Let

*k* be a positive even integer, and

*H*^{*}_{k} be the set of all normalized Hecke primitive eigencuspforms of weight

*k* for

*Γ*=

*SL*_{2}(

*Z*). The Fourier expansion of

*f*∈

*H*^{*}_{k} at the cusp ∞ is defined by

*f*(

*z*)=

λ

_{f}(

*n*)

*n*^{(k-1)/2}*e*^{2πinz}, where

*λ*_{f}(

*n*) is the eigenvalue of the (normalized) Hecke operator

*T*_{n}. The Omega result for the summatory function

λ

_{f}(

*n*^{i})λ

_{f}(

*n*^{j}) is investigated. Set

*E*_{1,2}(

*f*,

*x*)=

λ

_{f}(

*n*^{i})λ

_{f}(

*n*^{j})-

*c*_{j-1}*x*, i=1,

*j*=2,3,

where

*c*_{1},

*c*_{2} is a suitable constant. Then it is proved that

*E*_{1,2}(

*f*,

*x*)=

*Ω*(

*x*^{5/12}),

*E*_{1,3}(

*f*,

*x*)=

*Ω*(

*x*^{7/16}).