Harder's conjecture for Picard modular forms

Let $m$ and $n$ be in the critical range for the algebraic Hecke character $\psi_m$, and define

$$Q(m,n)=\frac{\Lambda(\psi_m,n-1)}{\Lambda(\psi_m,n)}.$$

Suppose a prime $\ell>m$ divides the denominator of $Q(m,n)$. Harder's conjecture. There should exist a Picard modular cusp-form Hecke eigenform of weight

$$(b,a+3)=(m-n,2n-m+1)$$

whose Hecke eigenvalues $\lambda_{\nu_p}$, for primes $p\equiv_3 1$, satisfy

$$\lambda_{\nu_p}\equiv_\ell \bar{\nu}_p^{a+b+2}+(p^{a+1}+1)\nu_p^{b+1}.$$

This predicts congruences between Picard modular forms and critical-value denominators in the spirit of Harder's conjectures.