| A recent development in Algebraic Number Theory is Khare and Khare---Winterberger proof of Serre's Modularity Conjecture on two---dimensional mod p representations of Gal(Q¯/Q). Using the link between mod p modular forms and mod p Galois representations that this important theorem provides, we formulate a conjectural mass formula for the asymptotics with p of the number of two---dimensional, odd, irreducible mod p Galois representations of Q, of fixed conductor N. |
