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Properties

Label 21.27
Level 21
Weight 27
Dimension 290
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 864
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 27 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(864\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{27}(\Gamma_1(21))\).

Total New Old
Modular forms 428 298 130
Cusp forms 404 290 114
Eisenstein series 24 8 16

Trace form

\( 290 q + 927834 q^{3} + 229261882 q^{4} + 1369811514 q^{5} - 8536522182 q^{6} - 206701386638 q^{7} - 145511403486 q^{8} - 7062457367592 q^{9} + O(q^{10}) \) \( 290 q + 927834 q^{3} + 229261882 q^{4} + 1369811514 q^{5} - 8536522182 q^{6} - 206701386638 q^{7} - 145511403486 q^{8} - 7062457367592 q^{9} - 22167524088372 q^{10} - 149800800256122 q^{11} - 235628271836322 q^{12} + 812249320199202 q^{13} - 1728805821698568 q^{14} + 2221400696785968 q^{15} - 45134932117039294 q^{16} + 18645482228466288 q^{17} - 19034268710577564 q^{18} + 272009058569737026 q^{19} + 106999407486460584 q^{21} + 818008988665135572 q^{22} + 2725821732215594784 q^{23} + 1143784203774156354 q^{24} + 8597829193702641548 q^{25} + 1217525422709094282 q^{26} + 9003081993671434188 q^{27} + 20721577187015863658 q^{28} - 45689552624031883212 q^{29} + 106870854607514534544 q^{30} - 40222819526549378058 q^{31} + 103026098844643451478 q^{32} + 367448169486165843786 q^{33} - 979771137293504201952 q^{34} + 578241488368926698610 q^{35} - 2510211150503648734074 q^{36} - 1012238555105829976480 q^{37} + 801272180499144616254 q^{38} + 1002169161952491783186 q^{39} - 2766881195911677615024 q^{40} - 3989345882912246772792 q^{42} + 2669627609822742568292 q^{43} - 19948955188452657859464 q^{44} + 20636720221922603220042 q^{45} - 57553394901956126505132 q^{46} + 20285984451396923955138 q^{47} + 66766062902364615556950 q^{48} + 96907552174582547478296 q^{49} - 45855246707449756144314 q^{50} - 34056826079755292498472 q^{51} + 108358576910937305449272 q^{52} + 69471742440693254729748 q^{53} + 2543682418694114271756 q^{54} - 126550507128586767202884 q^{55} + 284958330248832594957810 q^{56} + 152287155077420557854828 q^{57} - 1272773113175024345868480 q^{58} + 762496299039757797906132 q^{59} + 6876405425832118140156 q^{60} - 491135922692483649994266 q^{61} - 43028206449574589340642 q^{63} - 293475219907256831776634 q^{64} - 3188135823758912720846862 q^{65} - 2140375424712395504967432 q^{66} + 6000244628958214077338182 q^{67} - 11132216750578028371227324 q^{68} + 2467788446030805532771200 q^{69} + 8504286134817817385848740 q^{70} + 1446040314081028133378616 q^{71} - 10824406399097157383927106 q^{72} + 6658279481386788112363260 q^{73} + 17776714846655353878600786 q^{74} - 9852953421569645066339100 q^{75} + 7596163793877042048419052 q^{76} - 162582841581297386316408 q^{77} + 52044688380801331580816904 q^{78} - 10241541387106173433252286 q^{79} - 100507355250111746775856032 q^{80} + 40505402918497663452444192 q^{81} + 57863293908054328052805708 q^{82} - 120538829066759430466067694 q^{84} - 1573544676072069970744488 q^{85} + 42653613768254319174797586 q^{86} + 122498900178887229161466972 q^{87} - 517364393112268629341307864 q^{88} + 32705838342477493615239492 q^{89} + 429615821025221586481602948 q^{90} - 138429248892806864234724084 q^{91} + 35164678975853860289455116 q^{92} - 74746291069280431755967704 q^{93} + 7233461308665348142836924 q^{94} - 81084184786808604027819798 q^{95} - 312966702874396715906325210 q^{96} - 603381806168290536905032056 q^{97} + 528230598904963649013981210 q^{98} + 237402191078121151262454192 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{27}^{\mathrm{new}}(\Gamma_1(21))\)

We only show spaces with odd 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
21.27.b \(\chi_{21}(8, \cdot)\) 21.27.b.a 52 1
21.27.d \(\chi_{21}(13, \cdot)\) 21.27.d.a 34 1
21.27.f \(\chi_{21}(10, \cdot)\) 21.27.f.a 34 2
21.27.f.b 36
21.27.h \(\chi_{21}(2, \cdot)\) 21.27.h.a 2 2
21.27.h.b 132

Decomposition of \(S_{27}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{27}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{27}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)