# Properties

 Label 324.1 Level 324 Weight 1 Dimension 8 Nonzero newspaces 3 Newform subspaces 5 Sturm bound 5832 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$324 = 2^{2} \cdot 3^{4}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$3$$ Newform subspaces: $$5$$ Sturm bound: $$5832$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(324))$$.

Total New Old
Modular forms 280 64 216
Cusp forms 10 8 2
Eisenstein series 270 56 214

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 8 0 0 0

## Trace form

 $$8q + q^{7} + O(q^{10})$$ $$8q + q^{7} - 6q^{10} + q^{13} - 2q^{19} - q^{25} - 2q^{31} - 8q^{37} - 2q^{43} + q^{61} + 6q^{64} + q^{67} - 8q^{73} + q^{79} + 12q^{82} + 2q^{91} + q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(324))$$

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
324.1.c $$\chi_{324}(161, \cdot)$$ None 0 1
324.1.d $$\chi_{324}(163, \cdot)$$ 324.1.d.a 1 1
324.1.d.b 1
324.1.f $$\chi_{324}(55, \cdot)$$ 324.1.f.a 2 2
324.1.f.b 2
324.1.g $$\chi_{324}(53, \cdot)$$ 324.1.g.a 2 2
324.1.j $$\chi_{324}(19, \cdot)$$ None 0 6
324.1.k $$\chi_{324}(17, \cdot)$$ None 0 6
324.1.n $$\chi_{324}(7, \cdot)$$ None 0 18
324.1.o $$\chi_{324}(5, \cdot)$$ None 0 18

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(324))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(324)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 2}$$