Let t∈N be squarefree and St:=(0110)⊥(0110)⊥(−2t). We consider Mt(m):={M∈Z5×5;MtrStM=m2St}, Γt:=Mt(1) and Mt:=⋃m∈NMt(m). The Hecke algebra H:=H(Γt,Mt) is the tensor product of its p-primary components Hp:=H(Γt,⋃k∈N0Mt(pk)). These p-primary components are polynomial rings over Z in Γtdiag(1,1,p,p2,p2)Γt,Γtdiag(1,p,p,p,p2)Γt and Γtdiag(p,p,p,p,p)Γt, which are algebraically independent.It is well known that the orthogonal group is isomorphic to the maximal discrete extension Σt of the paramodular group of degree two and level t. We transfer this result to the Hecke algebra H for Σt.Furthermore, Σt is isomorphic to the discriminant kernel of Γt. The corresponding Hecke algebra is not commutative if t>1.More generally, we consider the orthogonal group O(2,n+2), n∈N, and describe a fundamental set of its operation on the upper half space. For S Euclidian, i.e. such S which admit a kind of Euclidian algorithm, we descibe a system of representatives for the right and double cosets of the similarity matrices. We can calculate the number of classes if det(S)=1.The last chapter deals with applications on modular forms and Hecke algebras in the case that S is Euclidian. We transfer known boundaries for cusp forms. The Eisenstein series are simultaneous Hecke eigenforms. If det(S)=1, in particular for the E8 lattice, we provide a commutation theorem for the orthogonal Φ-operator and the T(p)-operator. As a result, we show that all Hecke eigenforms of the T(p)-operator with non-vanishing zeroth Fourier coefficient are already multiples of Eisenstein series. We complete the thesis with the result that in this case the T(p)-operators are self-adjoint