Part III Modular Forms


Useful online resources

Example sheets

Solutions have been removed until after my 2010 Warwick course ends — DL 2010-09-14.

Crash course on Sage

For some of the example sheet questions you will need to use a computer. The computer algebra system that I personally get along best with is Sage, which was created by William Stein (author of one of our course texts). Sage is based on the programming language Python, which is very simple and easy to learn.

If you want to download Sage, then by all means go ahead; but you don't have to. There is a public Sage server with a Web interface, (*). To do anything, click on the link to create a username and password, and then log in.

You will see a welcome page. Click the link to "view published worksheets". There should be somewhere on the list a worksheet entitled "Part III Modular Forms -- Some Level 1 Forms". Go to this, then click the link in the top right corner marked "Edit a copy".

You will see a page with some text and some boxes containing Sage code. Click in the first of these, and press Shift+Enter (or click the "Evaluate" link). Keep going down through the sheet, evaluating the boxes in turn; this will walk you through an example very similar to a question on the first example sheet (calculating the matrix of the Hecke operator T3 on M28). Remember you are working in a copy of my example worksheet, so you can change the code however you like, and see what results you get!

(* Please don't do anything stupid, like trying to crash it -- it will just be withdrawn from public use, and a very valuable community resource will be lost.)

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Last updated 2009-05-13