It’s no secret that Sprint, the nation’s third largest mobile service provider, opposes AT&T’s proposed $39 billion takeover of T-Mobile. Sprint CEO Dan Hesse testified before Congress earlier this month that the deal could do “irreparable harm” to consumers by creating a “1980s-style duopoly” in which two giants, AT&T and Verizon, would dominate the market.

Now, Sprint has formally registered its objections with the Federal Communications Commission, which is scrutinizing the deal along with the Justice Department.

In a 377-page Petition to Deny (.pdf) filed Tuesday, Sprint warned that...