Abstract
AbstractWe describe an algorithm for computing a $${\mathbb {Q}}$$
Q
-rational model for the quotient of a modular curve by an automorphism group, under mild assumptions on the curve and the automorphisms, by determining q-expansions for a basis of the corresponding space of cusp forms. We also give a moduli interpretation for general morphisms between modular curves.
Funder
Engineering and Physical Sciences Research Council
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
Reference27 articles.
1. Assaf, E.: Computing classical modular forms for arbitrary congruence subgroups. arXiv:2002.07212v1 (2020)
2. Atkin, A.O.L., Ching Winnie Li, W.: Twists of newforms and pseudo-eigenvalues of $$W$$-operators. Invent. Math. 48(3), 221–243 (1978)
3. Atkin, A.O.L., Lehner, J.: Hecke operators on $$\Gamma _{0}(m)$$. Math. Ann. 185, 134–160 (1970)
4. Banwait, B. S., Cremona, J. E.: Computing the modular curves$${X}_s(13)$$, $${X}_{ns}(13)$$and$${X}_{A_4}(13)$$using modular symbols in Sage (annotated Sage code), ancillary file to arXiv:1306.6818, see also https://github.com/JohnCremona/X13/blob/main/X13.ipynb
5. Baran, B.: Normalizers of non-split Cartan subgroups, modular curves, and the class number one problem. J. Number Theory 130(12), 2753–2772 (2010)
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献