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Tau lepton decays with up to two
π
0
s in the final state –
τ
+
→
π
+
ν
¯
τ
,
ρ
+
(
π
+
π
0
)
ν
¯
τ
, and
a
1
+
(
π
+
π
0
π
0
)
ν
¯
τ
– are used to study the performance of the barrel region of the silicon-tungsten electromagnetic calorimeter (Si-W ECAL) of the International Large Detector (ILD) at the future
e
+
e
-
International Linear Collider. Correct reconstruction of the tau decay mode is crucial for constraining the spin state of tau lepton and measuring the Higgs boson CP state in
H
→
τ
+
τ
-
decays. We find that about 95 % of
π
+
ν
¯
τ
, and 90 % of
ρ
+
ν
¯
τ
and
a
1
+
ν
¯
τ
decays produced by the
e
+
e
-
→
Z
0
∗
→
τ
+
τ
-
process at an
e
±
beam energy of 125 GeV are correctly reconstructed. In a smaller ILD detector, with the inner Si-W ECAL radius reduced by about 20 %, these efficiencies are reduced by at most 2 %. The
π
0
mass resolution remains below 10 %. Since failures in tau lepton reconstruction are mainly due to photons, an increase of the ILD magnetic field from 3.5 to 4 T does not bring any significant improvement.