# Properties

 Label 243.1 Level 243 Weight 1 Dimension 3 Nonzero newspaces 2 Newform subspaces 2 Sturm bound 4374 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$243 = 3^{5}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$4374$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(243))$$.

Total New Old
Modular forms 192 99 93
Cusp forms 3 3 0
Eisenstein series 189 96 93

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 3 0 0 0

## Trace form

 $$3 q + O(q^{10})$$ $$3 q - 3 q^{19} - 3 q^{28} - 3 q^{37} + 3 q^{64} + 6 q^{73} + 3 q^{91} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(243))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
243.1.b $$\chi_{243}(242, \cdot)$$ 243.1.b.a 1 1
243.1.d $$\chi_{243}(80, \cdot)$$ 243.1.d.a 2 2
243.1.f $$\chi_{243}(26, \cdot)$$ None 0 6
243.1.h $$\chi_{243}(8, \cdot)$$ None 0 18
243.1.j $$\chi_{243}(2, \cdot)$$ None 0 54