Let
D
D
be the incidence graph of the projective plane over
F
3
\mathbb {F}_3
. The Artin group of the graph
D
D
maps onto the bimonster and a complex hyperbolic reflection group
Γ
\Gamma
acting on
13
13
dimensional complex hyperbolic space
Y
Y
. The generators of the Artin group are mapped to elements of order
2
2
(resp.
3
3
) in the bimonster (resp.
Γ
\Gamma
). Let
Y
∘
⊆
Y
Y^{\circ } \subseteq Y
be the complement of the union of the mirrors of
Γ
\Gamma
. Daniel Allcock has conjectured that the orbifold fundamental group of
Y
∘
/
Γ
Y^{\circ }/\Gamma
surjects onto the bimonster.
In this article we study the reflection group
Γ
\Gamma
. Our main result shows that there is homomorphism from the Artin group of
D
D
to the orbifold fundamental group of
Y
∘
/
Γ
Y^{\circ }/\Gamma
, obtained by sending the Artin generators to the generators of monodromy around the mirrors of the generating reflections in
Γ
\Gamma
. This answers a question in Allcock’s article “A monstrous proposal” and takes a step towards the proof of Allcock’s conjecture. The finite group
PGL
(
3
,
F
3
)
⊆
A
u
t
(
D
)
\operatorname {PGL}(3, \mathbb {F}_3) \subseteq \mathrm {Aut}(D)
acts on
Y
Y
and fixes a complex hyperbolic line pointwise. We show that the restriction of
Γ
\Gamma
-invariant meromorphic automorphic forms on
Y
Y
to the complex hyperbolic line fixed by
PGL
(
3
,
F
3
)
\operatorname {PGL}(3, \mathbb {F}_3)
gives meromorphic modular forms of level
13
13
.