TITLE: Verifying coefficients of modular forms
QUESTION [14 upvotes]: Hi,
I was wondering about good  techniques that one can use to show that given certain coefficients, they are the Fourier coefficients of a cusp form, assuming we know the desired weight and level.  I am aware of Weil's "converse theorem", but am not aware of any examples of it being used to prove something is a modular form.  So, even a pointer to an example of that would be useful. I'm curious if there are other more direct methods as well. Thanks!

REPLY [2 votes]: The search for a modular form of some weight and level, whose Fourier coefficients match a given list of initial coefficients, has been implemented in PARI/GP with the function mfsearch.