## Defining parameters

 Level: $$N$$ = $$24 = 2^{3} \cdot 3$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$3$$ Newform subspaces: $$4$$ Sturm bound: $$128$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(24))$$.

Total New Old
Modular forms 60 21 39
Cusp forms 36 17 19
Eisenstein series 24 4 20

## Trace form

 $$17q + 2q^{2} + q^{3} + 20q^{4} + 14q^{5} - 14q^{6} + 4q^{7} - 76q^{8} - 47q^{9} + O(q^{10})$$ $$17q + 2q^{2} + q^{3} + 20q^{4} + 14q^{5} - 14q^{6} + 4q^{7} - 76q^{8} - 47q^{9} + 36q^{10} - 28q^{11} - 56q^{12} - 74q^{13} - 100q^{14} - 18q^{15} - 96q^{16} + 134q^{17} + 166q^{18} + 64q^{19} + 56q^{20} - 72q^{21} + 448q^{22} + 336q^{23} + 532q^{24} + 11q^{25} + 56q^{26} - 107q^{27} + 176q^{28} - 138q^{29} - 252q^{30} - 556q^{31} - 248q^{32} - 148q^{33} - 1332q^{34} - 336q^{35} - 1028q^{36} + 30q^{37} - 776q^{38} + 90q^{39} - 1016q^{40} + 518q^{41} + 756q^{42} + 432q^{43} + 1152q^{44} + 126q^{45} + 1768q^{46} - 168q^{47} + 2296q^{48} + 621q^{49} + 1970q^{50} + 998q^{51} + 1744q^{52} - 130q^{53} - 2114q^{54} + 632q^{55} - 1864q^{56} + 224q^{57} - 2476q^{58} + 596q^{59} - 3792q^{60} - 218q^{61} - 2108q^{62} - 468q^{63} - 1552q^{64} - 2780q^{65} + 1352q^{66} - 2072q^{67} + 2976q^{68} + 24q^{69} + 5048q^{70} - 848q^{71} + 3964q^{72} + 170q^{73} + 1568q^{74} - 1745q^{75} + 1864q^{76} + 672q^{77} - 2088q^{78} - 76q^{79} - 2112q^{80} + 721q^{81} - 5372q^{82} - 1508q^{83} - 6216q^{84} + 1148q^{85} - 760q^{86} + 630q^{87} - 2576q^{88} - 466q^{89} + 3564q^{90} + 4944q^{91} + 1728q^{92} + 240q^{93} + 6888q^{94} + 6392q^{95} + 6424q^{96} - 1630q^{97} + 3354q^{98} + 3860q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(24))$$

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
24.4.a $$\chi_{24}(1, \cdot)$$ 24.4.a.a 1 1
24.4.c $$\chi_{24}(23, \cdot)$$ None 0 1
24.4.d $$\chi_{24}(13, \cdot)$$ 24.4.d.a 6 1
24.4.f $$\chi_{24}(11, \cdot)$$ 24.4.f.a 2 1
24.4.f.b 8

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(24))$$ into lower level spaces

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