Hecke operator
= Hecke operator
{c}
{title2=$T_p$}
{wiki}
For a prime $p$, one normalization of the weight-$k$ Hecke operator at level one is
$$
(T_pf)(\tau)=p^{k-1}f(p\tau)
+\frac1p\sum_{b=0}^{p-1}f\left(\frac{\tau+b}{p}\right).
$$
If $f=\sum_na_nq^n$, then
$$
T_pf=\sum_n\left(a_{pn}+p^{k-1}a_{n/p}\right)q^n,
$$
where $a_{n/p}=0$ unless $p$ divides $n$.
= Hecke operator on modular forms
{c}
{synonym}