Spectral multiplicity conjecture for Maaß newforms

Let $q$ be an odd positive integer, and let $s(q)$ denote the number of distinct odd primes $p$ for which $p^2$ divides $q$. Consider the new part of the discrete spectrum of the Laplacian on $\Gamma_0(q)\backslash\mathbb{H}$. Spectral multiplicity conjecture. The multiplicity of an eigenvalue $\lambda>1/4$ is bounded above by $2^{s(q)}$, and this bound is attained for a positive proportion of eigenvalues. The conjecture proposes an upper bound complementary to the paper's lower bounds, attributing multiplicity to quadratic twisting; the source gives no resolution.