## 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

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

## 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

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