Cable frequency

It doesn't. Clockrate on the cable is some 33 MHz. They use clever coding to transmit multiple bits at once. (Like your modem takes 56 kBps over a 3 kHz voice channel.)

If you care for the details: Google for "4B/5B block encoding"

It does. See this page for an oscillograph view of 100Base-TX.

The symbol time is 8ns, which translates to a wire symbol rate of 125 MHz.

That's wrong for 100Base-TX.

56 kbps is a digital transmission. Multiple bits are not transmitted at the same time on a 56 kbps link.

Slower modem standards use modulation schemes to transmit the information content of multiple bits with one symbol.

This is true. 100Base-TX uses 4B5B block encoding first (therefore the bitrate is 125 MHZ * 4 / 5 * 1 Bit = 100 MBit/s). Then going downwards it uses MLT-3 coding to reduce the necessary bandwith by going from a binary (0,1) to a three level code (-1, 0, +1) but keeping the symbol rate of 125 MHz.

See

and the patent why MLT-3 moves the main portion of the necessary bandwidth spectrum to well below 100 MHz.

The combination of these techniques brings a reduction in necessary bandwith (MLT-3) paired with an opportunity to recover the clock (4B5B encodes into 5 bit sequences that are never 00000 and never 11111, but always mixture of 0's and 1's.)

Ralf