Hello, My name is Michael Neururer and I'm a PhD student at the University of Nottingham. My research is in the area of modular forms, for a few details see my CV. I have been using Sage in my research and participated at various conferences related to Sage like the Sage Days 61 and the LMFDB conference at the ICTP in Trieste.
I am interested in the proposed project 'Computation of q-expansions of modular forms attached to elliptic curves at all cusps.' for two reasons: - I believe I have a good background knowledge to contribute to it. From my previous research on an Eichler-Shimura isomorphism for modular forms of real weight I am familiar with the modular symbols method, which can be used to compute q-expansions of newforms at infinity. In one of my current projects (in collaboration with Martin Dickson) we analyse what spaces of modular forms are generated by products of Eisenstein series. We extend a result from Kohnen and Martin (2008), that they showed for prime levels, to square-free levels but the method we use is a lot harder to apply in the case of non square-free levels. Working on this project I learned how to find Fourier-expansions at other cusps than infinity by using Atkin-Lehner operators, in the square-free case (see papers by Asai T. and Merel) and I also encountered some of the difficulties that arise in the non square-free case. - I think understanding more about q-expansions in the non square-free case might help me with extending the result that I obtained with M. Dickson to non square-free levels. Could you please send me some additional details on the project, concerning the implementation Hao Chen has in mind? Best regards, Michael Neururer -- You received this message because you are subscribed to the Google Groups "sage-gsoc" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-gsoc. For more options, visit https://groups.google.com/d/optout.
CV.pdf
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