
752 P.2d 790 (1987)
107 N.M. 75
In the Matter of the Termination of Parental Rights of Maria Del Jesus JASSO, a/k/a Maria Del Jesus De Los Angeles, and of Antonio Cantu Torres, with respect to Antonio T., Jr., Leslie Anne T., Favian T., and Rosalinda T., Children.
STATE of New Mexico, ex rel., HUMAN SERVICES DEPARTMENT, Petitioner-Appellee,
v.
Maria Del Jesus JASSO, a/k/a Maria Del Jesus De Los Angeles, Respondent-Appellant.
No. 10135.
Court of Appeals of New Mexico.
September 29, 1987.
Steve H. Mazer, Albuquerque, for respondent-appellant.
Angela L. Adams, General Counsel, Peter Klages, John F. Petoskey, Asst. General Counsels, Santa Fe, for petitioner-appellee.
Jonathan M. Diener, Peter M. Cubra, Albuquerque, guardians ad litem.

OPINION
FRUMAN, Judge.
This case involves the termination of respondent's parental rights. The judgment of termination was filed on March 11, 1987. Respondent filed a motion for a new trial on March 23, 1987. The trial court conducted a hearing on the motion and rendered an oral decision denying the motion on April 13, 1987. On June 4, 1987, the trial court entered its order denying the motion for new trial. Respondent filed her notice of appeal on June 29, 1987. Our calendar notice proposed dismissal based on the untimely filing of the notice of appeal. Respondent has filed a memorandum in opposition to the calendar notice. For the reasons that follow, we dismiss the appeal.
A notice of appeal is required to be filed within thirty days after the filing of the judgment or order being appealed. SCRA 1986, 12-201(A). The judgment terminating respondent's parental rights was filed on March 11, 1987. Therefore, since an extension of time for filing the notice of appeal was neither sought nor granted, the last day for filing the notice was April 10, 1987. In her memorandum in opposition, respondent claims that her prior counsel's motion to withdraw gave reference to her intention to appeal, and, by granting the motion, the trial court impliedly granted an extension of time to appeal. We find no *791 reference in the motion to withdraw, or in the order granting the motion, of an intention to appeal. An extension of time to file an appeal does not arise by implication, and respondent's reference to White v. Singleton, 88 N.M. 262, 539 P.2d 1024 (Ct.App. 1975), does not provide authority to support this contention. The extension must be asked for and granted. R. 12-201(E). There is nothing in the record to show that a request for an extension of time in which to file the appeal had been made to the trial court.
Respondent claims that the order being appealed is the order denying her motion for a new trial and, therefore, the appeal is timely. The denial of a motion for a new trial is generally not appealable. Public Serv. Co. v. First Judicial Dist. Court, 65 N.M. 185, 334 P.2d 713 (1959); Harrison v. ICX, Illinois-California Express, Inc., 98 N.M. 247, 647 P.2d 880 (Ct. App. 1982). Where an appeal may properly be taken from a judgment, but has not been taken, a subsequent order refusing to amend or modify the judgment is not appealable, since the denial order merely confirms the finality of the judgment. Public Serv. Co. v. First Judicial Dist. Court. Respondent cites to Franco v. Federal Bldg. Serv., Inc., 98 N.M. 333, 648 P.2d 791 (1982), and Phelps Dodge Corp. v. Guerra, 92 N.M. 47, 582 P.2d 819 (1978), to support her argument that an order denying a motion for a new trial is appealable, regardless of how the motion is framed. We do not read these two cases as stating these propositions or as supporting this argument.
Respondent also claims that this court should accept jurisdiction because issues of general public interest and fundamental personal due process rights are at stake. In support of this claim, respondent cites to SCRA 1986, 12-216(B). We do not read this rule as permitting an extension of time in which to appeal; rather, the rule relates to raising certain issues on appeal when they were not raised below. See St. Vincent Hosp. v. Salazar, 95 N.M. 147, 619 P.2d 823 (1980).
Our courts have stated that the timely filing of a notice of appeal is jurisdictional. See Public Serv. Co. v. Wolf, 78 N.M. 221, 430 P.2d 379 (1967). Regardless of the potential merits of the arguments respondent has set forth in her docketing statement, this court does not have the prerogative of enlarging its jurisdictional limitations to consider those merits. See State v. Brinkley, 78 N.M. 39, 428 P.2d 13 (1967); Brazfield v. Mountain States Mut. Casualty Co., 93 N.M. 417, 600 P.2d 1207 (Ct.App. 1979).
Based upon the foregoing, we dismiss this appeal.
IT IS SO ORDERED.
BIVINS and APODACA, JJ., concur.
