I am trying to get some insight into the Deligne/Scholl construction of the motive of a modular form. First of all I would like to understand the case of weight two, especially when there is complex multiplication. Unfortunately in his paper "[Motives for modular forms](https://doi.org/10.1007/BF01231194)" Scholl says 

"We do not treat here the case $k = 0$, which corresponds to cusp forms of weight 2; the associated motives are then given by the Jacobians of modular curves, and are well understood."

**Question 0**: Could anyone explain this or give a readable reference? 

More precisely, I am interested in the following question. If $E$ is an elliptic curve over a number field $K$, one can look at the Chow motive with rational coefficients
$$
h^1(E)
$$ cut off from the total motive $(E, \nabla, 0)$ by $\nabla$ minus the two projectors associated to some rational point (over an extension of $K$ if necessary). In general, this motive is indecomposable. 

However, when $E$ has complex multiplication by a quadratic imaginary field $F=\mathbb{Q}(\sqrt{-d})$, one gets a decomposition of $h^1(E)_F$ into two rank 1 motives with coefficients in $F$. 

On the other hand, one can look to the weight two modular form $f$ attached to $E$ (modularity in the CM case, which is much easier!). Thanks to the construction quoted by Scholl one gets a rank two motive with coefficients in the field generated by the Fourier coefficients of $f$.

**Question 1**: (General elliptic curve) What is the relation between these two motives? One would like to say there are the same, but the coefficient field are different,  aren't?

**Question 2** (CM case): Does the geometric construction using Jacobians of modular forms also give the decomposition into two pieces of rank one? If so, how?