# Properties

 Label 24.2 Level 24 Weight 2 Dimension 5 Nonzero newspaces 3 Newform subspaces 3 Sturm bound 64 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$24 = 2^{3} \cdot 3$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$3$$ Newform subspaces: $$3$$ 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

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

## 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 available 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