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Replication Descent and $J$-Finality of Replicable Functions
We show that replication carries congruence symmetry down an explicit level tower. If a normalized replicable function $f$, holomorphic on the upper half-plane, is invariant under $Γ_0(N)$, then its $n$th replicate is invariant under $Γ_0(N/(N,n))$. Thus every replicate whose index is divisible by $
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