I understand and share quid's bewilderment. There are easily more than 5000 articles whose main theme can be considered, without stretching too much, as "congruencies between Fourier coefficients of modular forms - and generalizations", including some of the most famous of the last four decades, like the one proving Fermat's last theorem.
The theory of congruences between modular forms has blossomed in many directions. You may want to look at work of Serre, Katz, Hida, Mazur, Ribet, Wiles (and others) in the 70's and 80's for the beginning of the story.