The electron cooling project for RHIC luminosity upgrade and future projects such as eRHIC (electron-ion collider) demand cavities operating at high average current and high bunch charge in CW energy recovery mode. This paper describes the investigation of Higher Order Modes (HOMs) in such a cavity. This work is part of an ongoing effort to develop a 5-cell superconducting cavity for such high current and high bunch charge energy-recovery superconducting linac. The frequency of the cavity is 703.75 MHz with an iris of 17cm and two ferrite absorbers for HOM damping. The main focus of this paper is to identify and investigate possible trapped HOM modes that might result in multibunch instabilities. Detailed MAFIA calculations were performed using the e-module for different end cell geometries. Results from these calculations will be presented. Beam breakup results using TDBBU due to dipole HOM's will also be presented. A beam breakup threshold of above 1.8 A was calculated.