This is FM, nothing is that simple!
The carrier amplitude is not a simple function of the modulation index (m), it varies as a Bessel function.
At certain values of m the carrier disappears, the so called Bessel nulls, just past these nulls the carrier increases to some value before again decreasing to zero at the next null. The values of m for the first 3 nulls are 2.405, 5.520 & 8.654.
Incidentally this provides an accurate method of calibrating deviation if you have a spectrum analyser.
See for example
http://cp.literature.agilent.com/lit...988-5677EN.pdf (hint 6)
Oops Dave beat me to it.
I should add that for FM the total power is constant so as Dave has said the total sideband power must come from a reduction in carrier power.
Jim