  Let $k$ be an even positive integer, $p$ be a prime and $m$ be a nonnegative
integer. We find an upper bound for orders of zeros (at cusps) of a linear
combination of classical Eisenstein series of weight $k$ and level $p^m$. As an
immediate consequence we find the set of all eta quotients that are linear
combinations of these Eisenstein series and hence the set of all eta quotients
of level $p^m$ whose derivatives are also eta quotients.
