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Properties

Label 21.29
Level 21
Weight 29
Dimension 314
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 928
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 29 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(928\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{29}(\Gamma_1(21))\).

Total New Old
Modular forms 460 322 138
Cusp forms 436 314 122
Eisenstein series 24 8 16

Trace form

\( 314 q - 16967532 q^{3} + 3078955674 q^{4} + 523998774 q^{5} - 112303850982 q^{6} + 1309233788130 q^{7} - 4660833964878 q^{8} + 56955976774146 q^{9} + O(q^{10}) \) \( 314 q - 16967532 q^{3} + 3078955674 q^{4} + 523998774 q^{5} - 112303850982 q^{6} + 1309233788130 q^{7} - 4660833964878 q^{8} + 56955976774146 q^{9} + 79806643403436 q^{10} + 2065797035189514 q^{11} + 4995030710905878 q^{12} - 18475068228474730 q^{13} + 41276958417780984 q^{14} - 60546631211997900 q^{15} + 12636887989308290 q^{16} - 559870433407979424 q^{17} - 951006419363058636 q^{18} + 2896250690114076842 q^{19} + 14264480885754161430 q^{21} + 15711238997731513956 q^{22} - 31799003284533176640 q^{23} + 95310304519556188938 q^{24} - 174719447286819011728 q^{25} + 174498280945355229786 q^{26} + 515341569544795915104 q^{27} - 1240655703568608412726 q^{28} + 1782434676256181380188 q^{29} - 4897680071931524970984 q^{30} + 3710496805132420191950 q^{31} - 9103306753281228477210 q^{32} - 1293366707225437938060 q^{33} + 12967203408095425287552 q^{34} - 30075736347830787095034 q^{35} - 64622824592990764730442 q^{36} - 38841721827591713992212 q^{37} + 77788098286141441252590 q^{38} + 16367639278551068463534 q^{39} + 207027709611648791735904 q^{40} + 112639421943882972280224 q^{42} + 174469970752641213214836 q^{43} + 1481373466779853180252152 q^{44} - 1092050853946636996710252 q^{45} + 1867942318992168503464500 q^{46} - 983068955199081895772394 q^{47} - 2240761369273135068643050 q^{48} + 3123763254230384373520100 q^{49} + 615321564310910860737894 q^{50} - 3124034545381097503733574 q^{51} + 8564625882165042584325080 q^{52} - 3604168680413688782204076 q^{53} - 23087889820437622657035132 q^{54} + 10344813163592877381886164 q^{55} - 32561452152813186274948398 q^{56} + 841501101904275909595536 q^{57} - 12156039826339507487780832 q^{58} - 9336816316468930884608916 q^{59} - 106020206735625689181319164 q^{60} + 55809162797098237089372998 q^{61} - 33787214991754615176546564 q^{63} + 16149976773736873991478246 q^{64} + 151078773161250685489553478 q^{65} - 284882894476044287956432704 q^{66} + 229871494337549027006065198 q^{67} + 508552937533675496636115156 q^{68} + 169115035167555802681774284 q^{69} - 826392794131924497158151804 q^{70} + 424767804293571959191640760 q^{71} + 886907886207894468697663686 q^{72} - 1022033643328651545536013160 q^{73} - 636084902184743905099694190 q^{74} + 652932103603085226105865404 q^{75} + 296611286944679556618431084 q^{76} - 2051479623113702924869814904 q^{77} - 81129182159330120242561800 q^{78} + 712580096162062920724827682 q^{79} - 2830746293928998258099456880 q^{80} + 754205648269619385021181158 q^{81} + 1195024180159617098211483228 q^{82} + 3759108939817912665450680274 q^{84} + 9731304285542170274356810704 q^{85} - 12092450392025027418681421470 q^{86} + 378680320784770618795754952 q^{87} + 20276559456902854984279170408 q^{88} + 1074727194435948798031715100 q^{89} - 25700204102461519168946383116 q^{90} - 1641024830421155964709952980 q^{91} + 24429661050315871142131995180 q^{92} - 5183098360169002874029924602 q^{93} - 14031972400522725614187669972 q^{94} + 26915075821864824957619532334 q^{95} - 13128504577098248079162758058 q^{96} + 62103529261184125350555125096 q^{97} - 7748676469670377829794211142 q^{98} - 64054360047699630847152441972 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{29}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.29.b \(\chi_{21}(8, \cdot)\) 21.29.b.a 56 1
21.29.d \(\chi_{21}(13, \cdot)\) 21.29.d.a 38 1
21.29.f \(\chi_{21}(10, \cdot)\) 21.29.f.a 36 2
21.29.f.b 38
21.29.h \(\chi_{21}(2, \cdot)\) 21.29.h.a 2 2
21.29.h.b 144

Decomposition of \(S_{29}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{29}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{29}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{29}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)