2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131497We determine the abelianization of the symmetric mapping class group of a double unbranched cover using the Riemann theta constant, Schottky theta constant, and the theta multiplier. We also give lower bounds of the abelianizations of some finite index subgroups of the mapping class group.23 pages, 5 figuresGeometric Topology55R40; 32G15; 14H37; 14H40text