Argh, the message I just posted I accidentally deleted as it had an extra photo in it, lol. I will try again.
I was looking for the same requirements last year and found this bag on Amazon.ca (ship to in Canada) for $27cdn at the time:
Baiyu Multi Function Bike Bicycle Rack Bag Seat Cargo Bag Rear Pack Trunk Pannier Handbag Shoulder Bags Bike Pouch Back Seat Packs Rear Rack Tail Packets 13L (Black) : Amazon.ca: Sports & Outdoors
www.amazon.ca
Note the only sellers on Amazon.ca right now that carrying it are asking for double the price I paid. If you're in Canada and can find a 13L bag like this for a good price it's an option to consider.
For the U.S. I did find the same bag (different branding but same specs) by searching 13L trunk bag:
Note in the link above the second photo confirms the 40cm length.
Here are a couple photos of my bag for real world reference:
View attachment 55848
View attachment 55849
The thread wkearney99 linked to with actual battery mounts is awesome, more secure for sure. As long as you're not doing crazy off road riding then the bag is a good option and gives you extra space to carry water bottles and snacks (or other stuff) with your battery within.
Good luck!