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Function: mssplit
Section: modular_symbols
C-Name: mssplit
Prototype: GGD0,L,
Help: mssplit(M,H,{dimlim}): M being a full modular symbol space, as given by
msinit, and H being a subspace, split H into Hecke-simple subspaces.
If dimlim is present and positive, restrict to dim <= dimlim.
Doc:
Let $M$ denote a full modular symbol space, as given by \kbd{msinit}$(N,k,1)$
or $\kbd{msinit}(N,k,-1)$ and let $H$ be a Hecke-stable subspace of
\kbd{msnew}$(M)$. This function split $H$ into Hecke-simple subspaces. If
\kbd{dimlim} is present and positive, restrict to subspaces of dimension
$\leq \kbd{dimlim}$. A subspace is given by a structure allowing quick
projection and restriction of linear operators; its first component is a
matrix with integer coefficients whose columns form a $\Q$-basis of the
subspace.
\bprog
? M = msinit(11,8, 1); \\ M_8(Gamma_0(11))^+
? L = mssplit(M, msnew(M));
? #L
%3 = 2
? f = msqexpansion(M,L[1],5); f[1].mod
%4 = x^2 + 8*x - 44
? lift(f)
%5 = [1, x, -6*x - 27, -8*x - 84, 20*x - 155]
? g = msqexpansion(M,L[2],5); g[1].mod
%6 = x^4 - 558*x^2 + 140*x + 51744
@eprog\noindent To a Hecke-simple subspace corresponds an orbit of
(normalized) newforms, defined over a number field. In the above example,
we printed the polynomials defining the said fields, as well as the first
5 Fourier coefficients (at the infinite cusp) of one such form.
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