Let
Γ
⊂
P
S
L
2
(
R
)
\Gamma \subset \mathrm {PSL}_{2}(\mathbb {R})
be a Fuchsian subgroup of the first kind acting on the upper half-plane
H
\mathbb {H}
. Consider the
d
2
k
d_{2k}
-dimensional space of cusp forms
S
2
k
Γ
\mathcal {S}_{2k}^{\Gamma }
of weight
2
k
2k
for
Γ
\Gamma
, and let
{
f
1
,
…
,
f
d
2
k
}
\{f_{1},\ldots ,f_{d_{2k}}\}
be an orthonormal basis of
S
2
k
Γ
\mathcal {S}_{2k}^{\Gamma }
with respect to the Petersson inner product. In this paper, we will give effective upper and lower bounds for the supremum of the quantity
S
2
k
Γ
(
z
)
:=
∑
j
=
1
d
2
k
|
f
j
(
z
)
|
2
I
m
(
z
)
2
k
S_{2k}^{\Gamma }(z):=\sum _{j=1}^{d_{2k}}\vert f_{j}(z)\vert ^{2}\,\mathrm {Im}(z)^{2k}
as
z
z
ranges through
H
\mathbb {H}
.