For infinitely many supersingular primes, the exceptional p-adic constant in the coupling of mock modular forms with newforms is non-zero.
American Mathematical Society Colloquium Publications, 64
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Cusp forms as $p$-adic limits circumventing $p$-adic version of the Legendre period relation
For infinitely many supersingular primes, the exceptional p-adic constant in the coupling of mock modular forms with newforms is non-zero.