I have been searching for quite a while if PARI / GP has a function to compute the trace form of a given newform, namely, the sum of the newform with its Galois conjugates. The only thing I've been able to find out is how to compute the trace form of the full space of newform, namely, the sum of all trace forms of an eigenbasis.
Is someone aware of a function that does what I need ?
Also, do you know if instead we can code it, lets say, if there exists a function that computes the Galois group of the field of coefficients and then let us apply it to a given modular form.