Every word in Sanskrit can be further divided in to letters that cannot be divided further.
In this context, what are the letters, that are further indivisible, used to form om ॐ in sanskrit?
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The Omkāra is made up of 3 letters: (1) akāra - अ; (2) ukāra - उ; (3) makāra - म and also an anusvāra (ardhamātrā).
It is often a misconception that it has only the first three letters but the Upanishads are clear that it has even an anusvāra. So you will pronounce it as Om and let the ma resonate after for a bit in the mouth/ nose area.
The Nādabindūpaniṣad verse 1 beautifully describes the components of Omkāra in the form of a swan:
अकारो दक्षिणः पक्ष उकारस्तूत्तरः स्मृतः । मकारं पुच्छमित्याहुरर्धमात्रा तु मस्तकम्॥१॥
The syllable A is considered to be its (the bird Om's) right wing;the syllable U, its left; the syllable M, its tail; and the ardhamātrā (half-metre) is said to be its head.
A better description of the Omkāra can be found in the Praṇavopaniṣad:
It has 3 full matra (a, u, m) and one half matra (anusvāra) and that is its auspicious Shiva form. (Verse 3b)
The Rigveda, Earth, Gārhapatya Agni and Lord Brahma are described as the syllable ‘a’ by knowers or Brahman (verse 4)
The Yajurveda, Antariksha, Dakshinagni and Lord Vishnu are known as the syllable ‘u’ (verse 5)
The Samaveda, Dyuloka, Ahvaniya Agni and Lord Shiva are described as the syllable ‘m’ (verse 6)
One can better understand the components of Om by looking at the Tamil and Telugu symbols for it though all scripts focus on mainly the anusvāra and omit the makāra altogether, while yet pronouncing it as a makāra and omitting to pronounce the makāra in combination with the anusvāra.
Mandukya Upanishad says that OM is a Combination of (A + U + M)
That same Self, from the point of view of the syllable, is Om, and viewed from the stand point of the letters, the quarters are the letters, and the letters are the quarters. The letters are A, U and M.(Mandukya Up 8)
Vaisvanara seated in the waking state is the first letter A, owing to its all-pervasiveness or being the first. He who knows thus verily accomplishes all longings and becomes the first. Taijasa seated in the dream is U, the second letter of Om, owing to the similarity of excellence or intermediate position. He who knows thus verily advances the bounds of his knowledge and becomes equal to all and none who is not a knower of Brahman is born in his family. Prajna seated in the state of deep sleep is M, the third letter of Om, because of his being the measure or the entity wherein all become absorbed. He who knows thus measures all this and absorbs all.(Mandukya Up 9-11)
Alright, let me just add few more words. The Kaankal Malini Tantra describes the Varna-Samuha. According to it varna from अ to अः are of SatvaGuna. From क to थ are RajoGuna and remaining of TamoGuna. It says:
आदावसौ जायते च शब्दब्रह्म सनातन: । वसुजिह्वा कालरात्र्या रूद्रडाकिन्यलंकृता । विषबीजं श्रृतिमुखं घ्रुवं हालाहल प्रिये ॥ॐ॥१८॥
Om is made of three Varnas, Vasujihvā Aa-Kara (अ), kaalaraatri U-Kara (उ) and RudraRupe Anuswara. This word (ॐ) is BrahamaRoopee, and is VishvaRoop for this Apprent world. That is, it destroys the Maya and is the Mouth of "what is heard" (श्रृतिमुखं).
The components of Om is explained very well in Shiva Puran.
"The syllable “A” came first from northern face; the syllable “U” from the western; the syllable “M” from the southern and the Bindu (dot) from the eastern face. The Nāda (mystical sound) came from the middle face. Thus the complete set cropped up in five-fold form. Then all of them united in the syllable of “Om”.
-from Shiv Puran, Vidyeswara Samhita, Chapter 10, verse 18,19.
"4. The syllable Om means an excellent boat to cross the ocean of worldly existence. [Pra=of the Prakṛti i.e. the world evolved out of it. Navam—Nāvāṃ Varam—an excellent boat]
6-8. Or it may mean “that which leads to new knowledge.” After annihilating all actions it gives the persons who repeat the mantra or worship, a fresh knowledge of the pure soul. This Praṇava is two-fold (1) the subtle (2) the gross.
The subtle one is of a single syllable where the constituent five syllables are not differentiated clearly. The gross one is of five syllables where all the constituent syllables are manifest.
The subtle one is for the liberated living soul (jīvanmukta). The need for the contemplation of the meaning through the mantra is only upto the destruction of the physical body.
When the body is destroyed he completely merges in Śiva undoubtedly. The mere repeater of the mantra attains the yogic communion with Śiva certainly.
A person who repeats the mantra thirty-six crores of times certainly attains the yogic communion. The subtle Praṇava is again two-fold—the short, and the long.
13-15. The long one is present in the heart of the Yogins alone—separately in the form of “A” syllable, “U” syllable, “M” syllable, Bindu and Nāda. It is endowed with all the digits of the time sound. Śiva, Śakti and their union are indicated by “M” syllable ramified into three and this is called the short subtle Praṇava. The short Praṇava shall be recited and repeated by those who desire their all sins annihilated."
-from Shiv Puran, Vidyeswara Samhita, chapter 17.
OM is the Self, the Atman. Om is the means of liberation and freedom from the effects of ignorance. OM is indivisible, consists of three letters: A, U, and M. Every letter has different significance and represents the conscious states. The three states are waking, dreaming, and dreamless sleep, respectively, as well as the physical, astral, and causal levels of existence. When AUM is uttered, all the various parts of the vocal organ needed for speaking are used. AUM is a word that includes all sounds.
The letter ‘A’:- The letter A denotes to waking state or Vaisvanara (quarters of Atman). Vaiswanara, the first state of Self as the universal person in the physical being, corresponds to the first letter–A. Through the Japa and meditation of Om, they master the material world and control learn to control the senses themselves. The desires of masters are fulfilled because they are connected with the essence of creation and get the realization power.
The letter ‘U’:- Taijasa, the Self as the universal person in the mental state, resembles the letter. Taijasa and the letter U both are views in the dream state. In this state, Taijasa grows in wisdom and intellect and is highly honored. Two qualities that a person possessed in this quarter are: – A master of this state develops the knowledge of humanity and delivers the inner momentum to assist questing souls in accessing knowledge. A master adheres to the quality to becomes one with all human beings in a sense, and the master is so attuned and comfortable with other humans that the other is virtually his own Self. This quality appears in the great saints and yogis. Whether a poor or a king approaches them, he feels that they are the dear and his own. Om is the way to move the thoughts from the subconscious state to the conscious. Meditation on OM will empower the yogi to know all about himself and understands others as well. No one can fool him. Like, Sivananda Ji. He was always very kind and humorous, went right to the truth of things about people’s characteristics.
3.The letter ‘M’:- M is the state of deep sleep where neither desires any object nor sees any dream. And the third quarter is Prajna, whose sphere is dreamless sleep, the state of total bliss and happiness with satisfaction.