Eisenstein series are cusp forms?!

[ahorawa]

I found an example where the Eisenstein series seem to be cusp forms...

F:=QuadraticField(60);
prec := 10;
M:=GradedRingOfHMFs(F, prec);
N := Integers(F)*23;
H := HeckeCharacterGroup(N, [1,2]); 
chi := H.2^11;
M1chi := HMFSpace(M, N, [1,1], chi);
EisensteinBasis(M1chi);

[abhijit-mudigonda]

The narrow class number of $\mathbb{Q}(\sqrt{60})$ is $4$, and I think what might be happening here is that these forms vanish at the four cusps at infinity, but not at some of the other cusps. We know there are other cusps because the dimension of weight $1$ Eisenstein series is something like half the number of cusps.

I tried checking by squaring one of the basis vectors to see if I could put it in an upstairs space but it was taking too long, I'll try later with lower precision.

[edgarcosta]

There is something off here:

> F:=QuadraticField(60);
> prec := 10;
> M:=GradedRingOfHMFs(F, prec);
> N := Integers(F)*23;
> H := HeckeCharacterGroup(N, [1,2]);
> chi := H.2^11;
> M1chi := HMFSpace(M, N, [1,1], chi);
> foo := EisensteinBasis(M1chi);
> [[Coefficient(fbb, 0) : fbb in Components(f)] : f in foo];
[
[ 0, 0, 0, 0 ],
[ 0, 0, 0, 0 ],
[ 0, 0, 0, 0 ],
[ 0, 0, 0, 0 ]
]

[assaferan]

This space should not exist, as chi is not odd at infinity. This should return an error on creation, should be fixed in PR #390 .

[assaferan]

Ok, should really be fixed in PR #392