This expose represents an attempt to understand some of the recent work of Atkin, Swinnerton-Dyer, and Serre on the congruence properties of the q-expansion coefficients of modular forms from the point of view of the theory of moduli of elliptic curves, as developed abstractly by Igusa and recently reconsidered by Deligne. In this optic, a modular form of weight k and level n becomes a section of a certain line bundle Οββk on the modular variety Mn which βclassifiesβ elliptic curves with level n structure (the level n structure is introduced for purely technical reasons). The modular variety Mn is a smooth curve over β€[l/n], whose βphysical appearanceβ is the same whether we view it over β (where it becomes Ο(n) copies of the quotient of the upper half plane by the principal congruence subgroup Π(n) of SL(2,β€)) or over the algebraic closure of β€/pβ€, (by βreduction modulo pβ) for primes p not dividing n. This very fact rules out the possibility of obtaining p-adic properties of modular forms simply by studying the geometry of Mn ββ€/pβ€ and its line bundles Οββk ; we can only obtain the reductions modulo p of identical relations which hold over β.