Coefficient field of modular forms

[Baptiste <baptiste.peaucelle@uca.fr>]

Hello,

I recently started to deal with modular forms in Pari/gp and I would 
like to get the coefficient field of a given modular form. I've found 
two functions that should help me:

-mfparams, which is supposed to give a list [level, weight, character, 
P], where P defines the extension Q(f)/Q(character);

-f.mod, which is supposed to give a polynomial P defining the extension 
Q(f)/Q.

I've tried to use those two methods on the Eisenstein series E := 
mfeisenstein(6,Mod(7,9),Mod(4,9)) and I get the following results:

? E = mfeisenstein(6,Mod(7,9),Mod(4,9));
? mfparams(E)
%2 = [81, 6, 1, y]
? E.mod
%3 = t - 1
? mfcoefs(E,10)
%4 = [Mod(0, t^2 + t + 1), Mod(1, t^2 + t + 1), Mod(-31*t - 32, t^2 + t 
+ 1), Mod(0, t^2 + t + 1), Mod(1023*t + 31, t^2 + t + 1), Mod(3124*t - 
1, t^2 + t + 1), Mod(0, t^2 + t + 1), Mod(-16806*t - 16807, t^2 + t + 
1), Mod(-992*t + 31745, t^2 + t + 1), Mod(0, t^2 + t + 1), Mod(-3093*t + 
96876, t^2 + t + 1)]

The problem is, mfparams(E)[4] return y, so Q(f) should be equal to 
Q(chi) = Q (but the coefficients of E are in Q(t)/(t^2 + t + 1)), and 
E.mod return t - 1, so Q(f) should be equal Q, which is again not the case.

Did I do something wrong or is this behavior really strange?

Best regards,
Baptiste