Is the Arduino MEGA2560 R3 the smallest Arduino to drive a 5" Display?

Hello,
for a projekt i need to display simple symbols on 5" tft display without touch like ERM240128-2 with 240 x 128 dots . Input comes with push-button and rotary selector switch.
Have i to use the MEGA2560 or can i take a smaller one?
Thank you for helpfully suggestions, they give me a direction for my search.

Any help appreciated. Thanks.

240 x 128 = 30720 dots.
240/8 = 30 bytes wide
128/8 = 16 bytes high
16 x 30 bytes = 480 bytes of SRAM to hold the contents you want do display.
I'd say any '328P, 1284, 2560 based board could handle that.
How much other software does it need?

Looks like 16 IO pins, could likely use shift register for 8 data pins, most of the control signals, all but chip select really.

@CrossRoads
Thank you verry much,

it was verry helpfully. The software should be not so difficult. Read 6 button, read a panel encoder, check out a accu on a a/d port, give out some different frequency on 2 i/o ports, show this frequencys in big letters (that's why 5"). At first i have to count exactly how many i/o ports i have to use, but i think there are enough at the 2560 include 6 another i/o ports to check a status with pull up resistorsand and control digital resistors over SPI.

Once again many thanks