Rigorous expansions of modular forms at CM points, I: Denominators

Kavli Affiliate: Chris Xu

| First 5 Authors: Chris Xu, , , ,

| Summary:

We describe an algorithm to rigorously compute the power series expansion at
a CM point of a weight $2$ cusp form of level coprime to $6$. Our algorithm
works by bounding the denominators that appear due to ramification, and without
recourse to computing an explicit model of the corresponding modular curve. Our
result is the first in a series of papers toward an eventual implementation of
equationless Chabauty.

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