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We compute the mod homology of the spectrum of topological modular forms by proving a 2-local equivalence , where is an eight cell complex whose cohomology "doubles" the subalgebra of the Steenrod algebra generated by and . To do so, we give, using the language of stacks, a modular description of the elliptic homology of via level three structures. We briefly discuss analogs at odd primes and recover the stack-theoretic description of the Adams-Novikov spectral sequence for .