diff --git a/jupyter_server/services/kernels/websocket.py b/jupyter_server/services/kernels/websocket.py
index 299811800d..4c2c1c8914 100644
--- a/jupyter_server/services/kernels/websocket.py
+++ b/jupyter_server/services/kernels/websocket.py
@@ -13,32 +13,32 @@
 
 
 class KernelWebsocketHandler(WebSocketMixin, WebSocketHandler, JupyterHandler):  # type:ignore[misc]
-  """The kernels websocket should connect"""
+    """The kernels websocket should connect"""
 
-  auth_resource = AUTH_RESOURCE
+    auth_resource = AUTH_RESOURCE
 
-  @property
-  def kernel_websocket_connection_class(self):
-    """The kernel websocket connection class."""
-    return self.settings.get("kernel_websocket_connection_class")
+    @property
+    def kernel_websocket_connection_class(self):
+        """The kernel websocket connection class."""
+        return self.settings.get("kernel_websocket_connection_class")
 
-  def set_default_headers(self):
-    """Undo the set_default_headers in JupyterHandler
+    def set_default_headers(self):
+        """Undo the set_default_headers in JupyterHandler
 
         which doesn't make sense for websockets
         """
 
-  def get_compression_options(self):
-    """Get the socket connection options."""
-    return self.settings.get("websocket_compression_options", None)
+    def get_compression_options(self):
+        """Get the socket connection options."""
+        return self.settings.get("websocket_compression_options", None)
 
-  async def pre_get(self):
-    """Handle a pre_get."""
-    # authenticate first
-    user = self.current_user
-    if user is None:
-      self.log.warning("Couldn't authenticate WebSocket connection")
-      raise web.HTTPError(403)
+    async def pre_get(self):
+        """Handle a pre_get."""
+        # authenticate first
+        user = self.current_user
+        if user is None:
+            self.log.warning("Couldn't authenticate WebSocket connection")
+            raise web.HTTPError(403)
 
         # authorize the user.
         authorized = await ensure_async(
@@ -47,51 +47,51 @@ async def pre_get(self):
         if not authorized:
             raise web.HTTPError(403)
 
-    kernel = self.kernel_manager.get_kernel(self.kernel_id)
-    self.connection = self.kernel_websocket_connection_class(
-      parent=kernel, websocket_handler=self, config=self.config
-    )
-
-    if self.get_argument("session_id", None):
-      self.connection.session.session = self.get_argument("session_id")
-    else:
-      self.log.warning("No session ID specified")
-    # For backwards compatibility with older versions
-    # of the websocket connection, call a prepare method if found.
-    if hasattr(self.connection, "prepare"):
-      await self.connection.prepare()
-
-  async def get(self, kernel_id):
-    """Handle a get request for a kernel."""
-    self.kernel_id = kernel_id
-    await self.pre_get()
-    await super().get(kernel_id=kernel_id)
-
-  async def open(self, kernel_id):
-    """Open a kernel websocket."""
-    # Need to call super here to make sure we
-    # begin a ping-pong loop with the client.
-    super().open()
-    # Wait for the kernel to emit an idle status.
-    self.log.info(f"Connecting to kernel {self.kernel_id}.")
-    await self.connection.connect()
-
-  def on_message(self, ws_message):
-    """Get a kernel message from the websocket and turn it into a ZMQ message."""
-    self.connection.handle_incoming_message(ws_message)
-
-  def on_close(self):
-    """Handle a socket closure."""
-    self.connection.disconnect()
-    self.connection = None
-
-  def select_subprotocol(self, subprotocols):
-    """Select the sub protocol for the socket."""
-    preferred_protocol = self.connection.kernel_ws_protocol
-    if preferred_protocol is None:
-      preferred_protocol = "v1.kernel.websocket.jupyter.org"
-    elif preferred_protocol == "":
-      preferred_protocol = None
-    selected_subprotocol = preferred_protocol if preferred_protocol in subprotocols else None
-    # None is the default, "legacy" protocol
-    return selected_subprotocol
+        kernel = self.kernel_manager.get_kernel(self.kernel_id)
+        self.connection = self.kernel_websocket_connection_class(
+            parent=kernel, websocket_handler=self, config=self.config
+        )
+
+        if self.get_argument("session_id", None):
+            self.connection.session.session = self.get_argument("session_id")
+        else:
+            self.log.warning("No session ID specified")
+        # For backwards compatibility with older versions
+        # of the websocket connection, call a prepare method if found.
+        if hasattr(self.connection, "prepare"):
+            await self.connection.prepare()
+
+    async def get(self, kernel_id):
+        """Handle a get request for a kernel."""
+        self.kernel_id = kernel_id
+        await self.pre_get()
+        await super().get(kernel_id=kernel_id)
+
+    async def open(self, kernel_id):
+        """Open a kernel websocket."""
+        # Need to call super here to make sure we
+        # begin a ping-pong loop with the client.
+        super().open()
+        # Wait for the kernel to emit an idle status.
+        self.log.info(f"Connecting to kernel {self.kernel_id}.")
+        await self.connection.connect()
+
+    def on_message(self, ws_message):
+        """Get a kernel message from the websocket and turn it into a ZMQ message."""
+        self.connection.handle_incoming_message(ws_message)
+
+    def on_close(self):
+        """Handle a socket closure."""
+        self.connection.disconnect()
+        self.connection = None
+
+    def select_subprotocol(self, subprotocols):
+        """Select the sub protocol for the socket."""
+        preferred_protocol = self.connection.kernel_ws_protocol
+        if preferred_protocol is None:
+            preferred_protocol = "v1.kernel.websocket.jupyter.org"
+        elif preferred_protocol == "":
+            preferred_protocol = None
+        selected_subprotocol = preferred_protocol if preferred_protocol in subprotocols else None
+        # None is the default, "legacy" protocol
+        return selected_subprotocol