2024-11-012024-11-012011-01-010129-2021https://hdl.handle.net/11452/47318In this work we consider the representations of positive integers by quadratic forms F-1 = x(1)(2) + x(1)x(2) + 8x(2)(2) and G(1) = 2x(1)(2) + x(1)x(2) + 4x(2)(2) of discriminant 31 and we obtain some results concerning the modular forms (sci) (T; F, phi(tau s)). Moreover we construct a basis for the cusp form space S-4 (Gamma(0) (31), 1), and then we give some formulas for the number of representations of positive integer n by positive definite quadratic forms.eninfo:eu-repo/semantics/closedAccessRepresentations of positive integers by positive definite quadratic formsGeneralized theta seriesEisenstein seriesCusp formScience & technologyPhysical sciencesMathematicsArticle000217094900011137148351