1. The importance of the new month that falls out on Shabbat: This Shabbat that the new month falls out on is a most special Shabbat because on this Shabbat we become partners with G-d. Why? Shabbat is organically built by G-d into creation and sanctified by G-d every 7th day. The new month was given to us by G-d for us to establish and sanctify when in the rabbinical court they would announce “Sanctified, The new month is sanctified”. The new month is sanctified by the nation of Israel. So on this Shabbat G-d has input so to speak and so do we. Rabbi Biderman explains that “this is as if we are both “mechutanim”- parents of the bride and groom because we are both partners in this festive day and there is no greater closeness.”
2. The new month coming out on Shabbat has an arousal for repentance: The Maor Vashemesh explains the specialness of Shabbat and the new moon coming out together in which the divine presence is greatly elevated and there’s a special unity created in the higher worlds that is double that of a regular new moon. Therefore a human can disconnect from physicality and repent more effectively than on a regular new moon on a weekday.
3. The New month falling out on Shabbat is considered a holiday: the source for this is the verse at the end of Isaiah (66, 23): And it will be every month in its month and every Shabbat in its Shabbat all flesh will come to bow before me Says G-d”. This means when the new month falls out on Shabbat then all flesh should come to bow before G-d since the holiness of that day is great and there will be an arousal for repentance in all flesh.
The holy Rabbi Moshe Mordechai of Lelov proved that Shabbat of the new month is like a genuine holiday as the Talmud says: Rabbi Isaac says a man is obligated to visit his Rabbi during the holiday as the verse says: “why are you going to him (Elisha the Prophet) it is not a new month nor is it a Shabbat?” So why does the proof of the obligation to meet your rabbi on a holiday come from a verse that only mentions Shabbat and the new month and not the holidays? This tells us that Shabbat and the new month are considered holidays and when they come out together it’s even more so.
4. There’s a special blessing in our Mussaf prayer when the new month comes out on Shabbat: ‘Ata Yatzarta’ “You created your world”. On holidays that come out on Shabbat there aren’t any changes from the standard holiday prayers. This shows the great importance of when the new month falls out on Shabbat.
5. The Mussaf prayer has the same tune as our holiday mussaf: The holy books bring down that the wording of ‘Ata Yatzarta’ which we say on a Shabbat with the new month has many phrases from the holiday prayers. This is another fact that shows the holiday status and the specialness of a new month that falls out on Shabbat.