Paramodular forms of level 8 and weights 10 and 12

We study degree 2 paramodular eigenforms of level 8 and weights 10 and 12, and determine all their local representations. We prove dimensions by the technique of Jacobi restriction. A level divisible by a cube permits a wide variety of local representations, but also complicates the Hecke theory by involving Fourier expansions at more than one zero-dimensional cusp. We overcome this difficulty by the technique of restriction to modular curves. An application of our determination of the local representations is that we obtain the Euler 2-factor of each newform.