Are you using a plugin?
Right now you have quite a few input types that you aren’t using and are “hidden” from view but still include line height and line breaks, giving you that whitespace. Right now your form looks like this:
<form method="post" action="https://scripts.dreamhost.com/add_list.cgi">
<input type="hidden" name="list" value="info"><br>
<input type="hidden" name="domain" value="https://cegolden.com"><br>
<input type="hidden" name="url" value=""><br>
<input type="hidden" name="unsuburl" value=""><br>
<input type="hidden" name="alreadyonurl" value=""><br>
<input type="hidden" name="notonurl" value=""><br>
<input type="hidden" name="invalidurl" value=""><br>
<input type="hidden" name="emailconfirmurl" value=""><br>
<input type="hidden" name="emailit" value="1"><br>
Name: <input name="name"><br>
E-mail: <input name="email"><br>
<input type="submit" name="submit" value="Join Our Announcement List"><br>
<input type="submit" name="unsub" value="Unsubscribe"><br>
</form>
Except you are only using the bottom two Name: <input name="name"><br>
and E-mail: <input name="email"><br>
If you can edit the HTML directly, just delete all of the other input fields and line breaks.
Also, to keep your semantics looking alright, you should wrap the title for each field in <label>, which indicates that it is attached to the input field. You can also remove the and put the spacing in the label tag. So your final code should look like this:
<form method="post" action="https://scripts.dreamhost.com/add_list.cgi">
<label>Name: </label>
<input name="name">
<label>E-mail: </label>
<input name="email" type="email">
<input type="submit" name="submit" value="Join Our Announcement List"><br>
<input type="submit" name="unsub" value="Unsubscribe"><br>
</form>
See if that works.