The interplay of nearly degenerate orders in quantum materials can lead to a myriad of emergent phases. A prominent case is that of the high-Tc cuprates for which the relationship between superconductivity and a short-ranged, incommensurate charge density wave in the CuO2 planes involving the dx2-y2 orbitals (Cu-CDW) is a subject of great current interest. Strong modifications of the strength and coherence of this Cu-CDW have been achieved by applying large magnetic fields, uniaxial pressure, or via the interfacial coupling in cuprate/manganite multilayers. However, such modifications do not alter the dominant orbital character. Here we investigate cuprate/manganite multilayers with resonant inelastic X-ray scattering (RIXS) and show that a new kind of Cu-based density wave order can be induced that has not been previously observed in the cuprates. This order has an unusually small wave vector of Q = 0.096 reciprocal lattice units (r.l.u.), a large correlation length of about 40 nm, and a predominant dz2 orbital character, instead of the typical dx2-y2 character. Its appearance is determined by the hole doping of the manganite which is a key parameter controlling the interfacial charge transfer and orbital reconstruction. We anticipate that the observation of a previously unknown type of density wave order at the YBCO interface will allow for fresh perspectives on the enigmatic relation between superconductivity and charge order (CO) in the cuprates.