mffields

Function: mffields
Section: modular_forms
C-Name: mffields
Prototype: G
Help: mffields(mf): If mf is output by mfinit, gives the
 vector of polynomials defining each Galois orbit of the new space.
Doc: Given \kbd{mf} as output by \kbd{mfinit} with parameters
 $(N,k,\chi)$, returns the vector of polynomials defining each Galois orbit of
 newforms over $\Q(\chi)$.
 \bprog
 ? mf = mfinit([35,2],0); mffields(mf)
 %1 = [y, y^2 - y - 4]
 @eprog\noindent Here the character is trivial so $\Q(\chi) = \Q)$ and there
 are 3 newforms: one is rational (corresponding to $y$), the other two are
 conjugate and defined over the quadratic field $\Q[y]/(y^2-y-4)$.

 \bprog
 ? [G,chi] = znchar(Mod(3,35));
 ? zncharconductor(G,chi)
 %2 = 35
 ? charorder(G,chi)
 %3 = 12
 ? mf = mfinit([35, 2, [G,chi]],0); mffields(mf)
 %4 = [y, y]
 @eprog Here the character is primitive of order 12 and the two newforms are
 defined over $\Q(\chi) = \Q(\zeta_{12})$.

 \bprog
 ? mf = mfinit([35, 2, Mod(13,35)],0); mffields(mf)
 %3 = [y^2 + Mod(5*t, t^2 + 1)]
 @eprog This time the character has order 4 and there are two conjugate
 newforms over $\Q(\chi) = Q(i)$.