Some Non-congruence Subgroups and the Associated Modular Curves
نویسندگان
چکیده
In this paper, we study two families of normal subgroups of Γ0(2) with abelian quotients and their associated modular curves. They are similar to Fermat groups and Fermat curves in some aspects but very different in other aspects. Almost all of them are non-congruence subngroups. These modular curves are either projective lines or hyperelliptic curves. There are few modular forms of weight 1 for these groups. We also determine their cuspidal divisor class groups and show that these groups are finite.
منابع مشابه
Algebraic Curves Uniformized by Congruence Subgroups of Triangle Groups
We construct certain subgroups of hyperbolic triangle groups which we call “congruence” subgroups. These groups include the classical congruence subgroups of SL2(Z), Hecke triangle groups, and 19 families of arithmetic triangle groups associated to Shimura curves. We determine the field of moduli of the curves associated to these groups and thereby realize the groups PSL2(Fq) and PGL2(Fq) regul...
متن کاملOn the Arithmetic Self-intersection Number of the Dualizing Sheaf on Arithmetic Surfaces
We study the arithmetic self-intersection number of the dualizing sheaf on arithmetic surfaces with respect to morphisms of a particular kind. We obtain upper bounds for the arithmetic self-intersection number of the dualizing sheaf on minimal regular models of the modular curves associated with congruence subgroups Γ0(N) with square free level, as well as for the modular curves X(N) and the Fe...
متن کاملExperimental finding of modular forms for noncongruence subgroups
In this paper we will use experimental and computational methods to find modular forms for non-congruence subgroups, and the modular forms for congruence subgroups that they are associated with via the Atkin–Swinnerton-Dyer correspondence. We also prove a generalization of a criterion due to Ligozat for an eta-quotient to be a modular function.
متن کاملThe number of Fuzzy subgroups of some non-abelian groups
In this paper, we compute the number of fuzzy subgroups of some classes of non-abeilan groups. Explicit formulas are givenfor dihedral groups $D_{2n}$, quasi-dihedral groups $QD_{2^n}$, generalized quaternion groups $Q_{4n}$ and modular $p$-groups $M_{p^n}$.
متن کاملOn the Cuspidal Divisor Class Group of a Drinfeld Modular Curve
The theory of theta functions for arithmetic groups that act on the Drinfeld upper half-plane is extended to allow degenerate parameters. This is used to investigate the cuspidal divisor class groups of Drinfeld modular curves. These groups are nite for congruence subgroups and may be described through the corresponding quotients of the Bruhat-Tits tree by . The description given is fairly expl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015