Observations of transiting gas giant exoplanets have revealed a pervasive depletion of methane
1
–
4
, which has only recently been identified atmospherically
5
,
6
. The depletion is thought to be maintained by disequilibrium processes such as photochemistry or mixing from a hotter interior
7
–
9
. However, the interiors are largely unconstrained along with the vertical mixing strength and only upper limits on the CH
4
depletion have been available. The warm Neptune WASP-107b stands out among exoplanets with an unusually low density, reported low core mass
10
, and temperatures amenable to CH
4
, though previous observations have yet to find the molecule
2
,
4
. Here we present a JWST-NIRSpec transmission spectrum of WASP-107b that shows features from both SO
2
and CH
4
along with H
2
O, CO
2
, and CO. We detect methane with 4.2
σ
significance at an abundance of 1.0 ± 0.5 ppm, which is depleted by 3 orders of magnitude relative to equilibrium expectations. Our results are highly constraining for the atmosphere and interior, which indicate the envelope has a super-solar metallicity of 43 ± 8 × solar, a hot interior with an intrinsic temperature of
T
int
= 460 ± 40 K, and vigorous vertical mixing which depletes CH
4
with a diffusion coefficient of
K
zz
= 10
11.6±0.1
cm
2
s
−1
. Photochemistry has a negligible effect on the CH
4
abundance but is needed to account for the SO
2
. We infer a core mass of
, which is much higher than previous upper limits
10
, releasing a tension with core-accretion models
11
.