  We consider the value distribution of logarithms of symmetric power
L-functions associated with newforms of even weight and prime power level. In
the symmetric square case, under certain plausible analytical conditions, we
prove that certain averages of those values in the level aspect, involving
continuous bounded or Riemann integrable test functions, can be written as
integrals involving a density function (the "M-function") which is related with
the Sato-Tate measure. Moreover, even in the case of general symmetric power
L-functions, we show the same type of formula when for some special type of
test functions. We see that a kind of parity phenomenon of the density function
exists.
