In spite of this, I have been working hard lately to write code to compute some actual numbers for me. Garden variety calculators (even the fancy graphing kind) won't produce these numbers for me. There are some calculators for mathematicians that will do this sort of computation. See, for example:
What I'm trying to produce here are some numbers which determine certain kinds of modular forms. My code will eventually produce modular forms that even William Stein's lovely calculator doesn't (yet) find for me. In the meantime, I'm just trying to get it to work in the cases where I already have data to compare with mine. I finally got it to match up with some old tables of numbers from John Cremona. Here's a small sample:
The numbers in the table are eigenvalues for simultaneous eigenvectors for the matrices giving the action of Hecke operators T_p, where the p are, for example, the primes you see in the left hand column. (These are primes in the Gaussian integers.) The congruence subgroup in question here is Gamma_0(N) where the level N is given in the top row.
Getting my numbers to match up with his is like a return to the good old days when doing math included that so very satisfying part where you match your answer up with the one in the back of the book.
