A cusp form is a modular form for which the coefficient 
in the Fourier
series
 |
(1)
|
(Apostol 1997, p. 114). The only entire cusp form of weight 
is the zero function (Apostol 1997, p. 116). The
set of all cusp forms in 
(all modular forms of weight 
) is a linear subspace of 
which is denoted 
. The dimension of 
is 1 for 
, 16, 18, 20, 22, and 26 (Apostol 1997, p. 119). For
a cusp form 
,
 |
(2)
|
(Apostol 1997, p. 135) or, more precisely,
 |
(3)
|
for every 
(Selberg 1965; Apostol 1997, p. 136). It is conjectured that the 
in the exponent can be reduced to 
(Apostol 1997, p. 136).
