Re: Derivative of a modular form is not a modular form

[Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>]

* Emmanuel Royer, LMBP [2018-01-25 22:30]:
> Dear all,
> 
> The derivative of the Eisenstein series of weight 4 is not a modular form.
> 
> However,
> 
> M4=mfinit([1,4]);M6=mfinit([1,6]);
> E4=mfEk(4);E6=mfEk(6);
> dE4=mfderiv(E4);mfspace(M6,dE4)
> 
> returns 0 meaning that the derivative of weight 4 is in the newspace of weight 6.

Yes, this is expected.

(22:57) gp > ??14
[...]
   A  number of creation functions and operations are provided.   It is however
important  to  note  that  strictly  speaking  some  of these operations create
objects  which  are  not  modular  forms:  typical  examples  are derivation or
integration  of  modular forms,  the Eisenstein series E_2,  eta quotients,  or
quotients of modular forms. These objects are nonetheless very important in the
theory, so are not considered as errors; however the user must be aware that no
attempt  is  made to check that the objects that he handles are really modular.
[...]


I.e. no attempt is made to ensure that the quasi-modular object that you
create is indeed modular. And when it is not most functions will return junk.
I just improved mfspace documentation that apparently asserted that -1 would
be correctly returned when the function did not belong to the space. But all
that was provisional on the first assumption in the description : that f would
be a *modular* form. (Which it is not in your example.)

Cheers,

    K.B.
--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite de Bordeaux         Fax: (+33) (0)5 40 00 21 23
351, cours de la Liberation    http://www.math.u-bordeaux.fr/~kbelabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux.fr/  [PARI/GP]
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