Function: mfeigensearch
Section: modular_forms
C-Name: mfeigensearch
Prototype: GDG
Help: mfeigensearch(NK,{AP}): search for normalized rational eigen cuspforms
 with quadratic characters given a few initial coefficients. The meaning of
 the parameters is as follows:

 NK is of the form [N,k]: search given level N, weight k and quadratic
 character; note that the character is uniquely determined by (N,k).
 The level N can be replaced by a vector of allowed levels.

 AP is the search criterion, which can be omitted: a list of pairs
 [...,[p,a_p],...], where a_p is either a t_INT (exact match) or a t_INTMOD
 (match modulo the given integer).

 The result is a vector of newforms matching the search criteria, sorted by
 increasing level.
Doc:  search for a normalized rational eigen cuspform with quadratic
 character given restrictions on a few initial coefficients. The meaning of
 the parameters is as follows:

 \item \kbd{NK} governs the limits of the search: it is of the form
 $[N,k]$: search for given level $N$, weight $k$ and quadratic
 character; note that the character $(D/.)$ is uniquely determined by $(N,k)$.
 The level $N$ can be replaced by a vector of allowed levels.

 \item \kbd{AP} is the search criterion, which can be omitted: a list of
 pairs $[\ldots, [p,a_{p}], \ldots]$, where $p$ is a prime number and $a_{p}$ is
 either a \typ{INT} (the $p$-th Fourier coefficient must match $a_{p}$ exactly)
 or a \typ{INTMOD} \kbd{Mod}$(a,b)$ (the $p$-th coefficient must be congruent
 to $a$ modulo $b$).

 The result is a vector of newforms $f$ matching the search criteria, sorted
 by increasing level then increasing $|D|$.
 \bprog
 ? #mfeigensearch([[1..80],2], [[2,2],[3,-1]])
 %1 = 1
 ? #mfeigensearch([[1..80],2], [[2,2],[5,2]])
 %2 = 1
 ? v = mfeigensearch([[1..20],2], [[3,Mod(2,3)],[7,Mod(5,7)]]); #v
 %3 = 1
 ? F=v[1]; [mfparams(F)[1], mfcoefs(F,15)]
 %4 = [11, [0, 1, -2, -1, 2, 1, 2, -2, 0, -2, -2, 1, -2, 4, 4, -1]]
 @eprog
