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Search: id:A027364
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| A027364 |
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Coefficients of unique normalized cusp form Delta_16 of weight 16 for full modular group. |
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+0
3
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| 1, 216, -3348, 13888, 52110, -723168, 2822456, -4078080, -3139803, 11255760, 20586852, -46497024, -190073338, 609650496, -174464280, -1335947264, 1646527986, -678197448, 1563257180, 723703680, -9449582688, 4446760032, 9451116072, 13653411840, -27802126025, -41055841008
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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H. P. F. Swinnerton-Dyer, On l-adic representations and congruences for coefficients of modular forms, pp. 1-55 of Modular Functions of One Variable III (Antwerp 1972), Lect. Notes Math., 350, 1973.
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LINKS
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Index entries for sequences related to modular groups
Author?, Table of coefficients c16(n) of the weight 16 cusp form on Gamma_0(1) for n up to 1000
F. Q. Gouvea, Non-ordinary primes, Experimental Mathematics 6 195, 1997.
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FORMULA
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G.f.: q (1+240 Sum sigma_3(n)q^n; n=1..inf) Product (1-q^k)^24; k=1..inf. sigma_3(n) is the sum of the cubes of the divisors of n (A001158).
(E_4^4-E_6^2*E_4)/1728.
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EXAMPLE
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q^2+216*q^4-3348*q^6+13888*q^8+...
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MAPLE
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with(numtheory): DO := qs -> q*diff(qs, q)/2: E2:=1-24*add(sigma(n)*q^(2*n), n=1..100): delta16:=(-1/24)*(DO@@6)(E2)*E2+(9/8)*(DO@@5)(E2)*(DO@@1)(E2)-(45/8)*(DO@@4)(E2)*(DO@@2)(E2)+(55/12)*(DO@@3)(E2)*(DO@@3)(E2):seq(coeff(delta16, q, 2*i), i=1..40); with(numtheory): E2n:=n->1-(4*n/bernoulli(2*n))*add(sigma[2*n-1](k)*q^(2*k), k=1..100): qs:=(E2n(2)^4-E2n(3)^2*E2n(2))/1728: seq(coeff(qs, q, 2*i), i=1..40); (Ronaldo)
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CROSSREFS
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Cf. A000594 (cusp form of weight 12).
Sequence in context: A016911 A017055 A017139 this_sequence A017235 A017343 A017463
Adjacent sequences: A027361 A027362 A027363 this_sequence A027365 A027366 A027367
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KEYWORD
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sign,easy
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AUTHOR
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Paolo Dominici (pl.dm(AT)libero.it), njas
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EXTENSIONS
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More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 17 2005
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