Multiplicity one for Siegel cusp forms of degree 2 and full level

Let $S_k(\Gamma_2)$ be the space of holomorphic Siegel cusp forms of weight $k$ for $\Gamma_2=\operatorname{Sp}_4(\mathbb{Z})$. Let $f_1,f_2\in S_k(\Gamma_2)$ be Hecke eigenforms, and write $\lambda_{p^r}(f_i)$ for their Hecke eigenvalues. Multiplicity-one conjecture. If, for every prime $p$,

$$\lambda_p(f_1)=\lambda_p(f_2)\quad\text{and}\quad\lambda_{p^2}(f_1)=\lambda_{p^2}(f_2),$$

then there exists a constant $c$ such that $f_1=cf_2$. This is the degree-two, full-level analogue of multiplicity one for ${\rm GL}_2$ and remains unknown for cuspidal representations on ${\rm GSp}_4$.