Computations of Algebraic Modular Forms Associated with the Definite Quaternion Algebra of Discriminant 2

In this paper, we present an algorithm to compute a basis of the space ofalgebraic modular forms on the maximal order of the definite quaternion algebraof discriminant 2, and provide a database of such bases. One of ourmotivations is to study congruence relations of algebraic modular forms.