Derivative of a modular form is not a modular form

Emmanuel Royer, LMBP on Thu, 25 Jan 2018 22:30:42 +0100

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Derivative of a modular form is not a modular form

To: pari-users@pari.math.u-bordeaux.fr
Subject: Derivative of a modular form is not a modular form
From: "Emmanuel Royer, LMBP" <emmanuel.royer@uca.fr>
Date: Thu, 25 Jan 2018 15:30:35 -0600
Delivery-date: Thu, 25 Jan 2018 22:30:42 +0100

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.

Best regards,
Emmanuel

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