Non-ordinary primes and congruences for weakly holomorphic modular forms of level 2

2026/07/16 by Vladimir Nechaev
#math.NT

paper · pdf

Abstract

In this paper, we investigate the arithmetic properties of the Fourier coefficients of weakly holomorphic modular forms of weight k for the congruence subgroup Γ₀(2), which have poles exclusively at the cusp ∞. Using the structure of canonical bases and the explicit duality between the coefficients of spaces of weakly holomorphic modular forms, which have a pole only at ∞, we prove a general family of congruences modulo primes p ≥ 5 and derive several corollaries as examples of the theorem's application.

Related

• Congruences for coefficients of modular functions
• Weakly holomorphic modular forms in prime power levels of genus zero
• Non-zero coefficients of half-integral weight modular forms mod ℓ
• A Note on Congruences for Weakly Holomorphic Modular Forms
• Rationality and p-adic properties of reduced forms of half-integral\n weight