Let N and p>3 be two primes. We consider spaces of modular forms of weight 2 and of level N or N^2 with trivial character.
In the case of level N, Mazur in 1976 proved that there exits a cusp form congrunet to the (unique) Eisenstein series modulo p if and only if p divides N-1. Recently, Wake and Lang prove similar criterion in forms of level N^2  for another distinguished Eisenstein series, and when exits they also count how many such cusp forms using pseudodeformation theory. We will sketch their results and methods and then give a new result also using psedodeformation theory on Eisenstein congruences for another Hecke-eigen Eisenstein series in the space of level N^2 forms.