## Defining parameters

 Level: $$N$$ = $$144 = 2^{4} \cdot 3^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newforms: $$1$$ Sturm bound: $$1152$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(144))$$.

Total New Old
Modular forms 117 21 96
Cusp forms 5 1 4
Eisenstein series 112 20 92

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 1 0 0 0

## Trace form

 $$q + O(q^{10})$$ $$q - 2q^{13} - q^{25} + 2q^{37} + q^{49} + 2q^{61} - 2q^{73} - 2q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(144))$$

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
144.1.b $$\chi_{144}(55, \cdot)$$ None 0 1
144.1.e $$\chi_{144}(17, \cdot)$$ None 0 1
144.1.g $$\chi_{144}(127, \cdot)$$ 144.1.g.a 1 1
144.1.h $$\chi_{144}(89, \cdot)$$ None 0 1
144.1.j $$\chi_{144}(53, \cdot)$$ None 0 2
144.1.m $$\chi_{144}(19, \cdot)$$ None 0 2
144.1.n $$\chi_{144}(41, \cdot)$$ None 0 2
144.1.o $$\chi_{144}(31, \cdot)$$ None 0 2
144.1.q $$\chi_{144}(65, \cdot)$$ None 0 2
144.1.t $$\chi_{144}(7, \cdot)$$ None 0 2
144.1.v $$\chi_{144}(43, \cdot)$$ None 0 4
144.1.w $$\chi_{144}(5, \cdot)$$ None 0 4

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(144))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(144)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 2}$$