## Defining parameters

 Level: $$N$$ = $$24 = 2^{3} \cdot 3$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$3$$ Newforms: $$3$$ Sturm bound: $$64$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(24))$$.

Total New Old
Modular forms 28 9 19
Cusp forms 5 5 0
Eisenstein series 23 4 19

## Trace form

 $$5q - 2q^{2} - 3q^{3} - 4q^{4} - 2q^{5} + 2q^{6} - 4q^{7} + 4q^{8} - 3q^{9} + O(q^{10})$$ $$5q - 2q^{2} - 3q^{3} - 4q^{4} - 2q^{5} + 2q^{6} - 4q^{7} + 4q^{8} - 3q^{9} + 4q^{10} + 4q^{11} + 8q^{12} - 2q^{13} + 4q^{14} + 6q^{15} - 2q^{17} - 6q^{18} - 8q^{20} - 8q^{22} - 12q^{24} - 9q^{25} - 8q^{26} + 9q^{27} + 6q^{29} - 4q^{30} + 12q^{31} + 8q^{32} + 4q^{33} + 20q^{34} + 4q^{36} + 6q^{37} + 8q^{38} - 6q^{39} + 8q^{40} - 2q^{41} + 4q^{42} - 16q^{43} - 2q^{45} - 8q^{46} - 24q^{47} - 8q^{48} + q^{49} - 2q^{50} - 18q^{51} + 16q^{52} - 2q^{53} + 6q^{54} - 8q^{55} - 8q^{56} + 8q^{57} - 12q^{58} + 4q^{59} - 2q^{61} - 4q^{62} + 4q^{63} - 16q^{64} + 20q^{65} + 8q^{66} + 24q^{67} + 8q^{69} - 8q^{70} + 32q^{71} + 12q^{72} + 2q^{73} + 16q^{74} + 11q^{75} - 24q^{76} + 8q^{78} + 12q^{79} - 11q^{81} - 36q^{82} - 4q^{83} - 8q^{84} - 4q^{85} - 8q^{86} - 18q^{87} + 16q^{88} - 26q^{89} - 4q^{90} - 8q^{93} + 24q^{94} - 8q^{95} + 24q^{96} - 22q^{97} + 6q^{98} - 12q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$

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
24.2.a $$\chi_{24}(1, \cdot)$$ 24.2.a.a 1 1
24.2.c $$\chi_{24}(23, \cdot)$$ None 0 1
24.2.d $$\chi_{24}(13, \cdot)$$ 24.2.d.a 2 1
24.2.f $$\chi_{24}(11, \cdot)$$ 24.2.f.a 2 1