  There are various reasons why a naive analog of the Maeda conjecture has to
fail for Drinfeld cusp forms. Focussing on double cusp forms and using the link
found by Teitelbaum between Drinfeld cusp forms and certain harmonic cochains,
we observed a while ago that all obvious counterexamples disappear for certain
Hecke-invariant subquotients of spaces of Drinfeld cusp forms of fixed weight,
which can be defined naturally via representation theory. The present work
extends Teitelbaum's isomorphism to an adelic setting and to arbitrary levels,
it makes precise the impact of representation theory, it relates certain
intertwining maps to hyperderivatives of Bosser-Pellarin, and it begins an
investigation into dimension formulas for the subquotients mentioned above. We
end with some numerical data for $A=\mathbb{F}_3[t]$ that displays a new
obstruction to an analog of a Maeda conjecture by discovering a conjecturally
infinite supply of $\mathbb{F}_3(t)$-rational eigenforms with combinatorially
given (conjectural) Hecke eigenvalues at the prime $t$.
