Asp.net MVC ajax submit for forms in a Modal [duplicate]

I am trying to submit a form using ajax when in a modal. So far the closest I have come to making that work is this:

@model AppStudio.Data.ViewModels.RolesDetailsViewModel
@section scripts{
    @Scripts.Render("~/bundles/jquery.unobtrusive-ajax")
}
<div id="roleDetails" class="modal">
    <div class="col-sm-12">
        @if (Model.Id == null)
        {
            <h2>Add Role</h2>
        }
        else
        {
            <h2>Edit Role</h2>
        }
        <hr />
    </div>
    @using (Ajax.BeginForm("SaveRole", new AjaxOptions() {
            InsertionMode = InsertionMode.Replace
    }))
    {
        @Html.AntiForgeryToken()
        <div class="col-sm-12">
            <div class="form-group">
                @Html.HiddenFor(m => m.Id)
                @Html.HiddenFor(m => m.ApplicationId)
            </div>
            <div class="form-group">
                @Html.LabelFor(m => m.RoleName)
                @Html.TextBoxFor(m => m.RoleName, new { @class = "form-control col-sm-12" })
                @Html.ValidationMessageFor(m => m.RoleName)
            </div>
            <div class="form-group">
                <div class="clearfix">
                    <button type="submit" class="btn btn-primary pull-right">Save</button>
                    <a href="#" class="btn btn-default pull-right" rel="modal:close">Cancel</a>
                </div>
            </div>
        </div>
    }
</div>

However, when I submit this, it redirects me to a new page with my inputs

I then tried removing the ajax.beginform and replacing it with beginform and changing my submit button to a href link like this:

<a href="#" id="save" class="btn btn-primary pull-right">Save</a>

I also added this script on top:

   <script>
        $(document).ready(function (e) {
            $("#save").click(function () {
                alert("test");
            });
        });
    </script>

However, what this results in is the url having a # added to it only. Is there a way to do do ajax submits in a modal? I tried searching around but haven't found much so far.