login
A352095
Dimension of the space of Siegel cusp forms of genus 3 and weight 2n.
1
0, 0, 0, 0, 0, 0, 1, 1, 3, 4, 6, 9, 14, 17, 27, 34, 46, 61, 82, 99, 135, 165, 208, 261, 325, 389, 490, 584, 708, 852, 1023, 1200, 1445, 1687, 1984, 2327, 2717, 3133, 3663, 4199, 4838, 5557, 6360, 7225, 8267, 9344, 10587, 11968, 13489, 15126, 17037, 19023
OFFSET
0,9
COMMENTS
There are no nonzero Siegel cusp forms of genus 3 and odd weight.
Sequence satisfies linear recurrence of order 54 for a(n) when n > 57.
LINKS
S. Tsuyumine, On Siegel modular forms of degree three, Amer. J. Math., 108 (1986), 831-832.
Index entries for linear recurrences with constant coefficients signature (1,0,0,0,0,2,-1,-1,1,0,-1,-1,-1,2,-1,-2,2,1,0,0,-1,3,0,-3,2,0,0,0,-2,3,0,-3,1,0,0,-1,-2,2,1,-2,1,1,1,0,-1,1,1,-2,0,0,0,0,-1,1)
FORMULA
G.f.: p/q with p,q given in Sage program.
a(n) = A027634(n) - A029143(n).
EXAMPLE
The space of weight 18 Siegel cusp forms of genus 3 has dimension 4.
PROG
(Sage)
R.<x> = PowerSeriesRing(ZZ, 100)
p = -x^56 + x^55 - x^54 - x^51 - 3*x^48 + x^47 - 3*x^46 - 2*x^45 - 2*x^44 - 3*x^43 - 4*x^42 - 2*x^41 - 7*x^40 - 3*x^39 - 8*x^38 - 4*x^37 - 10*x^36 - 6*x^35 - 10*x^34 - 9*x^33 - 9*x^32 - 9*x^31 - 13*x^30 - 5*x^29 - 15*x^28 - 6*x^27 - 11*x^26 - 10*x^25 - 8*x^24 - 8*x^23 - 11*x^22 - 4*x^21 - 10*x^20 - 5*x^19 - 6*x^18 - 5*x^17 - 6*x^16 - 2*x^15 - 6*x^14 - 2*x^13 - 3*x^12 - 3*x^11 - 2*x^10 - x^9 - 2*x^8 - x^6;
q = x^54 - x^53 - 2*x^48 + x^47 + x^46 - x^45 + x^43 + x^42 + x^41 - 2*x^40 + x^39 + 2*x^38 - 2*x^37 - x^36 + x^33 - 3*x^32 + 3*x^30 - 2*x^29 + 2*x^25 - 3*x^24 + 3*x^22 - x^21 + x^18 + 2*x^17 - 2*x^16 - x^15 + 2*x^14 - x^13 - x^12 - x^11 + x^9 - x^8 - x^7 + 2*x^6 + x - 1;
(p/q).list()[:30]
CROSSREFS
Sequence in context: A152950 A005626 A227561 * A030712 A025000 A147790
KEYWORD
nonn
AUTHOR
Andy Huchala, Mar 09 2022
STATUS
approved