sage: E = EllipticCurve('37a') sage: f = E.modular_form() sage: plot(f) ...Look at the code you get when you type

Regarding how should plot, probably there should be options, e.g., it could plot using a generic function for plotting a complex valued function, and all arguments to 's plot should get passed on to that generic function. But, you'll need to compute rigorous bounds on the number of terms of the -expansion that should be used, but allow the user to override them. See the paper by Kevin Grosvenor at

http://modular.math.washington.edu/papers/ell_graphs/ell_graphs.pdf

http://www.math.lsu.edu/~verrill/fundomain/Write something like her program, but for SAGE. Here's an email she sent me (today!):

From: "Helena Verrill" <[email protected]> To: [email protected] Subject: Re: very fast GMP on OSX Macbook Date: Tue, 1 Aug 2006 05:14:29 -0500 Hi William, Thanks for sending the info about the upgrade. I guess I should start using the SAGE graphics - I ought to get the fundamental domains pictures working in SAGE. Have you met my students, Maya and Cristian? [...] Thanks for the link to the wiki page. It looks like a great meeting. Best wishes, Helena

http://modular.math.washington.edu/sage/doc/html/ref/module-sage.modular.dims-doc.htmlDraw graphs of some of these functions, as a function of , as a function of , and as a function of both.