You can only associate one single scalar value with each unique string key. However, thanks to references, which are scalar values, that's not as limiting as that sounds.

%Elementsfreq =
  ( 'Alpha' => [ 37, [ 0, 0, 4, 26, 0, 7 ] ],
    'Beta'  => [ 40, [ 1, 38, 0, 0, 0, 1 ] ],
    'Gamma' => [  3, [ 1, 1, 0, 0, 0, 1  ] ] );
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You would use $count = $Elementsfreq{Beta}[0] to retrieve that 40, or $count = $Elementsfreq{Alpha}[1][3] to grab that 26. The square brackets produce references to unnamed arrays.

Your pseudocode gave curly braces for your lists of values. Curly braces similarly produce references to unnamed hashes. If you meant them to be hashes, then replace the innermost square brackets in my example.

This is a somewhat advanced topic, but perldoc perllol should get you started with complex data structures.