You are looking for the Shannon-Hartley theorem. Borrowing Wikipedia's summary, because it's better than what I can come up with:
In information theory, the Shannon–Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified bandwidth in the presence of noise.
The Shannon-Hartley theorem states that the theoretical maximum bandwidth of a communications channel can be stated as:
$$ C = B \log_2{\left( 1 + \frac{S}{N} \right)} $$
where $C$ is the channel capacity in bits per second, $B$ is the bandwidth of the channel in Hz, $S$ is the average received signal power over the bandwidth, $N$ is the average noise power received over the bandwidth, and $S$ and $N$ are in the same unit (here, watts, or a multiple thereof). Notice that no communications channel in practice (not even a crystal-clear FM transmission or studio CD recording) is completely free of noise, so you will always have a $N > 0$. The theorem does not state how to achieve this channel capacity.
It follows from this that if you know the bandwidth, the signal strength received and the noise level, you can compute the maximum theoretical data rate. Transmission frequency does not enter into the picture, although it could place a practical limit on the achievable transmission bandwidth because antennas for lower frequencies tend to be more narrow-band due to employing various forms of matching networks which are not needed when antenna sizes are a considerable fraction of a full-sized antenna for the transmission frequency range employed.
Note that this allows you to compute the maximum theoretical data rate at which transmission is somehow possible practically without errors. This data rate will not always be achievable in practice, and in fact a lot of transmission mode research has gone into getting as close to the theoretical maximum data rate as possible. A transmission actually at the Shannon-Hartley limit would most likely look like white noise across the transmission bandwidth unless you know what to look for; compare ultra-wideband, or the signals used by late-generation dial-up telephone modems.
Since a large factor in the equation is the received signal-to-noise (S/N) ratio, you can increase the achievable transmission rate within a given bandwidth "simply" by increasing transmitter output power, or antenna gain. Conversely, in situations where bandwidth is extremely limited, such as on 136 kHz, the transmission bandwidth is reduced by reducing the data rate. In situations where signal is hard to come by, such as in communication with faraway space probes or again on 136 kHz, the data rate is reduced in order to match the available S/N ratio.
Wikipedia has several examples applying the theorem that you may be interested in.