We investigated the low-temperature and high-field thermodynamic and ultrasonic properties of SrCu_{2}(BO_{3})_{2}, which exhibits various plateaux in its magnetization curve above 27 T, called a magnetic Devil's staircase. The results of the present study confirm that magnetic crystallization, the first step of the staircase, occurs above 27 T as a first-order transition accompanied by a sharp singularity in heat capacity C_{p} and a kink in the elastic constant. In addition, we observe a thermodynamic anomaly at lower fields around 26 T, which has not been previously detected by any magnetic probes. At low temperatures, this magnetically hidden state has a large entropy and does not exhibit Schottky-type gapped behavior, which suggests the existence of low-energy collective excitations. Based on our observations and theoretical predictions, we propose that magnetic quadrupoles form a spin-nematic state around 26 T as a hidden state on the ground floor of the magnetic Devil's staircase.