Unexpected primes of good reduction in quotients of modular and Shimura curves

For the Shimura curves $X_0^D(N)$ the primes of bad reduction are those dividing DN. One would expect that the quotients by Atkin—Lehner involutions would inherit these primes of bad reduction, but this is not always the case. In this talk, I explain how we classify the unexpected primes of good reduction of Atkin–Lehner quotients of modular and Shimura curves of squarefree levels. This is joint work with Sun Woo Park and John Voight.