## Defining parameters

 Level: $$N$$ = $$165 = 3 \cdot 5 \cdot 11$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$2$$ Sturm bound: $$1920$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(165))$$.

Total New Old
Modular forms 166 60 106
Cusp forms 6 4 2
Eisenstein series 160 56 104

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

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

## Trace form

 $$4 q - 2 q^{3} + O(q^{10})$$ $$4 q - 2 q^{3} + 2 q^{12} - 2 q^{15} - 4 q^{16} - 4 q^{25} - 2 q^{27} + 2 q^{33} + 4 q^{37} + 2 q^{48} + 4 q^{55} + 2 q^{60} - 4 q^{67} + 2 q^{75} + 4 q^{81} - 4 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(165))$$

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
165.1.b $$\chi_{165}(76, \cdot)$$ None 0 1
165.1.e $$\chi_{165}(56, \cdot)$$ None 0 1
165.1.g $$\chi_{165}(89, \cdot)$$ None 0 1
165.1.h $$\chi_{165}(109, \cdot)$$ None 0 1
165.1.i $$\chi_{165}(67, \cdot)$$ None 0 2
165.1.l $$\chi_{165}(32, \cdot)$$ 165.1.l.a 2 2
165.1.l.b 2
165.1.n $$\chi_{165}(19, \cdot)$$ None 0 4
165.1.o $$\chi_{165}(14, \cdot)$$ None 0 4
165.1.q $$\chi_{165}(26, \cdot)$$ None 0 4
165.1.t $$\chi_{165}(46, \cdot)$$ None 0 4
165.1.u $$\chi_{165}(2, \cdot)$$ None 0 8
165.1.x $$\chi_{165}(37, \cdot)$$ None 0 8

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(165))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(165)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 2}$$