msatkinlehner

Function: msatkinlehner
Section: modular_symbols
C-Name: msatkinlehner
Prototype: GLDG
Help: msatkinlehner(M,Q,{H}): M being a full modular symbol space of level N,
 as given by msinit, let Q | N, (Q,N/Q) = 1, and let H be a subspace stable
 under the Atkin-Lehner involution w_Q. Return the matrix of w_Q
 acting on H (M if omitted).
Doc: Let $M$ be a full modular symbol space of level $N$,
 as given by \kbd{msinit}, let $Q \mid N$, $(Q,N/Q) = 1$,
 and let $H$ be a subspace stable under the Atkin-Lehner involution $w_Q$.
 Return the matrix of $w_Q$ acting on $H$ ($M$ if omitted).
 \bprog
 ? M = msinit(36,2); \\ M_2(Gamma_0(36))
 ? w = msatkinlehner(M,4); w^2 == 1
 %2 = 1
 ? #w   \\ involution acts on a 13-dimensional space
 %3 = 13
 ? M = msinit(36,2, -1); \\ M_2(Gamma_0(36))^-
 ? w = msatkinlehner(M,4); w^2 == 1
 %5 = 1
 ? #w
 %6 = 4
 @eprog