Off to Hogwarts
It would seem The ministry didn't know about underage magic until you arrived at Hogwarts. Harry and Hermione Had already mastered every spell in there books. It seems that the sorting hat was the source of the trace. They were actually having fun with all the spell work they were doing.
Sirius Having lived the life of a pure blood also knew the spell to break the trace, and taught them.
Sirius Knew of the prophecy involving Harry, So he was a Black belt in judo, karate, and ti qoun do!
He made him practice defense on a regular basis.
Hermione was no slouch either, She was accomplished in the martial arts as well. When the headed for the train, at platform 9¾, it was like Christmas had come early. The Granger"s a Sirius of course were in tears because they would miss them.
They were on the train and settled in at 10:45 waving out the windows. Emma reached up to give them each one Final kiss before the train started moving. About ten minutes latter a red headed boy, opened the door, exclaiming "Can I sit here everywhere else is full." So they waved him in. "I'm Ron by the way, Ron Weasley." They looked at him. "I'm Harry, Harry Potter-Granger, and this is Hermione Granger." Ron looked up to Harry's Scar. "What do you Mean your Harry Potter aren't You?"
Harry thought this kid is really thick. "I was adopted, My parents were murdered and I was sent to an orphanage, Emma And Dan Granger are my adopted parents, and Hermione's Parents. I couldn't ask for better!"Hermione reached over and hugged him. Ron was puzzled " I never heard of Granger's in the wizarding world?" The two shook there heads. "We were raised Muggle, Hermione is muggle born, I know I was born in a wizard family but I get to see both sides. I love my family, And will not put up with insults." Ron being Ron Blows it. "But muggle's you must be kidding?" Harry stood up and opened the door. "Leave NOW!" Harry's Eyes were flashing bright Green power flowing from him. Ron exited in a big hurry leaving a wet trail behind him. Things were quiet for about a half hour after that until A blond boy with two guys that had no necks pushed in. "I heard Harry Potter is in this compartment." Harry heard about this bunch. "I'm Harry Potter-Granger, What may I do for you?" The blond fool looked at Hermione. "Potter I see you already hang out with the wrong sort. Dump the muggles Good wizard Families wouldn't soil..." Draco's mouth was closed with a fist under his chin, causing him to bite his tounge. His goons looked at Harry, and Harry spoke. "If you want to survive i would tell you this is the kind of fool that will GET YOU KILLED! Now leave!