  Let p be a prime number. The Hasse invariant is a modular form modulo p that
is often used to produce congruences between modular forms of different
weights. We show how to produce such congruences between forms of weights 2 and
p+1, in terms of group cohomology. We also show how our method works in the
contexts of quadratic imaginary fields (where there is no Hasse invariant
available) and Hilbert modular forms over totally real fields of even degree.
