Properties

 Label 24.22 Level 24 Weight 22 Dimension 135 Nonzero newspaces 3 Newform subspaces 7 Sturm bound 704 Trace bound 1

Defining parameters

 Level: $$N$$ = $$24 = 2^{3} \cdot 3$$ Weight: $$k$$ = $$22$$ Nonzero newspaces: $$3$$ Newform subspaces: $$7$$ Sturm bound: $$704$$ Trace bound: $$1$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{22}(\Gamma_1(24))$$.

Total New Old
Modular forms 348 139 209
Cusp forms 324 135 189
Eisenstein series 24 4 20

Trace form

 $$135 q - 574 q^{2} - 59051 q^{3} - 819756 q^{4} + 24476018 q^{5} - 114042446 q^{6} - 1870661068 q^{7} - 2157413692 q^{8} - 108090316433 q^{9} + O(q^{10})$$ $$135 q - 574 q^{2} - 59051 q^{3} - 819756 q^{4} + 24476018 q^{5} - 114042446 q^{6} - 1870661068 q^{7} - 2157413692 q^{8} - 108090316433 q^{9} + 23020559940 q^{10} + 107613766484 q^{11} - 687924344168 q^{12} + 332603423882 q^{13} + 1565450468972 q^{14} + 4077021553182 q^{15} - 7617963524320 q^{16} - 16890996533518 q^{17} + 5405788685974 q^{18} - 138737389164528 q^{19} + 72162740641304 q^{20} + 66544798630392 q^{21} - 390339758529696 q^{22} + 280994945120112 q^{23} - 231059606754236 q^{24} + 4466824763167221 q^{25} + 1821164548445192 q^{26} - 1353630927945167 q^{27} + 5597434107379696 q^{28} - 2925935714563878 q^{29} - 8590495744400412 q^{30} + 13663108162346980 q^{31} + 20291511717782536 q^{32} - 7865940076801156 q^{33} - 69879170769759188 q^{34} + 10563629972649936 q^{35} - 95925861444137636 q^{36} + 5798310242710770 q^{37} + 152044668976276888 q^{38} - 60171120514576854 q^{39} - 76062873051882904 q^{40} + 232218739915681154 q^{41} + 324884610368231172 q^{42} - 755371705017696992 q^{43} - 583729140892614912 q^{44} + 85342597760995218 q^{45} + 113423679571795016 q^{46} - 2469818058933334344 q^{47} + 791783284874536504 q^{48} + 346371282775734515 q^{49} + 3155333405061952034 q^{50} - 3564655633453139122 q^{51} + 1133310254292043760 q^{52} + 5133623792760853250 q^{53} + 3943544833417853422 q^{54} - 8297593283341950536 q^{55} - 1787796305200178632 q^{56} - 380519122922766928 q^{57} + 10365946054862180788 q^{58} - 6608991397155328348 q^{59} + 19469632430176651248 q^{60} + 17010947004343064858 q^{61} - 15146072229522685484 q^{62} + 1356850503593926524 q^{63} + 90965337376162782576 q^{64} + 10114787629510450732 q^{65} - 101229758773762370776 q^{66} + 30368480556368801592 q^{67} + 41027785784298520512 q^{68} + 5216938192355620104 q^{69} - 67395585926452925672 q^{70} - 116195913448325615792 q^{71} - 88781220597925583924 q^{72} + 22930068797837689334 q^{73} + 156212595524575515440 q^{74} + 9656180814360383203 q^{75} - 142384629677741769816 q^{76} - 83126402239689155424 q^{77} + 313972423760569758312 q^{78} + 508656598728859462468 q^{79} - 168480498883332591744 q^{80} + 635643124813330111063 q^{81} - 175693057753192993596 q^{82} + 703664539309701073804 q^{83} + 85921890008397568440 q^{84} - 250629266282997656828 q^{85} + 49699114310265976040 q^{86} - 134299208468008602090 q^{87} + 692567223615952556208 q^{88} - 1033604487723695607142 q^{89} - 1238305256646636229524 q^{90} + 1182027468024211137744 q^{91} + 461231995073255535744 q^{92} - 733314734961670912320 q^{93} - 1227549689171584487352 q^{94} + 2623786333753002706424 q^{95} - 492883702263262948904 q^{96} + 522376420324862068238 q^{97} + 1371753640376248773498 q^{98} + 1911648981737994649028 q^{99} + O(q^{100})$$

Decomposition of $$S_{22}^{\mathrm{new}}(\Gamma_1(24))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
24.22.a $$\chi_{24}(1, \cdot)$$ 24.22.a.a 2 1
24.22.a.b 3
24.22.a.c 3
24.22.a.d 3
24.22.c $$\chi_{24}(23, \cdot)$$ None 0 1
24.22.d $$\chi_{24}(13, \cdot)$$ 24.22.d.a 42 1
24.22.f $$\chi_{24}(11, \cdot)$$ 24.22.f.a 2 1
24.22.f.b 80

Decomposition of $$S_{22}^{\mathrm{old}}(\Gamma_1(24))$$ into lower level spaces

$$S_{22}^{\mathrm{old}}(\Gamma_1(24)) \cong$$ $$S_{22}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 8}$$$$\oplus$$$$S_{22}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 6}$$$$\oplus$$$$S_{22}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 4}$$$$\oplus$$$$S_{22}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 4}$$$$\oplus$$$$S_{22}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 3}$$$$\oplus$$$$S_{22}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 2}$$$$\oplus$$$$S_{22}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 2}$$