is trespass in the third degree. It is a class B misdemeanor which would have a maximum penalty of 30 days in jail. However, as this is your first arrest (or you would not have gotten a DAT) you won't have to worry about jail for something like this.
It is all but certain that when you show up in court for your arraignment and plead not guilty to the charge (which, by custom, all criminal defendants must do at their arraignment when first asked how they plead) that the DA will offer you a plea to the reduced charge of 140.05, a lesser form of trespass that is a criminal violation and not a crime. By that, I mean it is less than a misdemeanor. It's an infraction. Roughly, it's the criminal court equivalent of a traffic ticket. You could take the plea and still be able to say that you have never been convicted of a crime. It is supposed to seal in a year and drop off your record. You might have to pay a fine or do a couple of days of community service or they could give you a straight conditional discharge. (Go home. Be good. Stay out of trouble for a year or we can reopen this case on you).
And that, above is, at least in my experience, your worst case scenario. You might get offered something even better called an adjournment in contemplation of dismissal. An ACD is not a conviction at all. It involves taking no plea. It's a conditional dismissal. Charges are dismissed but if you get arrested for anything at all in 6 months, the case can reopen and start over again. If you don't have any further contact with the criminal justice system, it will automatically be sealed at the six month mark. AGain, you may have to pay a small fine or do some community service.
I always recommend having a lawyer when you appear in criminal court, because criminal matters can have lifetime consequences. And nobody specific will be interested in safeguarding your rights if you don't have a lawyer. The judge and DA won't deliberately hurt you, but their agendas are different. The judge just wants to get through his calendar quickly. The DA wants a conviction.
I have told you what I am fairly confident will be what will happen to you. If that's good enough for you, you can show up without a lawyer and plead not guilty when you are arraigned. If the ADA offers you the ACD right off of the bat you can tell the judge you are interested and your case is over, just like that. If the ADA offers you the violation of 140.05 and you don't have a lawyer, you can say, "Can I get an ACD judge?" Many times, for something like this, the answer is yes.
If the DA and judge say "no" you can do one of two things -- agree to plea to the violation offered, or ask the judge for an adjournment to come back with an attorney.
I should also add that some DAT parts have public defenders assigned to the courtroom who stand on all cases. So you may well have representation anyhow.