

A165686


Dimension of the space of Siegel cusp forms of genus 2 and weight 2k which are not SaitoKurokawa lifts of forms of genus 1.


0



0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 4, 5, 6, 8, 8, 11, 12, 14, 16, 19, 20, 24, 26, 29, 32, 37, 38, 44, 47, 51, 56, 62, 64, 72, 76, 82, 88, 96, 99, 109, 115, 122, 130, 140, 144, 157, 164, 173, 183, 195, 201, 216, 225, 236, 248, 263, 270, 288, 299, 312, 327, 344, 353, 374
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OFFSET

1,12


COMMENTS

Also the dimension of the largest Heckeclosed subspace of forms in S_k(Gamma_2) which satisfy the RamanujanPetersson conjecture. These forms are also characterized by the property that their (Andrianov) spinor zeta function does not have any pole.


REFERENCES

M. Eichler and D. Zagier, The Theory of Jacobi Forms, Birkhaeusser, 1985.
T. Oda, On the poles of Andrianov Lfunctions, Math. Ann. 256(3), p. 323340, 1981.
R. Weissauer, The Ramanujan conjecture for genus two Siegel modular forms (an application of the trace formula). Preprint, Mannheim (1993)


LINKS

Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,0,1,1,2,1,1,0,0,1,1,0,1).


FORMULA

Conjectured G.f.: x^10*(x^7+x^6x^2x1) / ((1x^2)*(1x^3)*(1x^5)*(1x^6)).  Colin Barker, Mar 30 2013


EXAMPLE

a(20)=1 because there is exactly one Siegel modular form of genus 2 and weight 20 which is not a lift of some form of genus 1.


CROSSREFS



KEYWORD

nonn,easy


AUTHOR

Kilian Kilger (kilian(AT)nihilnovi.de), Sep 26 2009


STATUS

approved



