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A027640
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Poincaré series [or Poincare series] for ring of modular forms of genus 2.
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4
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1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 3, 0, 2, 0, 4, 0, 4, 0, 5, 0, 6, 0, 8, 0, 7, 0, 10, 0, 11, 0, 12, 0, 14, 1, 17, 0, 16, 1, 21, 1, 22, 1, 24, 2, 27, 3, 31, 2, 31, 4, 37, 4, 39, 5, 42, 6, 46, 8, 52, 7, 52, 10, 60, 11, 63, 12, 67, 14
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OFFSET
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0,11
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COMMENTS
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a(k) for k>0 is the dimension of the space of Siegel modular forms of genus 2 and weight k (for the full modular group Gamma_2). - Kilian Kilger (kilian(AT)nihilnovi.de), Sep 24 2009
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REFERENCES
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B. Runge, On Siegel modular forms I, J. Reine Angew. Math., 436 (1993), 57-85.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,1,1,0,0,-1,-1,-1,1,0,0,1,-1,-1,-1,0,0,1,1,1,0,0,0,-1).
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FORMULA
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G.f.: (1+x^35)/((1-x^4)*(1-x^6)*(1-x^10)*(1-x^12)).
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MATHEMATICA
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Table[SeriesCoefficient[Series[(1+t^(35))/((1-t^4) (1-t^6)(1-t^(10)) (1-t^(12))), {t, 0, 100}], i], {i, 0, 100}] (* Kilian Kilger (kilian(AT)nihilnovi.de), Sep 24 2009 *)
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PROG
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(PARI) Vec((1+x^35)/((1-x^4)*(1-x^6)*(1-x^10)*(1-x^12)) + O(x^100)) \\ Colin Barker, Jul 27 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 100); Coefficients(R!( (1+x^35)/((1-x^4)*(1-x^6)*(1-x^10)*(1-x^12)) )); // G. C. Greubel, Aug 04 2022
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x^35)/((1-x^4)*(1-x^6)*(1-x^10)*(1-x^12)) ).list()
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CROSSREFS
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Cf. A165685 for the corresponding dimension of the space of cusp forms. - Kilian Kilger (kilian(AT)nihilnovi.de), Sep 24 2009
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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