The space M4(Γ0 (100; (5=:)) and Representation Numbers of Some Octonary Quadratic Forms

The determination of the number of representations of a positive integer by certain octonary quadratic forms are given in the literature. For instance, the formulas N(12a, 22b, 32c, 62d; n) for the nine octonary quadratic forms are given with a = 1, b = 2, c = 3 and d = 6. Moreover, the formulas for N(1a, 3b, 9c; n) for several octonary quadratic forms have been given by Alaca. Here, by using MAGMA, we determine the formulas, for N(1a, 5b, 25c; n) by Eisenstein series and eta quotients for several octonary quadratic forms whose theta functions are in M4 (Γ0 (100) , χ) .