Number Theory Seminar
in Northeast Seoul

Dimensions of spaces of modular forms

  Min Lee  (University of Bristol)

June 5 (Fri)  2026, 11:30 ~ 12:00  (Asan science building 525)

Asan science building 525

Abstract:   Martin conjectured that every non-negative integer can be expressed as the dimension of the space of newforms of weight 2 and level N for some positive integer N. Recently, Ross disproved this conjecture by showing that 67846 is not attained in this way, and proposed a counter-conjecture that the set of such dimensions has density zero among the non-negative integers. We prove a general form of Ross’ conjecture. This is joint work with Andrew R. Booker.