I had a strange dream

　I don't think eagles have a mysterious power or psychological effect on dreams, but if having that dream makes your life positive or an opportunity to look back at yourself, then this dream may have that meaning. Rather than the content, I think it's better to think of it as a good time to take a fresh look at yourself.
If this is what you call a nightmare, why did you do it? Are you hopeless about life? Did you just think of it as a dream? Did you think it was a good dream? Please keep that in mind, too.
I don't understand what three-pronged Buddha is, even if I haven't studied, but I learned how rich your imagination is. Please continue to live your life without abandoning this imagination.
PostScript
It may not be the answer you wanted, but if you talk about such a mysterious dream to someone other than a monk, there is no possibility or absence of being caught in fraud, etc., so please make a calm judgment about that.

It's better not to destroy my dreams, so I'll keep them quiet. ('omega') no
Apart from that, I'll say that.
It means that you walk the path of a Bodhisattva as a way of life.
This is because the path and practice of praying for the happiness of all lives is the Bodhisattva Path and the Bodhisattva Way.
Shari Rebun says “Profit Sentient Life, Bodhi, Shinshu, Bosatsu Goes to Enshi Enshi”
There is a saying that they benefit sentient beings, develop the Bodhisattva mind, practice the practice of the Bodhisattva, and “everyone” similarly enters silence (nirvana).
The spirit that humans should ultimately aim for, whether they are Buddhist disciples or not
A pledge and practice of “benefiting people, causing ambition, so that both yourself and your partner can be saved, and everyone will have the same peace of mind.” A vow is just a pledge, Kara Nembutsu. It is only when you become a way of life that you can help.
People who are called great saints live this way of life even if they are not Buddhists.
This is probably the result of thoroughly digging into one's own life and ultimately questioning how one should live. Should we deviate from that and follow the devious path, should we live mediocre and just for ourselves without doing anything, or should we walk the path of the Bodhisattva or Buddha to enlighten, seek comfort, and spread it?
I think that is the dividing road between the three paths.
The dream you saw is a dream, but since it probably comes from deep psychology, I think it indicated the path you should walk.
The DNA of life knows where humans should go genuinely and instinctively.

It is said that your family temple (the temple where you have become a parishioner) is the Shingon sect.

I read in a book that a long time ago in the Shingon sect, there was an item where the master would ask his disciple's dreams in detail over several days before some important ceremony or as an aid in judging the qualities of a disciple.
Currently, that's not the case...

I think it will have a deep meaning for you.

However, I just have to tell you this,
Don't talk too much about your dreams.
When it comes to the Shingon sect, it's easy to think that the attitude is that inspiration is OK,
Not all monks of the Shingon sect are like that,
There are many cases where I really dislike talking about that kind of thing so easily.

Speak only to people you really trust.

No matter how great your dreams are, they only have meaning for you. There are many cases where speaking easily to people causes confusion and misunderstandings, and in turn, it is not good for you.

> What kind of Buddha is the three-pronged Buddha, or is it an actual Buddha? ＜
I mean, all the Buddhas are connected deep within your heart.

As an aside, when I read the letters of the three-pronged Buddha, Zao Gongen at Kinpusen-ji Temple in Nara came to mind.
It is a Buddha who appeared pledging to save sentient beings over the past, present, and future generations.
If you have a chance, it might be a good idea to pray.

Ko-sama

This is Kawaguchi Hidetoshi. This is my humble answer to the question.

When it comes to dream judgment, it is certainly something that is actually done during Kanzō in Esoteric Buddhism.

I don't know in detail whether it is performed during the Kancho in the Japanese Shingon sect, Tendai sect, etc., but for example, in Tibetan Esoteric Buddhism, it is actually performed during the Kara Chakra Kanjo, Taizoukai Mandala Kanjo, etc.

However, there is also an official method for this, and the following has been omitted quite a bit, so I know that officially, on the night of the first day of Kancho, lay the blessed auspicious grass you received on that day under a pillow or mattress, and at the beginning of sleep, peacefully calm your mind in a sleeping position lying down on your right flank, and fall asleep while imagining the true image of Kancho while thinking about the true image of Kancho, and fall asleep with Sanbo Guiyi while keeping in mind the understanding of Bodhi Heart and emptiness It will be.

Also, dreams actually seen at dawn are subject to that judgment.

However, whether it's a good dream or a bad dream, it's important not to get too caught up, and in any case, I think it's essential not to be too arrogant, even if you have a bad dream, there is no need to be strangely depressed, and to nourish a sense of emptiness, or to nourish compassion and altruism.

It's really good that Ko-sama also had a dream where she felt a sense of euphoria about the Buddha this time, but instead of causing me to be strangely trapped, I think it would be good for this auspicious dream to further lead to three treasure devotion, nourishment of understanding bodhisattva and emptiness, and nourishment of mercy and altruism.

Also, regarding the handling of dreams, we have answered the following questions, so I hope you can take a look.

Question “My Real Mother's Death”
http://blog.livedoor.jp/hasunoha_kawaguchi/archives/1002972230.html

“... after all, dreams are nothing but illusions, and understanding that the reality of this world is also “like a dream” is important in understanding the “sky” in Buddhism, so I hope you can take this opportunity to know even just a little bit. ・・”

Kawaguchi Hidetoshi Gassho