A normalized modular eigenform f is said to be ordinary at a prime
p if p does not divide the p-th Fourier coefficient of f. We take
f to be a modular form of level $1$ and weight
$k\in\{12$,$\,16$,$\,18$,$\,20$,$\,22$,$\,26\}$ and search for primes where f is not
ordinary. To do this, we need an efficient way to compute the reduction
modulo p of the p-th Fourier coefficient. A convenient formula was
known for $k=12$; trying to understand it leads to generalized Rankin-Cohen
brackets and thence to formulas that we can use to look for non-ordinary
primes. We do this for $p\leq 1\,000\,000$.