  Recent measurements of magnetic field strength inside the radiative interior
of red giant stars open the way towards the characterization of the geometry of
stable large-scale magnetic fields. However, current measurements do not
properly constrain the topology of magnetic fields due to degeneracies on the
observed magnetic field signature on such $\ell=1$ mode frequencies. Efforts
focused towards unambiguous detections of magnetic field configurations are now
key to better understand angular momentum transport in stars. We investigate
the detectability of complex magnetic field topologies inside the radiative
interior of red giants. We focus on a field composed of a combination of a
dipole and a quadrupole (quadrudipole), and on an offset field. We explore the
potential of probing such magnetic field topologies from a combined measurement
of magnetic signatures on $\ell=1$ and quadrupolar ($\ell=2$) mixed mode
oscillation frequencies. We first derive the asymptotic theoretical formalism
for computing the asymmetric signature in frequency pattern for $\ell=2$ modes
due to a quadrudipole magnetic field. The degeneracy of the quadrudipole with a
dipole is lifted when considering both $\ell=1$ and $\ell=2$ mode frequencies.
In addition to the analytical derivation for the quadrudipole, we present the
prospect for complex magnetic field inversions using magnetic sensitivity
kernels from standard perturbation analysis for forward modeling. Using this
method, we demonstrate that offset fields may be mistaken for weak and centered
magnetic fields, resulting in underestimating magnetic field strength in
stellar cores. We emphasize the need to characterize $\ell=2$ mixed-mode
frequencies, (along with the currently characterized $\ell=1$ mixed modes), to
unveil the higher-order components of the geometry of buried magnetic fields,
and better constrain angular momentum transport inside stars.
