Was Jesus a Hellenized Jew?

Nowadays most scholars accept that Jesus Christ was a Jew.But could it be that he was a Hellenized Jew?

Meaning of Hellenized
First let's take a look at what Hellenized means. It means under the influence of Greek culture.

Spread of the Greek language during
 the Diadochi and Roman times.

After the conquests of Alexander the great ,Greek culture spread far and wide eastwards including the middle East, especially around Antioch (modern-day Turkey) ,Western Syria , Lebanon and Alexandria in Egypt.

A portion of the local Jewish population came under the influence of Greek civilization and became Hellenized.

Antioch was one of the two biggest centers of Hellenized Jews -the other being Alexandria where the Septuagint was produced - the first translation of the Hebrew Bible in Greek.

Mother toungue of Jesus Christ.
It is also widely accepted that the mother toungue of Jesus was Galilean Aramaic- a dialect of the Western branch of Aramaic.

All Western Aramaic dialects came under the influence of Greek - Galilean Aramaic, Nabbatean, Samaritan, Palmyrene and others.

Traits of Galilean
Galilean though poorly attested has features attained obviously under the influence of the Greek language.

Galilean tended to soften ejected and guttural consonants unlike dialects of Eastern Aramaic in the area (Greek lacks emphatic and guttural sounds). It had a lot of loanwords from Greek as well as Latin.The choice of words was also different something like the differences between American English and British English.Even the word order was different resembling in some cases that of Greek.

Hellenized Jews bilingual in Greek and Aramaic would often mix the two languages. So, Jesus apart from Galilean could probably speak Greek fluently as well as Hebrew to some extent and some Latin.

Hebrew was already a dead language- centuries ago- by that time for the lower-class Jews whose native language was Aramaic. Hebrew was still used as a language of liturgy though.

A speaker of Galilean would sound strange in Jerusalem and his accent would give him away immediately.

After a little while those who stood by came and said to Peter, “Surely you are also one of them, for your speech gives you away.” – Matthew 26:73

Furthermore Galilea was north of Jerusalem closer to Antioch, a big urban center of Hellenized Jews.

The above would also explain why the New Testament was written originally in Greek .

So, could Jesus Christ be a Hellenized Jew?

Sources
Differences of a dialect.
Hellenistic Judaism