One goal of mathematics education is to adapt features of digital learning materials to students' characteristics. This paper presents a multi-layered research approach to identify key aspects of mathematics students within the persona approach. Data for this research was collected from 5,624 mathematics students using an instrument focusing on 15 scales addressing psychological constructs. The data was analysed using factor analysis. The results of our study show that mathematical self-confidence, aspiration towards mathematics, performance orientation, intra- and interpersonal aspects of learning mathematics, and actions and reactions are the most pronounced persona dimensions of mathematics students. The dimensions of student personas identified in this research -- specifically aspiration towards mathematics, and intra- and interpersonal aspects of learning mathematics -- are the most critical novelty brought by this study.