OFFSET
1,12
COMMENTS
Also the dimension of the largest Hecke-closed subspace of forms in S_k(Gamma_2) which satisfy the Ramanujan-Petersson 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 L-functions, Math. Ann. 256(3), p. 323-340, 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^6-x^2-x-1) / ((1-x^2)*(1-x^3)*(1-x^5)*(1-x^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