  We study a class of meromorphic modular forms characterised by Fourier
coefficients that satisfy certain divisibility properties. We present new
candidates for these so-called magnetic modular forms, and we conjecture
properties that these functions should obey. In particular, we conjecture that
magnetic modular forms are closed under the standard operators acting on spaces
of modular forms (SL$_2(\mathbb{Z})$ action, Hecke and Atkin-Lehner operators),
and that they are characterised by algebraic residues and vanishing period
polynomials. We use our conjectures to construct examples of real-analytic
modular forms with poles.
