My macbook pro early 2011 hard drive formatted..how can install new macos?

Installing the MacOS on an Empty Drive:

Incompatibility may be the issue here. If so, then that is because your Mac does not have the hardware to go past a certain macOS.

I. Determine which macOS(s) can be Installed:

A. Start Here: Learn About Compatibility and how to Identify your Specific Mac Model - Apple Support

B. How to Verify:

I. Reveal your Model:

What is the Model of your Mac? To find out...

1. Go to: Apple menu
2. Click: About this Mac
3. View: Second Line-Down

then...

II. Compare the Results:

See if the Model you found is shown here:

• macOS Monterey is Compatible with these Computers - Apple Support
• macOS Big Sur 11 Hardware Requirements - Apple Support
• macOS Catalina 10.15 - Hardware Requirements - Apple Support
• macOS Mojave 10.14 - Hardware Requirements - Apple Support
• macOS High Sierra 10.13 - Hardware Requirements - Apple Support
• macOS Sierra 10.12 - Hardware Requirements - Apple Support
• OS X El Capitan 10.11 - Hardware Requirements - Apple Support
• OS X Yosemite 10.10 - Hardware Requirements - Apple Support

then...

III. Perform the Install:

A. First, Back Up your Mac First:  Be certain you Create a Time Machine Backup of your Mac, so that way you can have something to restore your Mac from, should anything go wrong with the reconfiguration.

B. Finally, Install the MacOS:

• Use WiFi or Ethernet: You an use Ethernet or WiFi. Using a hardware connection(Ethernet) is usually more reliable than a wireless one(WiFi). Use this adapter, if you have no Ethernet connection: Apple USB Ethernet Adapter - Apple
• Use Internet Recovery Mode: Hold these three keys down upon boot: Option-Command-R
• Use a Bootable Installer: Go Here: Create a Bootable Installer for macOS - Apple Support. Using Terminal, you'd connect a USB Flash Drive, and then install it with the following command. You need a different Mac to create one --ask a friend or family member if you may use their Mac to create it.

I recommend you look at the list TheLittles provided, and choose...

10.11 El Capitan.

later versions require a more modern httpS: internet connection, and are very difficult to download and install unless/until you get El Capitan Installed, because 10.11 DOES have modern encryption and the modern Mac App Store.

if you can't easily install El Capitan, try for the "original" MacOS for your machine, which will be likely be Lion, offered by invoking Recovery with Shift-Option-Command-R.

"On an Intel-based Mac, if you use Shift-Option-Command-R during startup, you might be offered the macOS that came with your Mac, or the closest version still available. "

from:

How to reinstall macOS - Apple Support