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A027640 Poincaré series [or Poincare series] for ring of modular forms of genus 2. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

COMMENTS

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

REFERENCES

J. Igusa, On Siegel modular forms of genus 2 (II), Amer. J. Math., 86 (1964), 392-412, esp. p. 402.

B. Runge, On Siegel modular forms I, J. Reine Angew. Math., 436 (1993), 57-85.

LINKS

Table of n, a(n) for n=0..69.

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).

MAPLE

(1+x^35)/((1-x^4)*(1-x^6)*(1-x^10)*(1-x^12));

MATHEMATICA

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 *)

CROSSREFS

Cf. A165685 for the corresponding dimension of the space of cusp forms. - Kilian Kilger (kilian(AT)nihilnovi.de), Sep 24 2009

Sequence in context: A128145 A128143 A292561 * A194666 A229946 A127460

Adjacent sequences:  A027637 A027638 A027639 * A027641 A027642 A027643

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 20 10:29 EST 2018. Contains 299385 sequences. (Running on oeis4.)