## Defining parameters

 Level: $$N$$ = $$24 = 2^{3} \cdot 3$$ Weight: $$k$$ = $$8$$ Nonzero newspaces: $$3$$ Newform subspaces: $$7$$ Sturm bound: $$256$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{8}(\Gamma_1(24))$$.

Total New Old
Modular forms 124 47 77
Cusp forms 100 43 57
Eisenstein series 24 4 20

## Trace form

 $$43 q - 14 q^{2} + 25 q^{3} - 236 q^{4} - 446 q^{5} - 14 q^{6} + 3052 q^{7} - 428 q^{8} - 8021 q^{9} + O(q^{10})$$ $$43 q - 14 q^{2} + 25 q^{3} - 236 q^{4} - 446 q^{5} - 14 q^{6} + 3052 q^{7} - 428 q^{8} - 8021 q^{9} - 284 q^{10} + 3028 q^{11} - 5144 q^{12} + 5154 q^{13} + 4636 q^{14} - 24138 q^{15} - 58208 q^{16} + 35626 q^{17} + 406 q^{18} + 70768 q^{19} + 175096 q^{20} - 11664 q^{21} - 210976 q^{22} - 307680 q^{23} - 110348 q^{24} + 137921 q^{25} + 424984 q^{26} + 257725 q^{27} + 517168 q^{28} - 106902 q^{29} - 275292 q^{30} - 91940 q^{31} - 893944 q^{32} - 309628 q^{33} + 777004 q^{34} - 35616 q^{35} + 3388 q^{36} + 469002 q^{37} - 823816 q^{38} + 332586 q^{39} - 745016 q^{40} + 442714 q^{41} + 759060 q^{42} + 249280 q^{43} + 1275264 q^{44} - 325134 q^{45} - 1789848 q^{46} - 2632248 q^{47} + 332920 q^{48} - 1087081 q^{49} + 324610 q^{50} + 264422 q^{51} - 517104 q^{52} + 455554 q^{53} + 65470 q^{54} + 8823992 q^{55} + 1643704 q^{56} - 761944 q^{57} - 2993516 q^{58} - 2921612 q^{59} - 2789712 q^{60} - 5417118 q^{61} + 5767172 q^{62} + 224532 q^{63} + 3123952 q^{64} + 3499100 q^{65} - 3707128 q^{66} - 3523448 q^{67} - 3735840 q^{68} - 2845800 q^{69} + 18413048 q^{70} + 1543616 q^{71} + 3815836 q^{72} - 2225746 q^{73} - 6468800 q^{74} + 6356935 q^{75} - 9297656 q^{76} + 7828800 q^{77} - 6804360 q^{78} - 11704484 q^{79} + 14369088 q^{80} + 15456235 q^{81} - 24941852 q^{82} - 11429812 q^{83} - 14932296 q^{84} - 6864252 q^{85} + 4738312 q^{86} + 16382574 q^{87} - 4684432 q^{88} + 5133874 q^{89} + 10622124 q^{90} + 14165376 q^{91} + 11004480 q^{92} - 10069704 q^{93} - 17782296 q^{94} - 78332168 q^{95} + 9297304 q^{96} + 4154870 q^{97} + 53030538 q^{98} + 16638212 q^{99} + O(q^{100})$$

## Decomposition of $$S_{8}^{\mathrm{new}}(\Gamma_1(24))$$

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
24.8.a $$\chi_{24}(1, \cdot)$$ 24.8.a.a 1 1
24.8.a.b 1
24.8.a.c 1
24.8.c $$\chi_{24}(23, \cdot)$$ None 0 1
24.8.d $$\chi_{24}(13, \cdot)$$ 24.8.d.a 14 1
24.8.f $$\chi_{24}(11, \cdot)$$ 24.8.f.a 2 1
24.8.f.b 4
24.8.f.c 20

## Decomposition of $$S_{8}^{\mathrm{old}}(\Gamma_1(24))$$ into lower level spaces

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