The specific connection between the Hecke operator and the t'Hooft Operator

Question

As I was reading some articles concern about the Selberg trace formula and its general form, I have noticed that the Selberg trace formula and its general form can be understand as the energy spectrum and its distribution in quantum physical system on the Riemannian surface. For example, the Selberg trace formula can be proved by using the energy spectrum distribution of free particles moving in the Poincare upper half plane, and Maass-Selberg trace formula can be proved by using the energy spectrum distribution of particles moving on a Riemann surface with magnetic flow. As I get deeper and deeper into this relating subjects, I discovered that Hecke operator can be used to study the trace formula of automorphic forms because the result of Hecke operator operating on a automorphic is still a automorphic form, So i was wondering if the Hecke operator has its physical understanding. Later when I was looking for information to this problem, I found that "Hecke operator"can be derived from the t'Hooft operator in Physics. However,when I consulted related materials to further understanding this problem ,I found that the Hecke operator related to t'Hooft operator was not the Hecke operator used in the research of automorphic forms.Now,here comes my questions: 1.Does the "Hecke Operator"that can be derived from "t'Hooft Operator" the same as the one used in research of automorphic forms? 2.If the two"Hecke Operator" are the same, then is there any materials that explains in detail the relationship between this two operator? 3.If the two"Hecke Operator"are not the same, then is there any physical understanding of the Hecke operator that is used in the research of automorphic forms? 4. I've come to noticed that the Selberg zeta function along with other zeta function that is defined on the Riemann surfaces can be expressed in the product of the characteristic polynomial of the holonomy, and the t'Hooft operator is a operator defined on the holonomy.So is there connection between this two things? If so, is there any materials can explain this relationship in details.