Counting Modular Forms by Rationality Field
Abstract
We investigate the distribution of degrees and rationality fields of weight 2 newforms. In particular, we give heuristic upper bounds on how often degree d rationality fields occur for squarefree levels, and predict finiteness if d≥7. When d=2, we make predictions about how frequently specific quadratic fields occur, prove lower bounds, and conjecture that Q(5) is the most common quadratic rationality field.
Fields of Study & Subjects
Advanced Algebra and Geometry
Analytic Number Theory Research
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Experimental Mathematics
- Pages
- 1–15
- Publication date
- 11 January 2026
- Language
- EN