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Note: You will not want to solve the last problem by hand. I suggest using SAGE which you can either use online or download for free. The command to generate the Fourier expansion of the kth Eisenstein series is "eisenstein_series_qexp(k)" (without the quotes). The one catch is that this Eisenstein series is normalized to have q coefficient 1, instead of constant term 1. However, it will be easy to see what you need to multiply by to get our E_k(z).
Last updated June 24, 2010 10:49:47 EDT