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We work out a non-trivial example of lifting a so-called weak eigenform to atrue, characteristic 0 eigenform. The weak eigenform is closely related toRamanujan's tau function whereas the characteristic 0 eigenform is attached toan elliptic curve defined over ${\mathbb Q}$. We produce the lift by showingthat the coefficients of the initial, weak eigenform (almost all) occur astraces of Frobenii in the Galois representation on the 4-torsion of theelliptic curve. The example is remarkable as the initial form is known not tobe liftable to any characteristic 0 eigenform of level 1. We use this exampleas illustrating certain questions that have arisen lately in the theory ofmodular forms modulo prime powers. We give a brief survey of those questions.

Dihedral Group, 4-Torsion on an Elliptic Curve, and a Peculiar Eigenform Modulo 4