Some people hold a gathering on the 40th day after the death of the family member serving food to all the invitees. Is this allowed?

Among the innovated matters that have appeared in some Muslim societies are celebrations to commemorate some of the dead, especially the scholars. These celebrations take place on the anniversary of the death of the person who is being commemorated, and they may take place a year or more after his death.

These celebrations vary from one person to another. If he was one of the common people or one of those who was thought to have knowledge even though he was ignorant, on the fortieth day after his death, his family commemorate his death, calling it “al-arba’een” (forty). They bring people together in a special tent or in the house of the deceased, and they bring Qur'an-readers to recite Qur'an, and they prepare a meal like a wedding feast, and they adorn the place with lights and comfortable furnishings. They go to great expense, and their purpose in doing this is to show off. No doubt this is haram, because it involves wasting money of the deceased for no legitimate purpose. It beings no benefit to the deceased himself and results in loss for his family. This is the case if there is no one among the heirs who is too young to be in charge of the money, so what do you think if there is someone like that among them! They may even finance that by means of a loan which involves Riba (interest) – we seek refuge with Allah from His Wrath. (Al-Ibadah’, p. 228)

Ibn Qayyim al-Jawziyyah said:  “One of the things that the Prophet (ﷺ) taught was to offer condolences to the family of the bereaved, but it is not part of his teachings to gather together to mourn and read Qur'an for him (the deceased), whether that is at the grave or elsewhere. All of that are bid’ah and a reprehensible innovation.” (Zayd al-Ma’aad, 1/527)

There was no one who had more knowledge than the Prophet (ﷺ), and there was no one whose way of calling others to Islam was better. No one had a nobler status or a higher rank than he did (ﷺ), for he is the best of all creation. [1]

Reference:

[1] http://islamqa.info/en/9055