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 Does anyone want a pretty Maass form?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?