## Defining parameters

 Level: $$N$$ = $$24 = 2^{3} \cdot 3$$ Weight: $$k$$ = $$5$$ Nonzero newspaces: $$3$$ Newform subspaces: $$5$$ Sturm bound: $$160$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(\Gamma_1(24))$$.

Total New Old
Modular forms 76 30 46
Cusp forms 52 26 26
Eisenstein series 24 4 20

## Trace form

 $$26 q - 6 q^{2} - 4 q^{3} + 20 q^{4} + 34 q^{6} + 20 q^{7} - 180 q^{8} + 314 q^{9} + O(q^{10})$$ $$26 q - 6 q^{2} - 4 q^{3} + 20 q^{4} + 34 q^{6} + 20 q^{7} - 180 q^{8} + 314 q^{9} - 332 q^{10} + 192 q^{11} + 160 q^{12} - 248 q^{13} + 420 q^{14} - 708 q^{15} - 864 q^{16} + 240 q^{17} - 394 q^{18} + 120 q^{19} + 168 q^{20} + 1224 q^{21} - 320 q^{22} + 956 q^{24} - 1962 q^{25} + 1008 q^{26} - 1540 q^{27} + 720 q^{28} + 2468 q^{30} + 3924 q^{31} + 3624 q^{32} + 1868 q^{33} + 5036 q^{34} - 5184 q^{35} - 2772 q^{36} - 2808 q^{37} - 6360 q^{38} - 5928 q^{39} - 5416 q^{40} + 720 q^{41} - 8084 q^{42} + 9080 q^{43} - 6720 q^{44} + 2752 q^{45} - 5096 q^{46} + 6264 q^{48} - 4034 q^{49} + 5394 q^{50} - 320 q^{51} + 14080 q^{52} + 14726 q^{54} + 8056 q^{55} + 7512 q^{56} + 1272 q^{57} + 7620 q^{58} + 13056 q^{59} - 9552 q^{60} + 8584 q^{61} - 8724 q^{62} + 724 q^{63} - 39568 q^{64} - 1344 q^{65} - 37800 q^{66} - 21768 q^{67} - 5616 q^{68} - 7360 q^{69} - 9272 q^{70} + 24980 q^{72} - 15052 q^{73} + 17400 q^{74} + 25852 q^{75} + 50712 q^{76} + 55280 q^{78} - 12588 q^{79} + 28512 q^{80} - 4326 q^{81} + 36180 q^{82} - 24000 q^{83} - 26024 q^{84} + 2816 q^{85} - 34344 q^{86} - 16068 q^{87} - 72560 q^{88} + 15600 q^{89} - 71572 q^{90} - 30096 q^{91} - 48096 q^{92} - 17528 q^{93} - 45864 q^{94} + 44312 q^{96} + 23540 q^{97} + 47778 q^{98} + 41728 q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(\Gamma_1(24))$$

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
24.5.b $$\chi_{24}(19, \cdot)$$ 24.5.b.a 8 1
24.5.e $$\chi_{24}(17, \cdot)$$ 24.5.e.a 4 1
24.5.g $$\chi_{24}(7, \cdot)$$ None 0 1
24.5.h $$\chi_{24}(5, \cdot)$$ 24.5.h.a 1 1
24.5.h.b 1
24.5.h.c 12

## Decomposition of $$S_{5}^{\mathrm{old}}(\Gamma_1(24))$$ into lower level spaces

$$S_{5}^{\mathrm{old}}(\Gamma_1(24)) \cong$$ $$S_{5}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 4}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 3}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 2}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 2}$$