I was reading the news and came across the word "modere". I wasn't sure what it meant so I searched it up using Lernu's dictionary and it shows that the word translates to "modestly" in English. Just as I was about to add this into a list I had, I noticed that "modera" was also in my list but it meant "moderate".

So after looking up some words, I found out that "modero" means "moderation" while "modesta" means "modest". "modere" also means "modestly" on the Majstro dictionary. However, on google translate, "modere" means "moderately". So, should I trust 2 dictionaries or google translate for this word?

TLDR:
modero = moderation
modera = moderate
so why does
modere = modestly
????????

Modera means not extreme. Modesta means humble,low worth, restrained, and is a special case of moderation, more orientated to a value assessment.

As a guideline think of modera as moderate in English and modesta as modest.

Perhaps in some contexts modere might be translated as modestly.

The most authoritative definitions of Esperanto words tend to be found in NPIV. This is accessible online with your Lernu password.

For a more detailed examination of usage goto the Tekstaro. Search with \bmoder\FI or \bmodest\FI.

I assume the dictionary you used is based on ESPDIC, which unfortunately contains a lot of weird translations and even mistakes. If you have a doubt, check PIV (as sudanglo said) or Reta Vortaro, which includes English translations (and even when it doesn't, it has Esperanto definitions).