|Date||Sep 13, 2018|
We introduce the notion of congruences (modulo a prime number) between modular forms of different levels. One of the main questions is to show the existence of a certain newform of an expected level which is congruent to a given modular form. (For instance, if a given modular form comes from an elliptic curve over the field of rational numbers, then this problem is known as "epsilon-conjecture".) We partially answer this question when a given modular form is an Eisenstein series.