Eigenfunction of all Hecke operators

Question

Let $f$ be a cusp form in $S_{16}$. I want to show $f$ is an eigenfunction of all Hecke operators, i.e., $T_n(f)=\lambda_nf$.

I know Eisenstien series are eigenfunctions of all Hecke operators, and by the spectral theorem the cusp form $\Delta$ is also an eigenfunction of all Hecke operators. But in general the product of eigenfunctions is not an eigenfunction.

Answer 1

$$S_{16}(SL_2(\Bbb{Z}))= \Delta\ M_4(SL_2(\Bbb{Z}))$$ is of dimension $1$