# Properties

 Label 124.1 Level 124 Weight 1 Dimension 4 Nonzero newspaces 1 Newforms 1 Sturm bound 960 Trace bound 0

## 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

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

## 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

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