Herod Antipas is mentioned a total of eleven times in the Gospels and the Book of Acts: Matt 14:1-11; Mark 6:14-29; 8:15; Luke 3:1; 3:19-22; 8:3; 9:7-9; 13:31-33; 23:5-16; Acts 4:27; 13:1. The Fourth Gospel ignores his completely (maybe because of the author's focus of Judea?) while Luke-Acts pays a lot of attention to him. Overall, the mood is quite negative when Antipas is mentioned.
The Markan depiction presents Antipas as being panicky because reports of Jesus' activities lead him to think that John the Baptist has been raised from the dead (6:14-29). It might seem at first as if Antipas is saying something like the "whack-a-mole" analogy: I cut off the head of one and another appears! But the Evangelist's language leads me to think that he thought Antipas was seriously concerned about the possibility of a resuscitated Baptist wandering the land because he speaks of Jesus' miracles as being "the powers working in him [ἐνεργοῦσιν αἱ δυνάμεις ἐν αὐτῷ]" as if the back-from-the-dead Baptist now has some sort of super force dwelling in him (v. 14). Mark uses this paranoia to introduce the story of how Antipas made an oath offering "anything...up to half my Kingdom" to Herodias' young daughter after she danced for him and his guest during his birthday feast. The girls asked her mother and Herodias told her to request the delivery of the Baptist's head on a platter. Antipas had imprisoned, but according to Mark he was well aware that the Baptist was "just and holy" (v. 20) and he actually enjoyed listening to the Baptist speak, even if the Baptist rebuked him for marrying his brother's wife. Apparently, according to the Evangelist, it was this rebuke that motivated Herodias to seek the Baptist's execution. Did she think that Antipas would listen to him, repent, and send her back to his half-brother? The Evangelist doesn't say and his "reason" for Antipas' decision differs from that of the historian Josephus who in Antiquities 18.5.109-119 presented the decision as preemptively intercepting any uprising the Baptist might cause against the elite.
The only other mention of Antipas in this Gospel comes in 8:15. Jesus warns against the "leaven" or corrupting influence of the Pharisees and Herod (Antipas). Our earliest writing Evangelist shows that for whatever strengths or weaknesses Antipas may have had as a ruler (historically, he seems to have been more stable than others) his memory would be tainted forever by his decision to behead the Baptist. If the Evangelist is to be trusted here then Antipas himself was haunted by his decision soon after he made it.