Hash keys always have to be unique, but there might be a way around your problem by restructuring your data. The value could be a hashref containing keys that store the count and the array:

Alpha => {
    count  => 37, 
    data   => [0,0,4,26,0,7], 
}, 
Beta => {
    count  => 40, 
    data   => [1,38,0,0,0,1], 
}, 
Gamma => {
    count  => 3, 
    data   => [1,1,0,0,0,1], 
},
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Notice that data in each hashref contains an arrayref, which is proably what you want (the orginal you posted would have made a hashref).