Print scaling factors in eta-products

modular_forms

I have the useful command:

EtaGroup(8).basis()[0].r(2)

which will return the first exponent in (eta_2)^-4 (eta_4)^12 (eta_8)^-8; namely -4. Similarly

EtaGroup(8).basis()[0].r(4)

will return 12 etc. I want to extract the scaling factors though. That is, I want to print 2 or 4 or 8 in the expression (eta_2)^-4 (eta_4)^12 (eta_8)^-8 How??

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answered 4 years ago

FrédéricC

5426 ●4 ●44 ●121

Like this

sage: e = EtaGroup(8).basis()[0]                                                
sage: e                                                                         
Eta product of level 8 : (eta_2)^-4 (eta_4)^12 (eta_8)^-8
sage: e._rdict                                                                  
{2: -4, 4: 12, 8: -8}

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Very nice. Did not know this function. Thank you!

FundamentalDomain ( 4 years ago )

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Asked: 4 years ago

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Last updated: Jan 19 '21

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