The determination of small dimensions of the Hilbert Modular Type Cusp forms of Weight Two over Real Quadratic Fields

The author has proved the dimension formula of the space of the Hilbert modular type cusp forms of weight two. We present further refinements of the dimension formula for a real quadratic number field Q(√D), and calculate it effectively. We tabulate the dimensions for square-free natural numbers D below 104 with the computer assistance. We also determine all the spaces of their dimension below 10.