We use the theory of congruences between modular forms to prove the existence of newforms with square-free level having a fixed number of prime factors such that the degree of their coefficient fields is arbitrarily large. We also prove a similar result for certain almost square-free levels.
CitacióDieulefait, L., Jimenez, J., Ribet, K. Modular forms with large coefficient fields via congruences. "research in number theory", 01 Maig 2015, vol. 1, núm. 2, p. 1-14.