i have post type name series and another name episodes in the homepage i show the series but rank them based on the one that has an episode added to it by time

this is the original code which is only showing by updated for series

    <?php 
        $wpquery = new WP_Query(array(
                "post_type"  => "series",
                "showposts"     => $lm,
                "ignore_sticky_posts" => 1,
                "no_found_rows"  => true,
                "update_post_term_cache" => false,
                "update_post_meta_cache" => false,
                "cache_results" => false,
                "orderby" => "modified"
            )); while($wpquery->have_posts()) : $wpquery->the_post();
            get_template_part('series');
        endwhile; ?>

i tried this

    <?php 
        $wpquery = new WP_Query(array(
                "post_type"  => "series",
                "showposts"     => $lm,
                "ignore_sticky_posts" => 1,
                "no_found_rows"  => true,
                "update_post_term_cache" => false,
                "update_post_meta_cache" => false,
                "cache_results" => false,
                'orderby' => array(
                        "post_type" => 'epsiode',   // taxonomy name
                        "orderby" => "modified",
                )
            )); while($wpquery->have_posts()) : $wpquery->the_post();
            get_template_part('series');
        endwhile; ?>

but did not work please help