1. Parshas Ki Sisa:

Aliyah of Levi for Parshas Haeigel:[1] The Levi is called up to read the Parshas Haeigel.[2] [Thus, it ends up that the Aliyos of Kohen and Levi of Parshas Ki Sisa include more than half of the verses in the Parsha [79 Pesukim out of 139]. This distribution of the verses in the first and second Aliyah is an age-old custom of many communities, and is based on the idea that we do not want a non-Levi to read from the portion discussing the sin of the golden calf which his ancestors were guilty of worshipping.]

If there is no Levi in Shul: There is no source which prohibits a Kohen or Yisrael from getting the Aliyah of Levi in which the Parshas Haeigel is read, and thus must be done if there is no Kohen or Levi in Shul.[3] In the event that there is a Kohen in Shul, but no Levi, then the Kohen is to receive also the Aliyah of Levi, as is usually done.[4]

If there is no Kohen in Shul:[5] In the event that there is no Kohen in Shul, then the Levi is to receive the Aliyah of Kohen and read up until the end of the Parshas Haeigel in Levi. The remaining verses until Shlishi are then to be read for the 2^nd Aliyah. Alternatively, one can divide one of the other Aliyos in two.

Reading in low voice:[6] The section of Parshas Haeigel in Parshas Ki Sisa is to be read in a low tone.

[1] See M”A 428:8 in name of Kneses Hagedola “Also, the custom is to call a Levi for the reading of the Eigel.”; Machatzis Hashekel ibid that the reason for this is because the Levi did not sin with the golden calf; Beir Heiytiv 428:7; Sefer Chaim 9:23; Kaf Hachaim 428:37; See also M”A 138:4; Noheig Katzon Yosef Ki Sisa, which is evident unlike the custom in M”A, as the Shelishi would read Parshas Haeigel; Imrei Halacha p. 233

[2] The reason: The tribe of Levi was the only tribe who did not sin with the golden calf, and it is hence most appropriate for them to read it rather than make someone who belongs to a different tribe which participated in the sin of the golden calf, read about his tribe’s sin. For this reason, we read an extraordinary number of verses in the first Aliyah of Kohen, up until the portion of the golden calf, in order so the entire portion discussing the golden calf can be read as Levi. [See M”A ibid; Machatzis Hashekel ibid]

The reason a Kohen is not given the Aliyah: Now, the reason that the Kohen does not read it, some say is because Aaron himself participated in the sin and was the one who built the golden calf to begin with. [Sefer Chaim 9:23; Kaf Hachaim 428:37]

[3] Beis Aba 4 p. 337

[4] Imrei Halacha 429 in name of many Poskei Doreinu; Beis Aba 4 p. 337

[5] Imrei Halacha 429 in name of many Poskei Doreinu; Beis Aba 4 p. 337

[6] M”A 428:8 in name of Kneses Hagedola