For many emerging data-centric computing applications, it is a key capability to efficiently store, manage, and access multidimensional data. To achieve this, many multidimensional index data structures have been proposed. However, when existing multidimensional index data structures are maintained on modern nonvolatile memories (NVMs), such as NAND flash memory, they often face challenges in effective management of multidimensional data and handling of memory medium peculiarities, such as the write-once property and the need for block reclamation of NAND flash memory. Without appropriate management, these challenges often result in serious amplification of the read/write traffic, which degrades the performance of multidimensional data structures. Motivated by the urgent needs of efficient multidimensional index data structures on modern NVMs, we propose the FIRM-tree, a time-efficient and space-economic index data structure for multidimensional point data on NAND flash memory. Unique to the prior work, the FIRM-tree holistically utilizes RAM and flash memory space, and dedicatedly leverages the page reprogrammability of modern NAND flash memory, to enhance data access performance and flash management overheads. We then verify our proposal through analytical and experimental studies, where the results are quite encouraging.