For what I have heard, Maass forms of (Laplacian) eigenvalue $1/4$ on modular surfaces are somewhat special. But I don't know where to look for explicit examples. (In fact, one form came here on MO http://mathoverflow.net/questions/22908/does-anyone-want-a-pretty-maass-form, but I am not sure I can figure out what it is from the description.)
So, can anyone help me with references?