  Bollob\'as proved that for every $k$ and $\ell$ such that $k\mathbb{Z}+\ell$
contains an even number, an $n$-vertex graph containing no cycle of length
$\ell \bmod k$ can contain at most a linear number of edges. The precise (or
asymptotic) value of the maximum number of edges in such a graph is known for
very few pairs $\ell$ and $k$. In this work we precisely determine the maximum
number of edges in a graph containing no cycle of length $0 \bmod 4$.
