Arc-zero conjecture for $\Delta_{k,4}$, $\Delta_{k,6}$, and $\Delta_{k,8}$

For integers $k\geq14$, consider the cusp forms $\Delta_{k,4}$, $\Delta_{k,6}$, and $\Delta_{k,8}$ defined by

$$\Delta_{k,\ell}=E_kE_\ell-E_{k+\ell},$$

where $E_j$ is the weight-$j$ Eisenstein series. The arc in the standard fundamental domain is the portion of the unit circle given by $|z|=1$.

Arc-zero conjecture. For $k\geq14$, all of the zeros of $\Delta_{k,4}$, $\Delta_{k,6}$, and $\Delta_{k,8}$ in the fundamental domain lie on the arc $|z|=1$.

This is a more specific prediction about the distribution of zeros in three low-$\ell$ cases. The supplied context does not state whether it has been proved or disproved.