Computing classical modular forms

Abstract

We discuss practical and some theoretical aspects of computing a database of classical modular forms in the L-functions and Modular Forms Database (LMFDB).

arXiv comment63 pages; minor edits, including a correction to Conjecture 8.5.1

References in corpus (9)

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• Class invariants by the CRT method
• Accelerating the CM method
• Tetrahedral Elliptic Curves and the local-global principle for Isogenies
• Root numbers and the parity problem
• The L-functions and modular forms database project
• Twist-minimal trace formulas and the Selberg eigenvalue conjecture
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Cited by in corpus (4)

• $\ell$-adic images of Galois for elliptic curves over $\mathbb{Q}$
• Rational torsion points on abelian surfaces with quaternionic multiplication
• On smooth plane models for modular curves of Shimura type
• Towards Flying through Modular Forms