Hi, the right shortcode is [newsletter_form] without any parameter. Nested shortcodes can be used to build a “custom” form. [newsletter] should better used only on Newsletter dedicated page.
If the shortcode is not working and it is shown on the page as written, it means your theme is not executing the shortcodes (rather a rare condition) or the plugin is not active on the frontend. Are you using optimization plugins that disable Newsletter on the frontend?
Check the System>Status panel, when possible we detect them.