I want to do double coset operators computations on modular forms of half integer weight and with character such as the trace operators that map modular forms of congruence subgroups $\Gamma_0(N)$ to modular forms of $\Gamma_0(M)$ where $M$ divides $N$. I know that there are commands in SAGE and PARI/GP that can compute action of certain Hecke operators (using modular symbols and trace formulas respectively).

However, can I compute action of arbitrary double coset operators using such computer algebra systems (in particular the trace operator mentioned above)?