def trace_jacobi_cusp_forms(k, m, l, n, kind="holomorphic"):
r"""
OUTPUT
Trace of $T(l) \circ W_n$ on the space
of holomorphic or skew-holomorphic Jacobi cusp forms
of weight $k$, index $m$ on $\mathoperator{SL}(2,Z)$.
INPUT
k -- weight
m -- index
l -- a Hecke operator index (rel. prime to the index $m$)
n -- an Atkin-Lehner involution index (i.e. exact divisor of $m$)
kind -- the string 'holomorphic' or 'skew-holomorphic'
NOTE
EXAMPLES
"""
k, m, eps = __check_jac_params(k, m, kind)
k, m, l, n = __check(k, m, l, n)
if 1 == k == eps:
raise NotImplementedError, "dimensions for skew-holomorphic cusp forms wt 1: not implemented"
if k < 1:
return 0
return (_sz_s(k, m, l, n) - eps * (-1) ** (k % 2) * _sz_s(k, m, l, m // n)) / 2
def trace_jacobi_eienstein_series(k, m, l, n, kind="holomorphic"):
r"""
OUTPUT
Trace of $T(l) \circ W_n$ on the space
of holomorphic or skew-holomorphic Jacobi Eisenstein series
of weight $k$, index $m$ on $\mathoperator{SL}(2,Z)$.
INPUT
k -- weight
m -- index
l -- a Hecke operator index (rel. prime to the index $m$)
n -- an Atkin-Lehner involution index (i.e. exact divisor of $m$)
kind -- the string 'holomorphic' or 'skew-holomorphic'
NOTE
EXAMPLES
"""
k, m, eps = __check_jac_params(k, m, kind)
k, m, l, n = __check(k, m, l, n)
raise NotImplementedError()
