Is there any religious basis for practices such as holding ceremonies on the seventh, fortieth, or fifty-second night…

It is obligatory for a deceased Muslim to be washed, shrouded, and buried after the funeral prayer is performed according to the prescribed method. (Kâsânî, Bedâ’i, 1/300, 306, 318) Apart from this, there is no religiously prescribed duty or ceremony tied to specific days or forms, such as holding a ceremony or prayer on the seventh, fortieth, or fifty-second day after death. None of these practices have any religious basis. Therefore, organizing ceremonies for the deceased on these days is considered an innovation (bid‘ah); “Every innovation is misguidance.” (Muslim, Jumu‘ah, 43 [867]; Abû Dâwûd, Sunnah, 6 [4606]) However, good deeds can always be performed and their reward dedicated to the soul of the deceased, and prayers may be offered on various occasions. (see Bukhari, Wasaya, 19 [2760]; Muslim, Zakat, 51 [1004])

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu