The Bases of M4(Γ0(71)‎)‎, M6(Γ0(71)‎)‎ and the Number of Representation of Integers

Abstract EN

Following a fundamental theorem of Hecke, some bases of S4(Γ0(71)) and S6(Γ0(71)) are determined, and explicit formulas are obtained for the number of representations of positive integers by all possible direct sums (111 different combinations) of seven quadratic forms from the class group of equivalence classes of quadratic forms with discriminant −71 whose representatives are x12+x1x2+18x22, 2x12±x1x2+9x22, 3x12±x1x2+6x22, and 4x12±3x1x2+5x22.