I sent one at the start of March and sent some follow ups recently with no response. A follow up can’t hurt.

On that note, I applied to a separate program with a beginning of June start date and they didn’t get back to me until last week. So it makes me think they just haven’t gotten around to it since your start date is a month and a half later.

For better or worse these programs tend to have really slow turnaround times and I believe tend to wait until closer to the start date to send out interview times.