Let Sp(2) denote the split symplectic group of rank 2 over Q. Fix a prime p. Let Kp be a parahoric subgroup of Sp(2,Qp). An arithmetic subgroup Γ is defined by Γ=Sp(2,Q)∩(Sp(2,R)K0), where K0=Kp∏v<∞,v≠pSp(2,Zv). In this paper, we calculate Arthurʼs L2-Lefschetz trace formula for Sp(2) in order to obtain an explicit formula for multiplicities of discrete series and some non-tempered unitary representations in the discrete spectrum of L2(Γ\Sp(2,R)) for each such Γ. From them we derive explicit multiplicity formulas for large discrete series, which are our main results. The multiplicity formulas are applied to a study on numbers of cuspidal automorphic representations of PGSp(2).