On Some Entire Modular Forms of Weights and for the Congruence Group Γ0(4N)

Entire modular forms of weights and for the congruence group Γ0(4N) are constructed, which will be useful for revealing the arithmetical sense of additional terms in formulas for the number of representations of positive integers by quadratic forms in 7 and 9 variables.

Construction of Entire Modular Forms of Weights 5 and 6 for the Congruence Group Γ0(4N)

Two classes of entire modular forms of weight 5 and two of weight 6 are constructed for the congruence subgroup Γ0(4N). The constructed modular forms as well as the modular forms from [Lomadze, Georgian Math. J. 1: 53-76, 1994] will be helpful in the theory of representation of numbers by the quadratic forms in 10 and 12 variables.