A063334 Dimension of the space of weight n cuspidal newforms for Gamma_1( 61 ).

-1, 126, 280, 435, 590, 745, 900, 1055, 1210, 1365, 1520, 1673, 1830, 1985, 2140, 2293, 2450, 2603, 2760, 2913, 3070, 3223, 3380, 3531, 3690, 3843, 4000, 4151, 4310, 4461, 4620, 4771, 4930, 5081, 5240, 5389, 5550, 5701, 5860, 6009, 6170

Offset

2,2

Links

Table of n, a(n) for n=2..42.

William A. Stein, Dimensions of the spaces S_k^{new}(Gamma_1(N))

William A. Stein, The modular forms database

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 1, 0, 1, 0, 0, 0, -1).

Formula

From Colin Barker, Feb 25 2016: (Start)

a(n) = a(n-4) + a(n-6) - a(n-10) for n>13.

G.f.: -x^2*(1 -126*x -280*x^2 -435*x^3 -591*x^4 -619*x^5 -621*x^6 -494*x^7 -340*x^8 -185*x^9 -29*x^10 +x^11) / ((1 -x)^2*(1 +x)^2*(1 -x +x^2)*(1 +x^2)*(1 +x +x^2)).

(End)

Mathematica

LinearRecurrence[{0, 0, 0, 1, 0, 1, 0, 0, 0, -1}, {-1, 126, 280, 435, 590, 745, 900, 1055, 1210, 1365, 1520, 1673}, 50] (* Harvey P. Dale, Feb 16 2025 *)

Crossrefs

Sequence in context: A249190 A356143 A254465 * A181262 A181255 A329807

Adjacent sequences: A063331 A063332 A063333 * A063335 A063336 A063337

Keyword

sign,changed

Author

N. J. A. Sloane, Jul 14 2001

Status

approved