An Improved Lower Bound on the Image of the 2-adic Character Map for the Heisenberg Algebra via Modular Linear Differential Equations

Daniel Barake, Cameron Franc

We describe families of MLDEs whose solutions are modular forms of level one that converge, $2$-adically, to a Hauptmodul on ${\Gamma }_0(2)$ by using a theorem of Serre. Then, we apply th…