  We present the first in a series of papers in T$h$e role of $E$nvironment in
shaping $L$ow-mass $E$arly-type $N$earby g$a$laxies (hELENa) project. In this
paper we combine our sample of 20 low-mass early types (dEs) with 258 massive
early types (ETGs) from the ATLAS$^{\mathrm{3D}}$ survey - all observed with
the SAURON integral field unit (IFU) - to investigate early-type galaxies'
stellar population scaling relations and the dependence of the population
properties on local environment, extended to the low-{\sigma} regime of dEs.
The ages in our sample show more scatter at lower {\sigma} values, indicative
of less massive galaxies being affected by the environment to a higher degree.
The shape of the age-{\sigma} relation for cluster vs. non-cluster galaxies
suggests that cluster environment speeds up the placing of galaxies on the red
sequence. While the scaling relations are tighter for cluster than for the
field/group objects, we find no evidence for a difference in average population
characteristics of the two samples. We investigate the properties of our sample
in the Virgo cluster as a function of number density (rather than simple
clustrocentric distance) and find that dE ages negatively correlate with the
local density, likely because galaxies in regions of lower density are later
arrivals to the cluster or have experienced less pre-processing in groups, and
consequently used up their gas reservoir more recently. Overall, dE properties
correlate more strongly with density than those of massive ETGs, which was
expected as less massive galaxies are more susceptible to external influences.
