A306936 Coefficients of q-expansion of Eisenstein series G_{9/2}(tau) multiplied by 240.

1, 2, 0, 0, 242, 480, 0, 0, 2640, 4322, 0, 0, 11040, 13920, 0, 0, 30962, 39360, 0, 0, 65760, 73920, 0, 0, 125280, 156002, 0, 0, 216960, 226080, 0, 0, 340560, 406080, 0, 0, 522962, 541920, 0, 0, 756960, 860160, 0, 0, 1033440, 1063200, 0, 0, 1424160, 1646402, 0, 0, 1907040, 1860000, 0, 0

Offset

0,2

Links

Table of n, a(n) for n=0..55.

H. Cohen, Sums involving the values at negative integers of L-functions of quadratic characters, Math. Ann. 217 (1975), no. 3, 271-285.

X. Wang and D. Pei, Modular Forms with Integral and Half-Integral Weights, Science Press Beijing, Springer Berlin Heidelberg, 2012. x+432 pp.

D. Zagier, Modular Forms of One Variable, Notes based on a course given in Utrecht, 1991. See page 50.

Prog

(Sage)
def a(n):
    if n==0: return 1
    if (n%4) not in [0, 1]: return 0
    D = Integer(n).squarefree_part()
    f = Integer(sqrt(n/D))
    if (D%4) not in [0, 1]: D, f = 4*D, f//2
    X = kronecker_character(D)
    s = sum([moebius(d)*X(d)*d^3*sigma(f/d, 7) for d in f.divisors()])
    return round((240*X.lfunction(100)(-3)*s).real()) # Robin Visser, Feb 24 2024

Crossrefs

Cf. A259825, A306934, A306935, A306937.

Sequence in context: A008551 A183896 A228073 * A027652 A350022 A348264

Adjacent sequences: A306933 A306934 A306935 * A306937 A306938 A306939

Keyword

nonn

Author

N. J. A. Sloane, Mar 16 2019

Extensions

More terms from Robin Visser, Feb 24 2024

Status

approved