Sphinx sidebar: include module's functions and class' methods

In Sphinx docs, I define a reference document like this:

Reference
=========

.. toctree::

   reference_api
   reference_cli
   reference_client
   reference_downloads
   reference_options
   reference_stats
   reference_utils

The reference_api document looks like this:

API module
==========

.. automodule:: aria2p.api
    :no-members:

API
---

.. autoclass:: aria2p.api.API
    :members:

Now I get this list in the sidebar:

Reference
  API module
    API

I would like to also add all the API methods that were documented through :members: in the sidebar, something like:

Reference
  API module
    API
      __init__
      add_magnet
      add_metalink
      ...

Is this possible? Should I change how Sphinx writes modules functions and classes' methods to add anchors to them, so the sidebar can display them?