论文标题
使用超级同学图表计算新形式
Computing newforms using supersingular isogeny graphs
论文作者
论文摘要
我们描述了一种算法，我们用来计算所有权重的Q扩展2最多2,000,000的质量水平的Q-Expansions，最多最多为6。我们还提出了一种算法，我们用来验证一种cusp形式的尺寸7或更多的dimension 7或更多，每个Atkin-Lehner eigenspace pripe prips prips for 10,000和1,000,000之间。我们的算法基于Mestre的Méthodedes图，涉及超级同学图和Wiedemann的算法，用于查找有限磁场上稀疏矩阵的最小多项式。
We describe an algorithm that we used to compute the q-expansions of all weight 2 cusp forms of prime level at most 2,000,000 and dimension at most 6. We also present an algorithm that we used to verify that there was only one cusp form of dimension 7 or more per Atkin-Lehner eigenspace for prime levels between 10,000 and 1,000,000. Our algorithm is based on Mestre's Méthode des Graphes, and involves supersingular isogeny graphs and Wiedemann's algorithm for finding the minimal polynomial of sparse matrices over finite fields.
