" 'The first of the Sabbaths cometh Mary Magdalene early, when it was yet dark, unto the sepulcher, and sees the stone taken away from the sepulcher' (John 20:1). (DLT: torahtimes.org).

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first...Sabbath: According to Leviticus 23:15, this was the first Sabbath after the annual Passover Sabbath."  The Greek phrase is Τη δε μια των σαββατων.  Wherever it occurs in the Scripture, it always occurs in a context such that it is the first Sabbath after Passover (including Acts 20:7 and 1Cor. 16:2).  It is a contraction of μια ημερα των σαββατων, which is to say the normal and ordinary phrase for the sabbath with the word first added onto the front.  It is equivalent to the Hebrew אחת השבתות, which solves the gender conflict problem.  The whole Greek phrase was simply borrowed from Hebrew where the word אחת is feminine.  The phrase may also be rendered more literalistically one of the sabbaths , however, the Hebrew word אחד, אחת stands for both the ordinal "first" and the cardinal "one".  Since the whole phrase is borrowed from Hebrew, and it takes place always just after the Passover (Mat. 28:1; Mark 16:2, 9; John 20:1, 19; Acts 20:7; 1Cor. 16:2), it is evident in the light of Lev. 23:15 that it does not mean just generally "one of the sabbaths".  It means specifically the "first of the sabbaths".

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comment: Various rationalizations  are offered for translating, "first day of the week".  Only two need serious comment: 

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(1) "First day from the Sabbath".  The problem here is that there is no pious usage of counting "from" the last Sabbath.  In pious usage, days were counted "to" the next Sabbath.  This opinion is mentioned in Thayer's Lexicon.  It also suffers from breaking up the implied idiom "first day of the sabbaths", which is "day of the sabbaths" with the word "first" added.   As "day of the sabbaths" (τη ημερα των σαββατων) always means the seventh day, the word "first" simply specifies which Sabbath, i.e. "the first".  The phrase is actually a Hebraism for  אחת השבתות. which absolves the Greek of a gender conflict.  One might suggest the term ראש השבתות or השבת הראשון for the first Sabbath, but these designations are too easily confused with the annual Sabbath, which actually is the head Sabbath for the seven Sabbath counting.

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(2) "First day to the Sabbath".  This is indeed the format of the pious usage in the Mishnah and Talmud corresponding to  אחד בשבת,  which is the same in meaning as   אחד לשבת.  However, this is late Hebrew pious usage.  The original non-pious usage is reflected in the Talmud an other ancient sources by an Aramaic equivalent of "one in the seven": חד בשבא, which in pre-Mishnaic Hebrew is אחד בשבע.   The Greek text in the gospels does not allow this late usage.  First, the Greek would have to be in the dative case to allow it, and second, the second objection stated under point one above applies.

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comment: Less serious suggestions have been made, which are as follows:

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(1) The word חדש can mean "new moon" or "month".  So we say "first of the month" (Gen. 8:5: אחד לחדש), or we can say "day of the new moon" (Ezek. 46:1, 6: יום החדש).  Could the meaning of σαββατων switch between "sabbath" and "week" like this?  No, because σαββατων is plural. It is like adding a "s" to month: "head of the months" (Exodos 12:2: ראש חדשים), or  "three months" (Gen. 38:24: שלש חדשים).  The pluralization  forces us to enumerate months rather than days of the month.  Likewise, the plural σαββατων suggests we should enumerate sabbaths rather than days of one week.

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(2) It has also been argued that some how the Greek σαββατων looses its normal plural sense when used for the sabbaths, i.e. ημερα των σαββατων means just one Sabbath day.  However, the literal translation is day of the sabbaths in the Jewish Greek mind, and the mind always makes the easiest sense it can make upon hearing something.  The plural is naturally given an internal sense to the sabbath.  It is conceived of as a day on which sabbaths take place, i.e. sabbaticals or restings.  In English we might call it a day of sabbatisms.   Because of this the plural is still significant.  And for the same reason supposing that sabbath ever meant "week", the only sense that can be gotten is with a plural, "first day of the weeks", for which discussion see point 3 below.  The term σαββατων was undoubtedly coined from the Hebrew term שבתון which is pronounced as close as can be to the Greek.  The Hebrew term means "sabbatism" or "resting".  The LXX in Lev. 23:32 translates it with σαββατων.  In Exodus 16:23 and other places it is translated αναπαυσις, which means "resting".  The only really significant difference in meaning is that the coined Greek word is plural, and it is explained how the Greek Jews would have thought about it above.   The Greek term σαββατα is also plural.  The LXX reads in Lev. 23:32, "You shall shall sabbath your sabbaths".  Again "sabbaths" (τα σαββατα) is viewed as sabbatisms—restings on the Sabbath.  This plural form was also chosen for its uncanny equivalence to the Aramaic שבתא.

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(3) Bullinger suggests "first day of the weeks".  It was shown above that the the normal idiom for the sabbath: ημερα των σαββατων = day of the sabbatisms, and likewise τα σαββατα = the sabbtisms on just one sabbath when it is used for one sabbath.   Bullinger retains the plural in The Companion Bible.  But his interpretation and translation are faulty since he rolls over the implied idiom: μια ημερα των σαββατων, which is simply the term day of the sabbtisms with μια added to the front, such that we get "first day of the sabbatisms" ≈ "first Sabbath", however, now the idiom opens up to "first of the sabbaths" pertaining to Lev. 23:15 since the plural now makes additional sense over seven Sabbaths.  The Hebrew term is אחת השבתות" (torahtimes.org).

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Daniel's Literal Translation and Commentary: (http://www.torahtimes.org/translation/joh2001.html)