Elliptic cohomology of classifying spaces of cyclic groups and higher level modular forms (Q1290991)

Let \(p\) be an odd prime. This paper shows that the elliptic cohomology \(E\ell\ell^*(BZ/p^n)\) of \(BZ/p^n\) can be described by level \(2p^m\) modular forms for \(0\leq m\leq n\) after suitable completion. Specifically, the authors describe \(K^*\otimes_{E\ell\ell}(E\ell\ell^*(BZ/p^n)[\zeta_{p^n}])_M^\wedge\), where \(\zeta_{p^n}\) is a primitive \(p^n\)-th root of unity, \(M\) is an arbitrary maximal graded ideal of \(E\ell\ell_*\) containing \((p,v_1)\), and \(K^*\) is the quotient field of \(E\ell\ell_*\). The key point is the description of the \(p^n\)-series of the formal group law in terms of higher level modular forms.