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We employ a modular method to establish the new result that two types of Eisenstein series to the tredecic base may be parametrised in terms of the eta quotients 
${\it\eta}^{13}({\it\tau})/{\it\eta}(13{\it\tau})$ and 
${\it\eta}^{2}(13{\it\tau})/{\it\eta}^{2}({\it\tau})$. The method can also be used to give short and simple proofs for the analogous cubic, quintic and septic theories.
