Let L be a totally real number field. Thanks to the work of P. Deligne and K. Ribet, the values zeta_L(1-k) for integers k \geq 2 can be realized as the leading coefficients of the q-expansion of suitable Hilbert modular forms defined over Q, called Eisenstein series. We exploit this to study the p-adic valuation of zeta_L(1-k) and various congruence properties for primes p which ramifies in L. This is joint work with E. Goren.