TINDER, Circuit Judge.

In 2003, Mark Hall pleaded guilty to one charge of conspiracy to possess with intent to distribute over 50 grams of cocaine base and more than 5 kg of a mixture containing cocaine. See 21 U.S.C. §§ 841(a)(1) and 846. In his written plea agreement, Hall acknowledged that the amount of crack cocaine involved in his offense was more than 1.5 kg. This is important, because the amount of crack involved in the offense controlled his sentence, having triggered the highest offense level he could receive for the controlled substance conviction. Pursuant to his plea agreement, Hall was sentenced in 2006 to 131 months' imprisonment (one-half of the low end of the Guidelines-recommended range of 262 to 327 months) because of his assistance to the government. See U.S.S.G. § 5K1.1. This was a binding sentencing recommendation, as allowed by Fed.R.Crim.P. 11(c)(1)(C).

In 2007, the United States Sentencing Commission amended the sentencing guidelines, reducing the base offense level for crack cocaine amounts in order to ameliorate the disparity between crack and powder cocaine sentences. U.S. Sentencing Guidelines Manual, supp. to app. C, 221-26 (2008) (amendment 706). The Commission gave retroactive effect to this amendment. See U.S.S.G. § 1B1.10(c). When Hall was sentenced, an offense involving 1.5 kg or more of cocaine base resulted in the highest drug base offense level of 38. U.S.S.G. § 2D1.1(c)(1) (2005). After the amendment, offenses involving between 1.5 and 4.5 kg of cocaine base triggered a base offense level of only 36, U.S.S.G. § 2D1.1(c)(2) (2007); the maximum drug base offense level of 38 now does not kick in until the crime involves 4.5 kg or more of cocaine base, id. § 2D1.1(c)(1) (2007).

Hall believed that, as a result of this amendment, he would be eligible for a reduced sentence, because he admitted in his plea agreement, remember, to possessing only more than 1.5 kg of cocaine base. If the amended guidelines apply to his sentence, a finding that he possessed only 1.5 kg drops his base offense level to 36; with the rest of his enhancements and reductions, he ends up with a total offense level of 35, which combined with his category III criminal history, results in a sentence of between 210 and 262 months. U.S.S.G. ch. 5, pt. A (Sentencing Table). Half of the low-end of this range is 105 months, which is below the statutory minimum for the offense, and 26 months less than his current sentence.

Hall filed a motion to modify his sentence pursuant to 18 U.S.C. § 3582(c)(2). That section allows "a defendant who has been sentenced to a term of imprisonment based on a sentencing range that has subsequently been lowered by the Sentencing Commission" to file a motion to reduce his sentence. In conjunction with his § 3582(c)(2) motion, Hall also filed a motion for an evidentiary hearing and an opportunity to present testimonial evidence proving that he was eligible, based on his drug quantity, for the lower sentence. Both motions were denied. Hall appeals.

We review the trial judge's determination of a § 3582(c)(2) motion, including the decision whether to appoint counsel or hold a hearing, for abuse of discretion. United States v. Young, 555 F.3d 611, 615 (7th Cir. 2009). Here, the district court relied on Hall's plea agreement to support his finding that Hall was not eligible for a modification of his sentence under 18 U.S.C. § 3582(c)(2). While paragraph 7(b) of the agreement set out Hall's admission that he possessed more than 1.5 kg of crack in connection with his offense, the district judge also looked at paragraph 5, where, in admitting the facts supporting the guilty plea, Hall generally admitted that over the course of the conspiracy offense he dealt in a far greater amount of cocaine in powder and crack form. We say "generally admitted" because paragraph 5 of the agreement is long on generalities and broad-ranging estimates but short on specifics and precision.

The judge relied, in denying the § 3582(c)(2) motion, on these key admissions from paragraph 5 about the quantity of drugs that Hall was dealing: "From about 1988 to April 1990, defendant . . . sold about 1 to 3 kilograms of powder cocaine per month. . . . From about April 1990 to 1993, defendant sold about 1 kilogram of cocaine per month. From about 1998 to 1999, defendant sold about 1/4 kilogram of crack cocaine . . . per month. From about 1999 to August 2000, defendant sold 1 to 2 kilograms of powder and crack cocaine every month."

Tallied up, the admitted conduct in the fifth paragraph of the plea agreement shows that the defendant was involved in sales of well over 4.5 kg of cocaine. The district court found that Hall was responsible, based on paragraph 5 of his agreement, for "various amounts of crack cocaine that totaled 23 to 43 kilograms for the time period [from] January 1998 through August 2000." On this basis, the trial court found that Hall was ineligible for a sentence adjustment and, without a hearing, refused to modify defendant's sentence. Keep in mind that this finding was made in addressing the § 3582(c)(2) motion, not at the original sentencing. For purposes of the original sentencing, the court and the parties were satisfied with a finding that the crack involved in Hall's offense exceeded 1.5 kg.

Here's the problem: all the cocaine (both crack and powder) sold in the conspiracy adds up to over 4.5 kg, and Hall's sentence was based solely on the crack cocaine amount. (Hall would have needed to be associated with sales of over 150 kg of powder cocaine to reach the top offense level for his crime; the government did not try to make this showing and our rough calculations come up with about 102 kg of total cocaine attributable to Hall after we construe the ambiguities in the agreement in his favor. We further doubt that, under U.S.S.G. § 1B1.10, Hall could be resentenced based on the powder cocaine involved in the conspiracy and the government does not press this argument.) The total amount of crack sold in connection with the conspiracy, as admitted in the two relevant paragraphs of the plea agreement, is unclear, and a reasonable reading of the facts could result in a finding that Hall's conduct involved less than 4.5 kg of crack. Thus, the district court ignored an ambiguity in the facts and misapprehended the content of Hall's plea admissions. Accordingly, we find that the district judge's denial of Hall's § 3582(c)(2) motion was an abuse of discretion. United States v. Paul, 542 F.3d 596, 599 (7th Cir. 2008) ("A court abuses its discretion when it resolves a matter in a way that no reasonable jurist would, or when its decision strikes us as fundamentally wrong [or] arbitrary. . . .").

Hall goes further to argue that on remand, he must be resentenced only on his admission that he possessed 1.5 kg of crack. He bases this on the statement in U.S.S.G. § 1B1.10(a)(3) that "proceedings under 18 U.S.C. § 3582(c)(2) and this policy statement do not constitute a full resentencing of the defendant." Hall therefore thinks that the judge should limit his resentencing to a specific application of the revised sentencing guideline for cocaine base amounts between 1.5 and 4.5 kg. Hall's argument proceeds from the theory that on resentencing, the judge will be bound only by the determination in paragraph 7(b) of the plea agreement and that considering paragraph 5 would be in essence a new factual finding. Such a factual finding on a § 3582(c)(2) motion, Hall argues, is improper. See United States v. Tidwell, 178 F.3d 946, 949 (7th Cir. 1999) (A § 3582(c) proceeding "is not a do-over of an original sentencing proceeding. . . ."). But, Hall ignores the fundamental ambiguity in his plea agreement — the admission to possessing more than 1.5 kg — and the import that this ambiguity has acquired since the amendment to the Guidelines. The question the district judge must answer is simple: How much more? This should be the subject of inquiry on remand.

One final question remains before we order a remand. The district court also relied on its consideration of the § 3553(a) factors as an alternate basis for denying the defendant's motion for resentencing. The court stated that it "would find — as it did at the time of sentencing — that a 262-327 month range is appropriate when considering the § 3553(a) factors. The very large quantities of crack cocaine involved, the past criminal conduct of the defendant in relation to the term imposed, the need for deterrence of like offenses, the protection of the public, and defendant's need for rehabilitation all support such a range." The question is whether this finding makes the district court's inaccurate factual determination harmless.

We think it does not; the court's application of the § 3553(a) factors was infected by the same error as its initial decision that Hall is not eligible for resentencing. As we have established, the court's determination, on Hall's motion to reduce his sentence, of the crack cocaine quantity involved in his offense was flawed; reliance on the same crack cocaine quantity in its alternative § 3553(a) analysis was therefore also flawed. Remand for an accurate determination is therefore appropriate.

We also note that there are a lot of thorny issues involved in the interplay between Rule 11(c)(1)(C) plea agreements and resentencing procedures under 18 U.S.C. § 3582(c)(2), namely whether Rule 11(c)(1)(C) plea agreements are subject to motions for resentencing. See United States v. Main, 579 F.3d 200, 202-04 (2d Cir. 2009) (collecting cases). Given the district court's decision, the parties' arguments and briefs, and our disposition of the case, we need not reach these issues, but the parties would do well to raise and fully brief them before the district court.

Accordingly, we REVERSE and REMAND for further proceedings consistent with this opinion.