Why has M1 grown a lot faster than M3 after the financial crisis? While the fed has printed a lot of money the last decade and the M1 money quantity growth rate has gone up significantly (red), the M3 growth rate (blue) is almost exactly the same as before the financial crisis.



In the euro area, M1 (red) has grown in the same rate as before, while M3 growth (blue) is significantly lower.



Why have M3 not followed the same quantitive expansion as M1?

And can this be an explanation for why we have not seen stronger inflation?
As you point out, central banks have "printed" a considerable amount of money since the 2008 crisis. The following chart of the US monetary base is one of clearest examples of this phenomenon.



The metric you seem to be pointing out through your question is known as the money multiplier: the ratio of broad money (e.g., M1, M2, or MZM) to the monetary base. As we can see with the following chart, in the US, the money multiplier has decreased since the 2008 crisis.



The money multiplier grows when banks and other financial institutions make loans. So in short, M3/MZM hasn't grown because a significant amount of the monetary base has just been kept in bank reserves without being loaned out. 



This has been used as an argument on the ineffectiveness of quantitative easing, and that we need to more directly put money into people's hands in order to stimulate the economy.

And if excess reserves were all loaned out and invested/spent, we should indeed see higher levels of inflation in the short term. If the money is invested/spent wisely, then productivity growth may offset that inflation on a longer term assuming we don't continue to increase the money supply.