mshecke

Function: mshecke
Section: modular_symbols
C-Name: mshecke
Prototype: GLDG
Help: mshecke(M,p,{H}): M being a full modular symbol space, as given by msinit,
 p being a prime number, and H being a Hecke-stable subspace (M if omitted),
 return the matrix of T_p acting on H (U_p if p divides the level).
Doc: $M$ being a full modular symbol space, as given by \kbd{msinit},
 $p$ being a prime number, and $H$ being a Hecke-stable subspace ($M$ if
 omitted) return the matrix of $T_p$ acting on $H$
 ($U_p$ if $p$ divides $N$). Result is undefined if $H$ is not stable
 by $T_p$ (resp.~$U_p$).
 \bprog
 ? M = msinit(11,2); \\ M_2(Gamma_0(11))
 ? T2 = mshecke(M,2)
 %2 =
 [3  0  0]

 [1 -2  0]

 [1  0 -2]
 ? M = msinit(11,2, 1); \\ M_2(Gamma_0(11))^+
 ? T2 = mshecke(M,2)
 %4 =
 [ 3  0]

 [-1 -2]

 ? N = msnew(M)[1] \\ Q-basis of new cuspidal subspace
 %5 =
 [-2]

 [-5]

 ? p = 1009; mshecke(M, p, N) \\ action of T_1009 on N
 %6 =
 [-10]
 ? ellap(ellinit("11a1"), p)
 %7 = -10
 @eprog