## Defining parameters

 Level: $$N$$ = $$24 = 2^{3} \cdot 3$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$3$$ Newform subspaces: $$5$$ Sturm bound: $$96$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(24))$$.

Total New Old
Modular forms 44 16 28
Cusp forms 20 12 8
Eisenstein series 24 4 20

## Trace form

 $$12q + 2q^{2} + 2q^{3} - 12q^{4} - 14q^{6} - 16q^{7} - 4q^{8} - 4q^{9} + O(q^{10})$$ $$12q + 2q^{2} + 2q^{3} - 12q^{4} - 14q^{6} - 16q^{7} - 4q^{8} - 4q^{9} - 12q^{10} - 32q^{11} + 16q^{12} + 20q^{13} + 36q^{14} + 12q^{15} + 32q^{16} - 8q^{17} + 62q^{18} + 36q^{19} + 72q^{20} - 12q^{21} + 48q^{22} - 52q^{24} - 72q^{25} - 96q^{26} - 46q^{27} - 176q^{28} - 172q^{30} + 16q^{31} - 88q^{32} + 20q^{33} - 68q^{34} + 96q^{35} + 108q^{36} - 12q^{37} + 40q^{38} + 132q^{39} + 248q^{40} + 40q^{41} + 220q^{42} + 196q^{43} + 64q^{44} + 64q^{45} + 152q^{46} - 72q^{48} - 100q^{49} - 118q^{50} - 224q^{51} - 160q^{52} - 202q^{54} - 296q^{55} - 168q^{56} + 12q^{57} + 4q^{58} - 128q^{59} + 48q^{60} - 172q^{61} + 204q^{62} - 176q^{63} + 240q^{64} + 96q^{65} + 216q^{66} - 252q^{67} + 112q^{68} - 64q^{69} + 40q^{70} - 124q^{72} + 440q^{73} - 120q^{74} + 178q^{75} - 72q^{76} - 160q^{78} + 400q^{79} - 96q^{80} + 108q^{81} - 348q^{82} + 160q^{83} + 88q^{84} + 256q^{85} + 88q^{86} + 492q^{87} - 48q^{88} - 200q^{89} + 44q^{90} + 168q^{91} + 96q^{92} - 44q^{93} - 168q^{94} - 40q^{96} - 40q^{97} + 170q^{98} - 32q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(24))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
24.3.b $$\chi_{24}(19, \cdot)$$ 24.3.b.a 4 1
24.3.e $$\chi_{24}(17, \cdot)$$ 24.3.e.a 2 1
24.3.g $$\chi_{24}(7, \cdot)$$ None 0 1
24.3.h $$\chi_{24}(5, \cdot)$$ 24.3.h.a 1 1
24.3.h.b 1
24.3.h.c 4

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(24))$$ into lower level spaces

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