The Basis Problem for Modular Forms on $\Gamma _0(N)$

The Basis Problem for Modular Forms on $\Gamma _0(N)$

by Hiroaki Hijikata, Arnold K. Pizer, Thomas R. Shemanske

159 pages· ISBN 9780821824818
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The "basis problem'' for modular forms (of degree one) is to find a basis for a space of modular forms with elements whose Fourier coefficients can be computed explicitly. The authors give a general treatment for all cases. The main idea in the solution is to consider two kinds of forms: theta series associated with special order, and bases of primitive neben space.

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