The automation of a large number of software engineering tasks is becoming possible thanks to Machine Learning (ML). Central to applying ML to software artifacts (like source or executable code) is converting them into forms suitable for learning. Traditionally, researchers have relied on manually selected features, based on expert knowledge which is sometimes imprecise and generally incomplete. Representation learning has allowed ML to automatically choose suitable representations and relevant features. Yet, for Android-related tasks, existing models like apk2vec focus on whole-app levels, or target specific tasks like smali2vec, which limits their applicability. Our work is part of a new line of research that investigates effective, task-agnostic, and fine-grained universal representations of bytecode to mitigate both of these two limitations. Such representations aim to capture information relevant to various low-level downstream tasks (e.g., at the class-level). We are inspired by the field of Natural Language Processing, where the problem of universal representation was addressed by building Universal Language Models, such as BERT, whose goal is to capture abstract semantic information about sentences, in a way that is reusable for a variety of tasks. We propose DexBERT, a BERT-like Language Model dedicated to representing chunks of DEX bytecode, the main binary format used in Android applications. We empirically assess whether DexBERT is able to model the DEX language and evaluate the suitability of our model in three distinct class-level software engineering tasks: Malicious Code Localization, Defect Prediction, and Component Type Classification. We also experiment with strategies to deal with the problem of catering to apps having vastly different sizes, and we demonstrate one example of using our technique to investigate what information is relevant to a given task.