Abstract
In this paper using the (p,k)- parametrization of theta functions and Eisenstein Series, developed by Alaca, Alaca and Williams, we obtain some new theta function identities and then use them to derive explicit formulae for the number of representations of a positive integer n by certain quadratic forms
Sigma(6)(k=1) a(k)(x(2k-1)(2) + x(2k-1)x(2k) + x(2k)(2)
in twelve variables where a(k) epsilon {1,2,4}.