I am studying the book "Harmonic maass forms and mock modular forms theory and applications"
In section 7.5, they deal with p-adic harmonic maass functions.
At first, they define the space $M_k(\Gamma_0(N);K)$
This is the space of weight k holomorphic and weakly holomorphic modular forms defined on the modular curve $Y_0(N)(K)$ over the field K.
I have difficulty understanding this definition.
What is $Y_0(N)(K)$? (I only know the basic stuffs for modular curve)
What is modular forms on this modular curve? (I'm familar with the classical modular forms)
Is there any reference to understand this definition?
Do I need to know the language of schemes?