how do you evaluate the p-adic modular form E_p-1 in the region |j|<1 background/motivation
let Ek denote the modular form of level one and weight k with q-expansion given by $E_k(q)=1- \frac{2k}{b_k}\sum_n \sigma_{k-1}(n)q^n$ where σi   is the divisor sum and bk is the k-th bernoulli number. for k = p – 1 the the denominators of this series don't contain any powers of  p and hence by the q-expansion principle Ep–1 defines a modular form over ℤp. that is,  Ep–1 ∈ H0(X0(1),  ℤp ⊗ ω⊗k) where X0(1) is the compactified modular curve for the full modular group, and ω is the pushforward of the canonical bundle on the universal elliptic curve over  ℤ. 
now i can use p-adic uniformisation to evaluate Ep–1 via its q-expansion at elliptic curves with j-invariant satisfying | j | > 1; in concrete terms this means formally inverting the power series for 1/j(q), and then evaluating *Ep–1(q) on the result.
i don't suppose one should expect to get a well-defined value in ℂp for Ep–1 evaluated at elliptic curves for which | j | < 1 (as you would for an modular form over ℂ) since this would mean choosing a non-vanishing differential on the universal elliptic curve over ℤp. the norm |Ep–1 |, however, is well defined, since any two choices of basis for the canonial bundle on a given elliptic curve can only differ by a unit.
of course the context i am interested in is when |Ep–1| is used to define the "overconvergent" region of the modular curve. this is (roughly) defined as the region of the $j$-line satisfying |Ep–1|>r for |r|<1. this region will (always) include part of the |j|<1 region.  in order to understand what |Ep–1|>r "means" in concrete terms, i was hoping to numerically compare |E4| and |j| for some specific ℂp-values of j near 0 (for primes p = 5, 7, 11 etc. for which j = 0 is supersingular).
anyway, my question is: 


how can i explicitly evaluate |Ep–1| at elliptic curves  with | j | < 1?     


 A: One has $j  = E_4^3/\Delta$.  In the region $|j|\leq 1$, one is parameterizing elliptic curves with good reduction, and so $\Delta$ is a unit.  Thus $|j| = |E_4|^3$.  This will help you
when $p = 5$.  
When $p = 7,$ one can write $j = 1278 + E_6^2/\Delta,$ hence $|E_6|^2 = | j - 1728|$ on
the region $|j| \leq 1$.  
For $p = 11$, these sort of explicit computations are harder (but maybe not much; see 
the added material below), because there are two supersingular $j$-invariants.  But the $p = 5$ and 7 cases will already be illustrative.
In the case when $p = 2$, I wrote something about this once, which appeared in an
appendix an article by Fernando Gouvea in a Park City proceedings volume.  A slightly
butchered version (missing figures, among other things) can be found on my
web-page (near
the bottom).  You might also look at the papers of Buzzard--Calegari
for related computations, as well as my thesis (available on my web-page) and later
work by Kilford and Buzzard--Kilford.  (There is, or at least once was, a cottage industry
based on combining these sorts of explicit computations with some more theoretical
estimates, to compute information about slopes of overconvergent $p$-adic modular forms
for various small primes $p$.)
Added in response to the comment below: For $p = 11$, one has 
$E_{10}  = E_4 E_6,$
so $E_{10}^6 = j^2(j-1728)^3 \Delta^5,$ and so when $|j| \leq 1,$ one has
$|E_{10}|^6  = |j|^2|j-1728|^3.$ Perhaps this will help?
