@dickfickling beat me to it, but
ultrathink is already explicitly called out in the public Anthropic documentation:
"Ask Claude to make a plan for how to approach a specific problem. We recommend using the word "think" to trigger extended thinking mode, which gives Claude additional computation time to evaluate alternatives more thoroughly. These specific phrases are mapped directly to increasing levels of thinking budget in the system: "think" < "think hard" < "think harder" < "ultrathink." Each level allocates progressively more thinking budget for Claude to use."
https://www.anthropic.com/engineering/claude-code-best-pract...
I don't know what the max allowable "budget_tokens" is for Claude 3.7 Thinking mode, but the SDK shows an example of 32k which matches up with the article's findings.