Computing newforms using supersingular isogeny graphs

We describe an algorithm that we used to compute the q-expansions of all weight 2 cusp forms prime level at most $$2,\!000,\!000$$ and dimension 6. also present verify there was only one form 7 or more per Atkin-Lehner eigenspace for levels between $$10,\!000$$ $$1,\!000,\!000$$ . Our is based on Mestre’s Méthode des Graphes, involves supersingular isogeny graphs Wiedemann’s finding minimal polynomial sparse matrices over finite fields.