"""
TESTS:

Test consistency between modular forms and modular symbols Eisenstein
series charpolys, which are computed in completely separate ways.

sage: for N in range(25,33):
...    m = ModularForms(N)
...    e = m.eisenstein_subspace()
...    f = e.hecke_polynomial(2)
...    g = ModularSymbols(N).eisenstein_submodule().hecke_polynomial(2)
...    print N, f == g
25 True
26 True
27 True
28 True
29 True
30 True
31 True
32 True

Another similar consistency check:
sage: for N in range(1,26):
...    eps = (N > 2 and DirichletGroup(N,QQ).0) or N
...    m = ModularForms(eps)
...    e = m.eisenstein_subspace()
...    f = e.hecke_polynomial(2)
...    g = ModularSymbols(eps).eisenstein_submodule().hecke_polynomial(2)
...    print N, f == g
1 True
2 True
3 True
4 True
5 True
6 True
7 True
8 True
9 True
10 True
11 True
12 True
13 True
14 True
15 True
16 True
17 True
18 True
19 True
20 True
21 True
22 True
23 True
24 True
25 True

We check that bug #8541 (traced to a linear algebra problem) is fixed::

    sage: f = CuspForms(DirichletGroup(5).0,5).0
    sage: f[15]
    30*zeta4 - 210
"""
