element in submodule

[Peng]

I encountered the following problem:

s is the trivial submodule of quo, where quo is a quotient module of modular symbol subspace.  

The zero element b of quo should be an element of s, but sage says no when I do the following process:

# create modular symbol subspace

sage: S = ModularSymbols(Gamma1(13),2).cuspidal_subspace()

# create the quotient module

sage: ker = S.module().subspace([0])

sage: quo=S.module()/ker

# now we have the submodule of quo

sage: s = quo.submodule([])

# we get zero of quo in the following way

sage: a = (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)

sage: aa=S.module()(a)

sage: b=quo(aa)

sage: b in s

it gives FALSE

Anybody has any idea where I am wrong? Thank you!