A computable wandering and tracelike vector for modular orbits in the Bergman space

We construct a function $Φ$ such that the orbit under the representation of PSL(2,Z) is an orthonormal basis for the Bergman space with weight $α=12$. Moreover, we show that $Φ$ is effectively computable as a holomorphic function on the upper half-plane (in the precise sense of computable analysis),