regular languages – How to proove L 2^n with Pumping lemma

Let $Sigma$ is the latin alphabet ({a,b,c…,x,y,z} – 26 letters).

Given language
$L = { alpha in Sigma^{*} |$

if $alpha$ cointaints $a$ then $N_{a}(alpha) = 4$

if $alpha$ cointaints $b$ then $N_{b}(alpha) = 8$

$quad vdots$

if $alpha$ cointaints $b$ then $N_{z}(alpha) = 2^{27}$

Prove that L is reagular.

Note: I did research and I have found that we can use Pumping lemma