Localization accessibility of Theorem summod5

The localization method is applied to the functions and congruences described above, with $L_{\alpha}=L_{\alpha}^{(0)}+L_{\alpha}^{(1)}$ lying in $\mathcal{M}(\mathrm{X}_0(10))$ and satisfying $L_{\alpha}\equiv 0\pmod{5^{\alpha}}$. Localization accessibility claim. Theorem summod5 is accessible via the localization method. The authors have not yet proved this application of localization, but believe it is accessible; the claim concerns a possible proof of the relation between the two congruence families.