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Abstract. In this paper, we consider stripping primes from the level of degree 2 cuspidal Siegel eigenforms. Specifically, given an eigenform of level N r under certain restrictions, where N is a prime, we construct an eigenform of level N , which is congruent in eigenvalues to our original form. To obtain our results, we use constructions of Eisenstein series and theta functions to adapt ideas from a level stripping result on elliptic modular forms.

It is known that all modular forms on SL 2 (Z) can be expressed as a rational function in η(z), η(2z) and η(4z). By using a theorem found in [Ono04], and calculating the order of vanishing, we can compute the eta-quotients for a given level. Using this count, knowing how many eta-quotients are linearly independent and using the dimension formula, we can figure out a subspace spanned by the eta-quotients. In this paper, we primarily focus on the case where N = p a prime.

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