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In the presence of crystalline symmetries, certain topological insulators present a filling anomaly: a mismatch between the number of electrons in an energy band and the number of electrons required for charge neutrality. In this paper, we show that a filling anomaly can arise when corners are introduced in C n-symmetric crystalline insulators with vanishing polarization, having as a consequence the existence of corner-localized charges quantized in multiples of e n. We characterize the existence of this charge systematically and build topological indices that relate the symmetry representations of the occupied energy bands of a crystal to the quanta of fractional charge robustly localized at its corners. When an additional chiral symmetry is present, e 2 corner charges are accompanied by zero-energy corner-localized states. We show the application of our indices in a number of atomic and fragile topological …