  Spectrum shape measurements in nuclear $\beta$ decay can be used to test
physics beyond the Standard Model with results being complementary to
high-energy collider experiments. In particular, Beyond Standard Model
sensitivity of the weak interaction is expressed through the so-called Fierz
interference term. Additionally, the $\beta$ spectrum shape is a useful tool to
probe Standard Model effects, among which the most prominent is \textit{weak
magnetism}, a higher-order recoil correction induced by nuclear pion exchange.
To study effects in the $\beta$ spectrum shape at a precision level competitive
with the LHC, a new spectrometer was designed and built. It consists of a 3D
low-pressure gas electron tracker and a plastic scintillator used for
triggering the data acquisition and recording the $\beta$ particle energy. In
this Letter, the results from $\beta$ spectrum shape measurements on the
allowed Gamow-Teller transition $^{114}\text{In} \rightarrow ^{114}\text{Sn}$
are presented, including a first extraction of the weak magnetism form factor
in the high nuclear mass range and a new estimate of the $90\%$ confidence
interval for the Fierz interference term.
