Formula for $q$-expansion of weight 2 modular forms

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Is there a general formula for finding the $q$-expansion of weight 2 modular forms?

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The problem is too deep and important to have a simple, tidy solution! About the best one can get is the approach described in Loic Merel's article "Universal Fourier expansions of modular forms".

EDIT: if you want tables for a specific weight and level, the LMFDB (L-functions and Modular Forms Database) is the place to go.