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?](https://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?



Examples of Maass forms with eigenvalue 1/4
One place you can look is the paper by [Booker and Strombergsson](http://www2.math.uu.se/~astrombe/papers/stfz14march06.pdf) which appeared in Crelle. Their aim is to verify the Selberg eigenvalue conjecture in a number of cases, and when there are Maass forms of eigenvalue $1/4$ these must be accounted for by finding corresponding Galois representations. See Section 5 of the paper for some explicit examples; of course there is a lot of other work on this, but the paper will give you more references. 


