Previously we observed that newforms obey a strict bias towards root number
+
1
+1
in squarefree levels: at least half of the newforms in
S
k
(
Γ
0
(
N
)
)
S_k(\Gamma _0(N))
with root number
+
1
+1
for
N
N
squarefree, and it is strictly more than half outside of a few special cases. Subsequently, other authors treated levels which are cubes of squarefree numbers. Here we treat arbitrary levels, and find that if the level is not the square of a squarefree number, this strict bias still holds for any weight. In fact the number of such exceptional levels is finite for fixed weight, and 0 if
k
>
12
k > 12
. We also investigate some variants of this question to better understand the exceptional levels.