On the evenness of coefficients of modular forms

Source abstract

We study the density of primes such that $a_p$ is divisible by a prime above $2$ for modular forms $f = \sum_{n \ge 1} a_n q^n$ of small levels. First, we reduce the problem to low weight and odd level, or a mod $2$ CM type form. Then, we provide calculations for the evenness of particular newforms. In particular, we provide a list of levels where this "evenness" can be computed exactly for all the forms with trivial nebentypus.