# Epilogue

# Epilogue

This epilogue describes some work on generalizations and applications, as well as a direction of further research outside the context of modular forms. Theorems 14.1.1 and 15.2.1 will certainly be generalized to spaces of cusp forms of arbitrarily varying level and weight. This has already been done for the probabilistic variant of Theorem 14.1.1, in the case of square-free levels (and of level two times a square-free number). Some details and some applications of Bruin's work, as well as a perspective on point counting outside the context of modular forms are described. Deterministic generalizations of the two theorems mentioned above will lead to deterministic applications.

*Keywords:*
modular forms, cusp forms, square-free levels, Peter Bruin

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