Modular forms with large coefficient fields via congruences

Details Modular forms with large coefficient fields via congruences Modular forms with large coefficient fields via congruences

2011-11-23

arxiv.org/abs/1111.5592v1

Mathematics

Number Theory

Scientific paper

In this paper we apply results from the theory of congruences of modular forms (control of reducible primes, level-lowering), the modularity of elliptic curves and Q-curves, and a couple of Frey curves of Fermat-Goldbach type, to show the existence of newforms of weight 2 and trivial nebentypus with coefficient fields of arbitrarily large degree and square-free or almost square-free level. More precisely, we prove that for any given numbers t and B, there exists a newform f of weight 2 and trivial nebentypus whose level N is square-free (almost square-free), N has exactly t prime divisors (t odd prime divisors and a small power of 2 dividing it, respectively), and the degree of the field of coefficients of f is greater than B.

Affiliated with

Also associated with

No associations

Rating

Modular forms with large coefficient fields via congruences does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Modular forms with large coefficient fields via congruences, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Modular forms with large coefficient fields via congruences will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-378125