show/hide this revision's text 2 Defined Gamma^0()

I am just a beginner in modular forms.. It seems for me that lots of the work has been done for the cases of spaces of modular forms for $\Gamma_0(N)$ or $\Gamma_1(N)$ with some Dirichlet character $\chi_d$.

I am curious about the cases $\Gamma^0(N)$ and $\Gamma^1(N)$ with some Dirichlet character $\chi_d$.

Here, $\Gamma^0(N)$ is the congruence subgroup of $SL_2(\mathbb{Z})$, consists of $A=(a_{ij})$, where the upper right corner $a_{12}\cong 0$ mod $N$.

Could anyone give me some reference or some idea about how to get space of modular forms of $\Gamma^0(N)$ and $\Gamma^1(N)$ with Dirichlet character $\chi_d$? Or is it possible to get them from the cases of $\Gamma_0$ and $\Gamma_1$?

Thank you so much
show/hide this revision's text 1

modular forms of Gamma^0(N) with some Dirichlet character

I am just a beginner in modular forms.. It seems for me that lots of the work has been done for the cases of spaces of modular forms for $\Gamma_0(N)$ or $\Gamma_1(N)$ with some Dirichlet character $\chi_d$.

I am curious about the cases $\Gamma^0(N)$ and $\Gamma^1(N)$ with some Dirichlet character $\chi_d$.

Could anyone give me some reference or some idea about how to get space of modular forms of $\Gamma^0(N)$ and $\Gamma^1(N)$ with Dirichlet character $\chi_d$? Or is it possible to get them from the cases of $\Gamma_0$ and $\Gamma_1$?

Thank you so much