On the computation of local components of a newform
نویسندگان
چکیده
1.1. The problem. Let f be a cuspidal newform for Γ1(N) with weight k ≥ 2 and character ε. There are well-established methods for computing such forms using modular symbols, see [Ste07]. Let πf be the corresponding automorphic representation of the adèle group GL2(AQ). (As there are numerous possible normalisations, we shall recall the construction in section 2.1 below.) This representation decomposes as a restricted tensor product over all places v of Q:
منابع مشابه
Erratum: "On the computation of local components of a newform"
Proposition 4.1 (1) of this article is not correct as stated. For instance, if ε is the quadratic Dirichlet character of conductor 15, then there are two newforms in Sk(Γ1(15), ε) with coefficients in Q, and these are twists of each other by the quadratic character of conductor 3, whereas the quantity u in the proposition is 0 here. I am grateful to Steve Donnelly for pointing out this example....
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عنوان ژورنال:
- Math. Comput.
دوره 81 شماره
صفحات -
تاریخ انتشار 2012