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It is proved that the theta series of an even lattice whose level is a powerof a prime $\ell$ is congruent modulo $\ell$ to an elliptic modular form oflevel~1. The proof uses arithmetic and algebraic properties of lattices ratherthan methods from the theory of modular forms. The methods presented here maytherefore be especially pleasing to those working in the theory of quadraticforms, and they admit generalizations to more general types of theta series asthey occur e.g. in the theory of Siegel or Hilbert modular forms.

Reduction mod $\ell$ of Theta Series of Level $\ell^n$