Linear independence of periods for the symmetric square L-functions

For Sₖ, the space of cusp forms of weight k for the full modular group, we first introduce periods on Sₖ associated to symmetric square L-functions. We then prove that for a fixed natural number n, if k is sufficiently large relative to n, then any n such periods are linearly independent. With some extra assumption, we also prove that for k≥ e¹², we can always pick up to log k/4 arbitrary linearly independent periods.