.g.a 2 2
21.36.g.b 180

Decomposition of \(S_{36}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{36}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{36}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{36}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{36}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)