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Assuming that $n$ is relatively prime to $D(Q)$, the determinant of the Gram matrix of $Q$, we show that $n$ is represented provided that \\[\n  n \\gg \\max \\{ N(Q)^{3/2 + \\epsilon} D(Q)^{5/4 + \\epsilon}, N(Q)^{2 + \\epsilon} D(Q)^{1 + \\epsilon} \\}. \\] Here $N(Q)$ is the level of $Q$. 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We study the problem of giving bounds on the largest positive integer $n$ that is locally represented by $Q$ but not represented. Assuming that $n$ is relatively prime to $D(Q)$, the determinant of the Gram matrix of $Q$, we show that $n$ is represented provided that \\[\n  n \\gg \\max \\{ N(Q)^{3/2 + \\epsilon} D(Q)^{5/4 + \\epsilon}, N(Q)^{2 + \\epsilon} D(Q)^{1 + \\epsilon} \\}. \\] Here $N(Q)$ is the level of $Q$. 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