Admin income formula:
A = (0.02)(M)(Tr+Tx+Fa+Mi)

A - Admin income
M - Management rating of governor
Tr - Trade income
Tx - Tax income
Fa - Farming income
Mi - Mining income

For example, Sparta on turn 1 on Easy campaign difficulty with Very High tax yields:
Tr = 8, Tx = 1483, Fa = 624, Mi = 0
It is governed by Kleomenes, a Management 3 general, so Admin income:

A = (0.02)(3)(8+1483+624) = 126.9
(in the actual game, the value is 126, all fractions appear to be rounded down, or in other words the modifier should not exceed 0.02 * M - in the case of Sparta it is 0.05957 and in the case of Syracuse it is 0.05999)

Many thanks to Owen for providing helpful insight.