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Wednesday, May 21, 2025

Entry 69

II. Level 2. The McKay-Thompson series of class 2B for the Monster.

j2B(τ)=(d1d2)24
Examples: 
j2B(1210)=26U125=26(1+52)12j2B(1258)=26U1229=26(5+292)12j2B(1+52)=26U65=26(1+52)6j2B(1+132)=26U613=26(3+132)6j2B(1+372)=26U637=26(6+37)6
which have class number h(d)=2.  The quadratic irrationals Un are fundamental units, solutions to Pell equations x2ny2=1 as discussed in Level 1.

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