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Furusawa has given an integral representation for the degree 8 L-function ofGSp(4) x GL(2) and has carried out the unramified calculation. The local p-adiczeta integrals were calculated in our earlier work under the assumption thatthe GSp(4) representation \pi is unramified and the GL(2) representation \tauhas conductor p. In the present work we generalize to the case where the GL(2)representation has arbitrarily high conductor. The result is that the zetaintegral represents the local Euler factor L(s,\pi \times \tau) in all cases.As a global application we obtain a special value result for a GSp(4) x GL(2)global L-function coming from classical holomorphic cusp forms with arbitrarilyhigh level for the elliptic modular form.

L-functions for GSp(4)xGL(2)in the case of high GL(2) conductor