Haya (Modesty) is part of Faith

What is Haya? This term covers a wide number of concepts. In English, it may be translated as modesty, shyness, self-respect, bashfulness, shame, honour, humility, etc. Islamically Haya is an attribute which pushes the believer to avoid anything distasteful or offensive.
Haya plays a huge role in the lives of Muslims because it is a very important part of our Iman (faith/belief). If we do not have any form of haya within us then it is most likely that our Iman is very weak. For as it states in the following hadith:
The Prophet Muhammad (peace be upon him) said:, "Faith (Belief) consists of more than sixty branches (i.e. parts). And Haya is a part of faith." (Bukhari)
The Prophet Muhammad (peace be upon him) said: "Every faith has an innate character. The character of Islam is modesty." (Hadith)
The Prophet(pbuh) also said: "Haya does not bring anything except good." (Bukhari)
The Prophet Muhammad (peace be upon him) said: "Indeed haya (modesty) and Iman are Companions. When one of them is lifted, the other leaves as well." (Hadith-Baihaqi)

The Prophet(pbuh) also said: "Haya comes from Iman; Iman leads to Paradise. Obscenity comes from antipathy; and antipathy leads to the fire." (Bukhari)

Allah say in the Quran:

"Say to the believing men that they should lower their gaze and guard their modesty: that will make for greater purity for them: and Allah is well acquainted with all that they do. And say to the believing women that they should lower their gaze and guard their modesty; that they should not display their beauty and ornaments except what (must ordinarily) appear thereof; that they should draw their veils over their bosoms and not display their beauty……." (Qur'an Nur, 30-31)

“Lo! the noblest of you, in the sight of Allah, is the best in conduct. Lo! Allah is Knower, Aware….”(Qur'an 49:13)