  Context. The most recent determination of the solar chemical composition,
using a time-dependent, 3D hydrodynamical model of the solar atmosphere,
exhibits a significant decrease of C, N, O abundances compared to their
previous values. Solar models that use these new abundances are not consistent
with helioseismological determinations of the sound speed profile, the surface
helium abundance and the convection zone depth. Aims. We investigate the effect
of changes of solar abundances on low degree p-mode and g-mode characteristics
which are strong constraints of the solar core. We consider particularly the
increase of neon abundance in the new solar mixture in order to reduce the
discrepancy between models using new abundances and helioseismology. Methods.
The observational determinations of solar frequencies from the GOLF instrument
are used to test solar models computed with different chemical compositions. We
consider in particular the normalized small frequency spacings in the low
degree p-mode frequency range. Results. Low-degree small frequency spacings are
very sensitive to changes in the heavy-element abundances, notably neon. We
show that by considering all the seismic constraints, including the small
frequency spacings, a rather large increase of neon abundance by about (0.5 +/-
0.05)dex can be a good solution to the discrepancy between solar models that
use new abundances and low degree helioseismology, subject to adjusting
slightly the solar age and the highest abundances. We also show that the change
in solar abundances, notably neon, considerably affects g-mode frequencies,
with relative frequency differences between the old and the new models higher
than 1.5%
