Let p r (n) denote the number of r-component multipartitions of n, and let S γ,λ be the space spanned by η(24z) γ φ(24z), where η(z) is the Dedekind's eta function and φ(z) is a holomorphic modular form in M λ (SL 2 (Z)). In this paper, we show that the generating function of p r ( m k n+r 24 ) with respect to n is congruent to a function in the space S γ,λ modulo m k . As special cases, this relation leads to many well known congruences including the Ramanujan congruences of p(n) modulo 5, 7, 11 and Gandhi's congruences of p 2 (n) modulo 5 and p 8 (n) modulo 11. Furthermore, using the invariance property of S γ,λ under the Hecke operator T ℓ 2 , we obtain two classes of congruences pertaining to the m k -adic property of p r (n).