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In this paper, we determine all modular forms of weights 36 ≤ k ≤ 56, 4 | k, for the full modular group SL 2 (Z) which behave like theta series, i.e., which have in their Fourier expansions, the constant term 1 and all other Fourier coefficients are non-negative rational integers. In fact, we give convex regions in R 3 (resp. in R 4 ) for the cases k = 36, 40 and 44 (resp. for the cases k = 48, 52 and 56). Corresponding to each lattice point in these regions, we get a modular form with thedoi:10.1090/s0025-5718-97-00872-7 fatcat:rcbkcrfbvva47eswjqz4o36siq