Computing ideals of a given norm in Quaternion algebra
Let B be the quaternion algebra over Q ramified at prime p and ∞ and O⊂B be a maximal order. How do you compute all integral right ideals I⊆O of a given norm?
Say l is prime. You know BrandtModule(p).hecke_matrix(l)
returns l-Brandt matrix of B and we can draw the l-Brandt graph from it, then O is a vertex and there are l+1 integral right O-ideals of norm l representing each of edge from O in general. I'd like to compute these l-neighbors of O.