Computing Congruences Between an Elliptic Curve with Integer   Coefficients and the Old Space
  We put together some known theoretical results and the fact that certain computations can be done efficiently in SAGE to come up with a fast algorithm for calculating congruence primes linking a newform with integer coefficients (i.e. a newform associated to an elliptic curve) with the old space at the same level. 
Randy Heaton
math.NT