Abstract In this article, for n ā„ 2 {n\geq 2} , we compute asymptotic, qualitative, and quantitative estimates of the Bergman kernel of Picard modular cusp forms associated to torsion-free, cocompact subgroups of SU ā¢ ( ( n , 1 ) , ā ) {\mathrm{SU}((n,1),\mathbb{C})} . The main result of the article is the following result. Let Ī ā SU ā¢ ( ( 2 , 1 ) , šŖ K ) {\Gamma\subset\mathrm{SU}((2,1),\mathcal{O}_{K})} be a torsion-free subgroup of finite index, where K is a totally imaginary field. Let ā¬ Ī k {{{\mathcal{B}_{\Gamma}^{k}}}} denote the Bergman kernel associated to the š® k ā¢ ( Ī ) {\mathcal{S}_{k}(\Gamma)} , complex vector space of weight-k cusp forms with respect to Ī. Let š¹ 2 {\mathbb{B}^{2}} denote the 2-dimensional complex ball endowed with the hyperbolic metric, and let X Ī := Ī \ š¹ 2 {X_{\Gamma}:=\Gamma\backslash\mathbb{B}^{2}} denote the quotient space, which is a noncompact complex manifold of dimension 2. Let | ā
| pet {|\cdot|_{\mathrm{pet}}} denote the point-wise Petersson norm on š® k ā¢ ( Ī ) {\mathcal{S}_{k}(\Gamma)} . Then, for k ā« 1 {k\gg 1} , we have the following estimate: sup z ā X Ī ā” | ā¬ Ī k ā¢ ( z ) | pet = O Ī ā¢ ( k 5 2 ) , \sup_{z\in X_{\Gamma}}|{{\mathcal{B}_{\Gamma}^{k}}}(z)|_{\mathrm{pet}}=O_{% \Gamma}(k^{\frac{5}{2}}), where the implied constant depends only on Ī.