## Defining parameters

 Level: $$N$$ = $$124 = 2^{2} \cdot 31$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newforms: $$1$$ Sturm bound: $$960$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(124))$$.

Total New Old
Modular forms 82 32 50
Cusp forms 7 4 3
Eisenstein series 75 28 47

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 0 4 0 0

## Trace form

 $$4q - 4q^{4} - 2q^{5} - 2q^{6} + O(q^{10})$$ $$4q - 4q^{4} - 2q^{5} - 2q^{6} + 2q^{13} + 2q^{14} + 4q^{16} - 2q^{17} + 2q^{20} - 2q^{21} - 2q^{22} + 2q^{24} + 4q^{30} - 4q^{33} - 2q^{37} - 2q^{38} - 2q^{41} - 2q^{52} + 2q^{53} + 4q^{54} - 2q^{56} + 2q^{57} + 4q^{62} - 4q^{64} + 2q^{65} + 2q^{68} - 4q^{70} - 2q^{73} + 4q^{77} - 4q^{78} - 2q^{80} + 2q^{81} + 2q^{84} + 4q^{85} - 2q^{86} + 2q^{88} + 2q^{93} - 2q^{96} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(124))$$

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
124.1.b $$\chi_{124}(63, \cdot)$$ None 0 1
124.1.c $$\chi_{124}(61, \cdot)$$ None 0 1
124.1.h $$\chi_{124}(37, \cdot)$$ None 0 2
124.1.i $$\chi_{124}(67, \cdot)$$ 124.1.i.a 4 2
124.1.k $$\chi_{124}(29, \cdot)$$ None 0 4
124.1.l $$\chi_{124}(35, \cdot)$$ None 0 4
124.1.n $$\chi_{124}(7, \cdot)$$ None 0 8
124.1.o $$\chi_{124}(13, \cdot)$$ None 0 8

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(124))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(124)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(31))$$$$^{\oplus 3}$$