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  2. MAMA/137 MAT3 MATHEMATICAL TRIPOS Part III Thursday 30 May ...

    https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2024/Paper_137.pdf
    27 Jun 2024: E2(τ) = 1 24. n=1. σ(n)qn,. where q = e2πiτ and σ(n) =. d|n d. Using the formula τ2E2(1/τ) = E2(τ) 6πiτ , prove. ... the formula. = q. n=1. (1 qn)24,. where S12(Γ(1)) is the unique cuspidal modular form of weight 12 satisfying = q O(q2) as q 0.

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