due to the 737 having greater than 30seats, it would be part 125 unless the operator has obtained operations specifications under 121 then it would be required to be operated to 121 standards-however I don't think that it could be operated under 135---but in general only one air carrier certification is given by the FAA-which would logically be the most restrictive operation undertaken by the operator...
§ 135.2 Compliance schedule for operators that transition to part 121 of this chapter; certain new entrant operators.
top
(a) Applicability. This section applies to the following:
(1) Each certificate holder that was issued an air carrier or operating certificate and operations specifications under the requirements of part 135 of this chapter or under SFAR No. 382 of 14 CFR part 121 before January 19, 1996, and that conducts scheduled passenger-carrying operations with:
(i) Nontransport category turbopropeller powered airplanes type certificated after December 31, 1964, that have a passenger seat configuration of 1019 seats;
(ii) Transport category turbopropeller powered airplanes that have a passenger seat configuration of 2030 seats; or
(iii) Turbojet engine powered airplanes having a passenger seat configuration of 130 seats.
(2) Each person who, after January 19, 1996, applies for or obtains an initial air carrier or operating certificate and operations specifications to conduct scheduled passenger-carrying operations in the kinds of airplanes described in paragraphs (a)(1)(i), (a)(1)(ii), or paragraph (a)(1)(iii) of this section.
(b) Obtaining operations specifications. A certificate holder described in paragraph (a)(1) of this section may not, after March 20, 1997, operate an airplane described in paragraphs (a)(1)(i), (a)(1)(ii), or (a)(1)(iii) of this section in scheduled passenger-carrying operations, unless it obtains operations specifications to conduct its scheduled operations under part 121 of this chapter on or before March 20, 1997.
(c) Regular or accelerated compliance. Except as provided in paragraphs (d), and (e) of this section, each certificate holder described in paragraph (a)(1) of this section shall comply with each applicable requirement of part 121 of this chapter on and after March 20, 1997 or on and after the date on which the certificate holder is issued operations specifications under this part, whichever occurs first. Except as provided in paragraphs (d) and (e) of this section, each person described in paragraph (a)(2) of this section shall comply with each applicable requirement of part 121 of this chapter on and after the date on which that person is issued a certificate and operations specifications under part 121 of this chapter.
(d) Delayed compliance dates. Unless paragraph (e) of this section specifies an earlier compliance date, no certificate holder that is covered by paragraph (a) of this section may operate an airplane in 14 CFR part 121 operations on or after a date listed in this paragraph unless that airplane meets the applicable requirement of this paragraph: but as you can see it gets involved
(1) Nontransport category turbopropeller powered airplanes type certificated after December 31, 1964, that have a passenger seat configuration of 1019 seats. No certificate holder may operate under this part an airplane that is described in paragraph (a)(1)(i) of this section on or after a date listed in paragraph (d)(1) of this section unless that airplane meets the applicable requirement listed in paragraph (d)(1) of this section:
§ 125.1 Applicability.
top
(a) Except as provided in paragraphs (b), (c) and (d) of this section, this part prescribes rules governing the operations of U.S.-registered civil airplanes which have a seating configuration of 20 or more passengers or a maximum payload capacity of 6,000 pounds or more when common carriage is not involved.
(b) The rules of this part do not apply to the operations of airplanes specified in paragraph (a) of this section, when
(1) They are required to be operated under part 121, 129, 135, or 137 of this chapter;
(2) They have been issued restricted, limited, or provisional airworthiness certificates, special flight permits, or experimental certificates;
(3) They are being operated by a part 125 certificate holder without carrying passengers or cargo under part 91 for training, ferrying, positioning, or maintenance purposes;
(4) They are being operated under part 91 by an operator certificated to operate those airplanes under the rules of parts 121, 135, or 137 of this chapter, they are being operated under the applicable rules of part 121 or part 135 of this chapter by an applicant for a certificate under part 119 of this chapter or they are being operated by a foreign air carrier or a foreign person engaged in common carriage solely outside the United States under part 91 of this chapter;
(5) They are being operated under a deviation authority issued under §125.3;
(6) They are being operated under part 91, subpart K by a fractional owner as defined in §91.1001 of this chapter; or
(7) They are being operated by a fractional ownership program manager as defined in §91.1001 of this chapter, for training, ferrying, positioning, maintenance, or demonstration purposes under part 91 of this chapter and without carrying passengers or cargo for compensation or hire except as permitted for demonstration flights under §91.501(b)(3) of this chapter.
(c) The rules of this part, except §125.247, do not apply to the operation of airplanes specified in paragraph (a) when they are operated outside the United States by a person who is not a citizen of the United States.
(d) The provisions of this part apply to each person on board an aircraft being operated under this part, unless otherwise specified.
(e) This part also establishes requirements for operators to take actions to support the continued airworthiness of each airplane.
unfortunately you need FAR 119 too
Electronic Code of Federal Regulations: