TITLE: Examples of component crossing between families of modular forms
QUESTION [5 upvotes]: Is there a reference that contains explicit examples of component crossing of Hida families at height one primes?  The paper of Emerton, Pollack, and Weston addresses component crossing obtained through level raising.  I am interested in examples caused by other phenomena (e.g. a CM family meeting another CM family coming from different imaginary quadratics or a CM family meeting a non-CM family.)  A question was previously asked that suggests such families exist:
Example of a non-smooth irreducible component of the generic fibre of a Hida family?
I am unable to find examples in the literature, but it's possible that I've looked in the wrong places.

REPLY [5 votes]: You can write down explicit examples of such crossing with Eisenstein series.  If one takes the $p$-adic family of Eisenstein series $E^{(p)}_k(\chi_1,\chi_2)$ and the family $E^{(p)}_k(\chi_2,\chi_1)$, then one sees explicitly (just look at $q$-expansions) that these families meet in weight 1 --- i.e. the order of the characters doesn't matter in weight 1.  
In the special case when $\chi_1$ is quadratic, $\chi_2$ is trivial and $\chi_1(p)=1$, there should even be some explicit CM family which also specializes in weight 1 to $E^{(p)}_1(\chi_1,1)$ coming from the the quadratic field cut out by $\chi_1$.