It is known that there exists a simple formula of the dimension of space of (holomorphic) modular forms on $\mathrm{SL}_{2}(\mathbb{Z})$ in terms of its weight. Also, we have similar but rather complicated formula for the case of congruence subgroups. (I heard that there is an algorithm that computes these dimensions, right?)
However, we don't know much about dimension of Maass forms. As I know, it is widely conjectured that dimension of the space of Maass cusp forms on $\mathrm{SL}_{2}(\mathbb{Z})$ with given eigenvalue is 0 or 1. Also, as we can see in this post and answers, it seems that there are some known upper bounds of dimension of level $q$ Maass wave forms in terms of $q$. Is there any concrete example that computes the exact value of dimensions?