A 5-adic congruence for a weight-1 noncongruence modular form

Let $f_1$ and $f_2$ be the normalized weight-$1$ forms for $\Gamma_1(5)$ described in the source, and set

$$f=\sqrt{f_1f_2}.$$

For a prime $p$ and $m$ with $c_{p^m}(f)\neq0$, define $t_m(f,n)=c_{np^m}(f)/c_{p^m}(f)$.

The 5-adic congruence conjecture. For $p=5$, $m\geq1$, and odd $n\geq1$, one has $c_{5^m}(f)\neq0$ and

$$t_m(f,5n)\equiv t_m(f,n)\pmod{5^{2m+4}}.$$

This pattern was suggested by computational data for a weight-$1$ noncongruence form. The source gives no proof or resolution status.