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
Keywords
Examples
The space of weight 18 Siegel cusp forms of genus 3 has dimension 4.
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)
Programs
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Sage
R.
= 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]
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