2 problems

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

Unbounded denominators conjecture. The Fourier coefficients of $f$ have bounded denominators if and only if $f$ is a cusp form for a congruence subgroup.