The space shows up like that because of the size of your logo. If you upload a smaller logo, then the entire header area (including the menu) will be smaller. The larger your logo is, the more space it will add to the header. You’ll need to shrink the logo if you want less space under the menu
The logo can be any size you want it to be. If you want to change the size of it, you can do so by first changing the size in your functions.php file –
//* Add support for custom header
add_theme_support( 'custom-header', array(
'width' => 360,
'height' => 164,
'header-selector' => '.site-title a',
'header-text' => false,
) );
Make sure you change the width and height to the exact size of your image to avoid having to crop your image. If you need to shrink your image in Photoshop or whatever photo software you use, you can. Just make sure you upload the exact size you have specified in your functions file.
Let me know if that helps.
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