Law

Hebrews 8:10 
I will put My laws in their mind and write them on their hearts. 

My old programming, what I was schooled in growing up in church, tells me the Ten Commandments are written in my heart so I will always follow them. However, were they not the laws of the old covenant? So what laws was God referring to?

Didn't He find fault with that covenant and declared it obsolete?

Hebrews 8:7-9,13 NKJV
7 For if that first covenant had been faultless, then no place would have been sought for a second. 8 Because finding fault with them, He says: “Behold, the days are coming, says the Lord, when I will make a new covenant with the house of Israel and with the house of Judah— 9 not according to the covenant that I made with their fathers in the day when I took them by the hand to lead them out of the land of Egypt; because they did not continue in My covenant, and I disregarded them, says the Lord. 13 In that He says, “A new covenant,” He has made the first obsolete. Now what is becoming obsolete and growing old is ready to vanish away.

The laws that God puts in our minds and writes on our hearts refer to the royal law of love,

Matthew 22:37-40 NKJV
37 Jesus said to him, “‘You shall love the Lord your God with all your heart, with all your soul, and with all your mind.’ 38 This is the first and great commandment. 39 And the second is like it: ‘You shall love your neighbor as yourself.’ 40 On these two commandments hang all the Law and the Prophets.”

the perfect law of liberty,

James 1:25 NKJV
25 But he who looks into the perfect law of liberty and continues in it, and is not a forgetful hearer but a doer of the work, this one will be blessed in what he does.

and the law of faith.

Romans 3:27 NKJV
27 Where is boasting then? It is excluded. By what law? Of works? No, but by the law of faith.

These are the laws of the new covenant.

So walk forth in liberty. Step out in faith. And do all things in love. These are the laws now written on our hearts.