Lucas congruences using modular forms

In this work, we prove that a sequence arising from modular forms under some prescribed conditions for Γ that is Γ₀(N) or an Atkin--Lehner extension of Γ₀(N) must satisfy the Lucas congruences modulo any prime. As an implication, we completely affirm all the conjectural Lucas congruences that were recently posed by Cooper and reinterpret a number of known results.