TY - JOUR
AU - Ono, Ken
AB - Abstract Here, a classical observation of Siegel is generalized by determining all the linear relations among the initial Fourier coefficients of a modular form on SL2(Z). As a consequence, spaces Mk are identified, in which there are universal p-divisibility properties for certain p-power coefficients. As a corollary, let f(z)=∑n=1∞af(n)qn∈Sk∩OL[[q]] be a normalized Hecke eigenform (note that q:=e2πiz), and let k ≡ δ(k) (mod 12), where δ(k) ∈ {4, 6, 8, 10, 14}. Reproducing earlier results of Hatada and Hida, if p is a prime for which k ≡ δ(k) (mod p−1), and p ⊂ OL is a prime ideal above p, a proof is given to show that af(p) ≡ 0 (mod p). 2000 Mathematics Subject Classification 11F33 (primary), 11F11 (secondary). © London Mathematical Society
TI - Linear Relations Between Modular form Coefficients and Non-Ordinary Primes
JO - Bulletin of the London Mathematical Society
DO - 10.1112/S0024609305004285
DA - 2005-06-01
UR - https://www.deepdyve.com/lp/oxford-university-press/linear-relations-between-modular-form-coefficients-and-non-ordinary-SPC2O9V9EO
SP - 335
EP - 341
VL - 37
IS - 3
DP - DeepDyve
ER -