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In this paper we construct an explicit interpolation formula for Schwartz functions on the real line. The formula expresses the value of a function at any given point in terms of the values of the function and its Fourier transform on the set {0,+/- 1,+/- 2,+/- 3The functions in the interpolating basis are constructed in a closed form as an integral transform of weakly holomorphic modular forms for the theta subgroup of the modular group.