  Coleman integrals is a major tool in the explicit arithmetic of algebraic
varieties, notably in the study of rational points on curves. One of the inputs
to compute Coleman integrals is the availability of an affine model. We develop
a model-free algorithm that computes single Coleman integrals between any two
points on modular curves. Using Hecke operators, any Coleman integral can be
broken down into a sum of tiny integrals. We illustrate this using several
examples computed in SageMath and Magma. We also suggest some future directions
for this work, including a possible extension to iterated Coleman integrals.
