## 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

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

## 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

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