A352095 Dimension of the space of Siegel cusp forms of genus 3 and weight 2n.

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

Andy Huchala, Table of n, a(n) for n = 0..20000

O. Taibi, Dimensions of spaces of level one automorphic forms for split classical groups using the trace formula, arXiv 1406.4247 [math.NT] (2014), 64-65.

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

Cf. A027634, A029143.

Sequence in context: A152950 A005626 A227561 * A030712 A025000 A147790

Adjacent sequences: A352092 A352093 A352094 * A352096 A352097 A352098

Keyword

nonn

Author

Andy Huchala, Mar 09 2022

Status

approved