mssplit

Function: mssplit
Section: modular_symbols
C-Name: mssplit
Prototype: GDGD0,L,
Help: mssplit(M,{H},{dimlim}): M being a full modular symbol space, as given by
 msinit, and H being a subspace (the new subspace if omitted), 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}$(M)$ (the full new subspace if $H$ is omitted). This function
 splits $H$ 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); \\ split 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.