Let G be a simply-connected semisimple algebraic group over an algebraically closed field K of characteristic p>0. Letπbe an automorphism of G coming from that of the Dynkin diagram of G, and Fn the n-th Frobenius morphism of G. We denote by Gπ(n) the finite group consisting of fixed points underπ·Fn in G, which is called a finite group of Lie type. In the present paper, we shall show how to determine the first Cartan invariant C(n)00 of Gπ(n), i.e. the multiplicity of the trivial module in its projective cover. The method used here is due to Jantzen's lectures at ECNU in 1984(cf.[J2]). As an example, we calculate this value for G being of type C2 and p=7, i.e. C(n)00 for Sp(4, 7n). When p>7, C(n)00 for Sp(4, pn) has been determined in[Ye4]. We shall use the notations mentioned in Jantzen's book[J4]unless otherwise indicated.