WOLOHOJIAN, J.

We consider whether admission of a ballistician's certificate in violation of the confrontation clause of the Sixth Amendment to the United States Constitution was harmless beyond a reasonable doubt and conclude that it was not.

The defendant, who was found near his truck that had a loaded gun in its unlocked glove compartment, was convicted, after a bench trial, of unlawful possession of a firearm (G. L. c. 269, § 10[h]), carrying a firearm without a license (G. L. c.

269, § 10[a]), and improper storage of a firearm (G. L. c. 140, § 131L[a]). All three crimes required the Commonwealth to prove that the gun was a "firearm" as defined in G.L. c. 140, § 121, specifically:

"a pistol, revolver or other weapon of any description, loaded or unloaded, from which a shot or bullet can be discharged and of which the length of the barrel or barrels is less than 16 inches or 18 inches in the case of a shotgun as originally manufactured."

G.L. c. 140, § 121, as appearing in St. 1998, c. 180, § 8. Although the Commonwealth's burden to prove the object a "firearm" in its statutory sense is not a heavy one, Commonwealth v. Nieves, 43 Mass. App. Ct. 1, 2 (1997), the Commonwealth must present sufficient evidence from which a fact finder could reasonably conclude both that the gun can fire a bullet and that it is within the specified dimensions. Commonwealth v. Paiva, 71 Mass. App. Ct. 411, 412-413 (2008).

At trial, the Commonwealth relied on G.L. c. 140, § 121A, as amended through St. 1996, c. 151, § 302, to meet its burden of proof both with respect to dimension and operability. Section 121A provides that a "certificate by a ballistics expert . . . shall be prima facie evidence of his findings as to whether or not the item furnished is a firearm" within the meaning of G.L. c. 140, § 121. The certificate in this case stated that the gun's barrel was four and one-half inches long and that the gun was test fired with no malfunctions. It also contained the ballistician's opinion on the ultimate issue of fact: namely, that the gun was a firearm "within meaning of and as defined in Massachusetts General Law Chapter 140 Section 121." See Commonwealth v. Sperrazza, 372 Mass. 667, 670 (1977) (whether gun is firearm within meaning of statute is question of fact); Commonwealth v. Nieves, 43 Mass. App. Ct. at 3 (same).

The defendant timely objected to the admission of the certificate, specifically arguing that its admission without an opportunity to confront the ballistician violated his Sixth Amendment confrontation right as explained in Crawford v. Washington, 541 U.S. 36 (2004). The objection was well-founded, and it was subsequently determined that it was error to admit the certificate over it. Melendez-Diaz v. Massachusetts, 129 S. Ct. 2527, 2542 (2009). See Morales v. Massachusetts, 129 S. Ct. 2858 (2009), in which the United States Supreme Court vacated the judgment of this court in Commonwealth v. Morales, 71 Mass. App. Ct. 587, 588-589 (2008), a case involving the admission of a ballistics certificate.

What remains, then, is to determine whether the error was harmless beyond a reasonable doubt. Chapman v. California, 386 U.S. 18. 24 (1967). It is the Commonwealth's burden to show that the "'wrongfully admitted evidence did not contribute to the verdicts." Commonwealth v. Charms, 443 Mass. 752, 765, cert. denied, 546 U.S. 870 (2005). The issue is not whether the remaining evidence was sufficient to support the convictions. See Commonwealth v. D'Agostino, 421 Mass. 281, 287 (1995) (even where remaining evidence was sufficient to support conviction, error was not harmless and conviction reversed); Commonwealth v. Alicia, 6 Mass. App. Ct. 904, 905 (1978) (same). Instead, we consider as a whole the context in which the error occurred, which may include, among other things, "(1) the relationship between the evidence and the premise of the defense; (2) who introduced the issue at trial; (3) the weight or quantum of evidence of guilt; (4) the frequency of the reference; and (5) the availability or effect of curative instructions." Commonwealth v. Isabelle, 444 Mass. 416, 419 (2005), citing Commonwealth v. Mahdi, 388 Mass. 679, 696-697 (1983). See Commonwealth v. Rodriguez, ante 235, 241 (2009).

Assessing these factors in toto, we are not persuaded that the Commonwealth has met its burden of demonstrating that the erroneous admission of the ballistician's certificate was harmless in this case. As to the first factor, it is true that the defense theory during closing was that the defendant did not know the firearm was in his truck, rather than that it was not a "firearm" within the meaning of the statute. Although this weighs in favor of the Commonwealth, we must also keep in mind the context in which the closing was made. The certificate was admitted over the defendant's objection on constitutional grounds by a judge who was also the trier of fact. The judge had also denied the defendant's motion for a required finding based on the same argument. At the time of trial, Massachusetts case law provided that admission of ballistics certificates without an opportunity to cross-examine the affiant did not violate the confrontation clause of the Sixth Amendment. Commonwealth v. Morales, 71 Mass. App. Ct. 587 (2008). See Commonwealth v. Verde, 444 Mass. 279, 283 (2005). It is neither realistic nor fair in these circumstances to place much weight on the fact that the defendant's closing did not attack the contents of the certificate.

We view the second factor similarly. Although the Common-wealth was the party that introduced the evidence at trial without a live witness, it did so in a legal landscape where that was permissible. Thus, we consider it equally unrealistic and unfair to place much weight on the fact that it was the Commonwealth that introduced the evidence.

The third factor requires more discussion. There was no direct evidence (apart from the certificate) that the gun was operable at the time of the offense. An inference of operability may be drawn where, as here, in addition to the admission of the gun, there is evidence that the gun was loaded at the time of the offense. Commonwealth v. Fancy, 349 Mass. 196, 204 (1965). Commonwealth v. Stallions, 9 Mass. App. Ct. 23, 26 (1980). However, a gun may be loaded and, at the same time, not capable of discharging a bullet due to a malfunction or misadjustment in the firing pin or some other part of the gun's mechanism.

Here, there was no evidence concerning the gun's mechanism. Nor was there evidence as to when, or if, the gun had previously been fired. Contrast Commonwealth v. Sylvester, 35 Mass. App. Ct. 906 (1993) (fact that gun was fired four or five times at officers was enough to show gun was in working order); Common-wealth v. Mendes, ante 390, 397 (2009) ("testimony of three audible shots, the three empty casings, and the smell of gun-powder" established operability of firearm beyond reasonable doubt). Thus, although the fact that the gun had ammunition in it bore on the question whether the gun was operable, it was not of such strength to conclude that the admission of the ballistics certificate did not contribute to the findings.

Turning to the fourth factor, the Commonwealth elicited testimony as to the contents of the certificate during its direct case. In addition, the Commonwealth relied on nothing other than the certificate during its closing to establish that the gun was a firearm within the meaning of G.L. c. 140, § 121.

The final factor does not directly apply in this case. This was a bench trial, and accordingly, there were no instructions, curative or otherwise. The factor is designed to assess whether the jury were instructed in such a way as to reduce or eliminate the risk that they considered the erroneously admitted evidence in reaching their verdict. Here, under the established Massachusetts case law at the time of the trial, the judge admitted the certificate over the defendant's objection and denied the defendant's motion for a required finding. Commonwealth v. Morales, 71 Mass. App. Ct. 587 (2008). We can presume that he instructed himself, in accordance with the Massachusetts case law, that the certificate could be considered as prima facie evidence that the gun was a firearm within the meaning of G.L. c. 140, § 121.

Considering all of these factors together, we cannot conclude that the admission of the ballistics certificate in this case did not contribute to the findings. Chapman v. California, 386 U.S. at 24.

Judgments reversed. Findings set aside.