### A combinatorial interpretation of Serre's conjecture on modular Galois representations

We state a conjecture concerning modular absolutely irreducible odd 2-dimensional representations of the absolute Galois group over finite fields which is purely combinatorial (without using modular forms) and proof that it is equivalent to Serre’s strong conjecture. The main idea is to replace modular forms with coefficients in a finite field of characteristic $p$, by their counterparts in the theory of modular symbols.