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AbstractWe presentp-adic algorithms for computing Hecke polynomials and Hecke eigenforms associated to spaces of classical modular forms, using the theory of overconvergent modular forms. The algorithms have a running time which grows linearly with the logarithm of the weight and are well suited to investigating the dimension variation of certainp-adically defined spaces of classical modular forms.doi:10.1112/s1461157011000155 fatcat:dh5dqplwwbgf7pfgv65aa4howy