Application of symbolic manipulation to Hecke transformations of modular forms in two variables

Cohn, Harvey; Deutsch, Jesse

doi:10.1090/S0025-5718-1987-0866104-6

Application of symbolic manipulation to Hecke transformations of modular forms in two variables
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by Harvey Cohn and Jesse Deutsch PDF

Math. Comp. 48 (1987), 139-146 Request permission

Abstract:

The Hecke transformation of modular forms in several variables generates nonsymmetric modular forms out of symmetric forms. This is useful since symmetric forms arise out of Eisenstein series and are easy to construct, while nonsymmetric forms are much harder to construct. A symbolic manipulation system is required because of the magnitude of the Fourier expansions. This process is carried out for Hilbert modular functions over $\mathbb {Q}(\sqrt 2 )$.

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