diff --git a/Tests/images/unknown_mode.j2k b/Tests/images/unknown_mode.j2k
new file mode 100644
index 00000000000..38719fe2561
Binary files /dev/null and b/Tests/images/unknown_mode.j2k differ
diff --git a/Tests/test_file_jpeg2k.py b/Tests/test_file_jpeg2k.py
index ed7ea4fcfbc..95b9b967b0d 100644
--- a/Tests/test_file_jpeg2k.py
+++ b/Tests/test_file_jpeg2k.py
@@ -335,6 +335,12 @@ def test_issue_6194() -> None:
         assert im.getpixel((5, 5)) == 31
 
 
+def test_unknown_j2k_mode() -> None:
+    with pytest.raises(UnidentifiedImageError):
+        with Image.open("Tests/images/unknown_mode.j2k"):
+            pass
+
+
 def test_unbound_local() -> None:
     # prepatch, a malformed jp2 file could cause an UnboundLocalError exception.
     with pytest.raises(OSError):
diff --git a/src/PIL/Jpeg2KImagePlugin.py b/src/PIL/Jpeg2KImagePlugin.py
index 39eb1c20314..e50cd7799a3 100644
--- a/src/PIL/Jpeg2KImagePlugin.py
+++ b/src/PIL/Jpeg2KImagePlugin.py
@@ -97,7 +97,7 @@ def next_box_type(self) -> bytes:
         return tbox
 
 
-def _parse_codestream(fp):
+def _parse_codestream(fp) -> tuple[tuple[int, int], str]:
     """Parse the JPEG 2000 codestream to extract the size and component
     count from the SIZ marker segment, returning a PIL (size, mode) tuple."""
 
@@ -122,7 +122,8 @@ def _parse_codestream(fp):
     elif csiz == 4:
         mode = "RGBA"
     else:
-        mode = ""
+        msg = "unable to determine J2K image mode"
+        raise SyntaxError(msg)
 
     return size, mode
 
@@ -237,10 +238,6 @@ def _open(self) -> None:
                 msg = "not a JPEG 2000 file"
                 raise SyntaxError(msg)
 
-        if self.size is None or not self.mode:
-            msg = "unable to determine size/mode"
-            raise SyntaxError(msg)
-
         self._reduce = 0
         self.layers = 0