the exceptional group $e_{7,3}$ has a symmetric space with hermitian tube structure. on it, henry kim wrote down low weight holomorphic modular forms that are ``singular'' in the sense that their fourier expansion has many terms equal to zero. the symmetric space associated to the exceptional group $e_{8,4}$ does not have a hermitian structure, but it has what might be the next best thing: a quaternionic structure and associated ``modular forms''. i will explain the construction of singular modular forms on $e_{8,4}$, and the proof that these special modular forms have rational fourier expansions, in a precise sense. this builds off of work of wee teck gan and uses key input from gordan savin.