Abstract. In this paper we extend a conjecture of Katsurada's characterizing the congruence primes of Saito-Kurokawa lifts of weight κ and full level in terms of the divisibility of L alg (κ, f ) to the case of odd square-free level. After stating the conjecture, we provide evidence for the conjecture by constructing a congruence.
We compute all degree 14 extensions of Q 7 up to isomorphism, and find that there are 654 such extensions. Additionally, we compute several invariants of these extensions in order to classify the associated Galois group of the Galois closure of each extension.
Abstract. In this article we construct Saito-Kurokawa lifts of mixed level. These are constructed via representation theoretic arguments originally used by Schmidt to construct congruence level and paramodular Saito-Kurokawa lifts.
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