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Properties

Label 21.24
Level 21
Weight 24
Dimension 264
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 768
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 24 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(768\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_1(21))\).

Total New Old
Modular forms 380 276 104
Cusp forms 356 264 92
Eisenstein series 24 12 12

Trace form

\( 264 q + 228 q^{2} + 177144 q^{3} - 6404558 q^{4} + 54033726 q^{5} - 3016459116 q^{6} + 7300166314 q^{7} - 29528539626 q^{8} - 99663185544 q^{9} + O(q^{10}) \) \( 264 q + 228 q^{2} + 177144 q^{3} - 6404558 q^{4} + 54033726 q^{5} - 3016459116 q^{6} + 7300166314 q^{7} - 29528539626 q^{8} - 99663185544 q^{9} - 339624554832 q^{10} - 4519088451438 q^{11} + 8321680350528 q^{12} - 35708819823722 q^{13} + 64935021317832 q^{14} - 164379210438348 q^{15} + 402064046532786 q^{16} + 148145034109512 q^{17} + 969861869184978 q^{18} + 171287577547702 q^{19} + 3461759704313124 q^{20} - 1993301661456294 q^{21} - 13326659145748704 q^{22} + 2175687843795048 q^{23} - 40234917354523200 q^{24} - 30125533587000426 q^{25} + 99460749106300314 q^{26} - 11118121133111046 q^{27} + 192799258198050282 q^{28} - 164455592546504472 q^{29} + 61803204810186870 q^{30} + 900220371894439174 q^{31} + 557739872550393870 q^{32} + 639686616609419568 q^{33} + 320085930817661700 q^{34} - 1001437665729458046 q^{35} + 10553097965533202922 q^{36} + 3694583765581110704 q^{37} - 11427790021042295658 q^{38} + 4711208082170777274 q^{39} + 24725371051652676456 q^{40} - 33243134643471426612 q^{41} + 18399356512824545406 q^{42} + 27528353013906247520 q^{43} - 25920171312246109992 q^{44} + 19171447529988097836 q^{45} + 77467128758838175524 q^{46} + 60443216038447100886 q^{47} - 100780455513339108000 q^{48} + 114435624032811001230 q^{49} + 427785018570188860242 q^{50} - 169700768888489114508 q^{51} - 317186879225184127496 q^{52} + 532526192427714341340 q^{53} + 523627938786252415914 q^{54} - 456883887889233161640 q^{55} - 834289515270207541422 q^{56} + 660983250754189933344 q^{57} - 35700744511861861464 q^{58} + 134347733517880584108 q^{59} - 1980267844046070924540 q^{60} + 211649448031575487810 q^{61} - 889176480965159644860 q^{62} - 243485036305144340322 q^{63} - 13718109685516092412922 q^{64} - 862928664757473785586 q^{65} + 8048009422175853422250 q^{66} + 4528412559377936365626 q^{67} - 3933691849471819545120 q^{68} - 472002661339460799048 q^{69} - 3182808407768870705904 q^{70} + 1875078317250420068364 q^{71} - 14964492572038606837986 q^{72} - 10223318464933325741060 q^{73} - 13446110192664671401338 q^{74} + 14531238723350634940146 q^{75} + 21773886922022648926024 q^{76} - 21422360947872301368648 q^{77} + 31770975160961377906752 q^{78} + 20365158177053572846542 q^{79} + 25722819388223373689016 q^{80} - 91606600539787252136292 q^{81} - 47565101828791293594984 q^{82} + 53622426163747643165148 q^{83} + 49970139474936546749676 q^{84} - 43439390998080646669992 q^{85} + 48429790723220630142822 q^{86} - 14658914543941486459116 q^{87} + 136213526475825497523564 q^{88} + 160298414243340817160040 q^{89} - 73604369628056533657320 q^{90} - 94761076015710588378968 q^{91} - 32057403480838651586496 q^{92} + 205632730696994026963878 q^{93} + 104923110016981030902312 q^{94} + 132976033369132643523234 q^{95} - 874197987796589871274668 q^{96} - 543702059718236295130004 q^{97} + 337880158213939044733350 q^{98} + 377741536098965639918172 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.24.a \(\chi_{21}(1, \cdot)\) 21.24.a.a 5 1
21.24.a.b 6
21.24.a.c 6
21.24.a.d 7
21.24.c \(\chi_{21}(20, \cdot)\) 21.24.c.a 60 1
21.24.e \(\chi_{21}(4, \cdot)\) 21.24.e.a 30 2
21.24.e.b 32
21.24.g \(\chi_{21}(5, \cdot)\) 21.24.g.a 2 2
21.24.g.b 116

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)