A modularity criterion for Klein forms, with an application to modular forms of level 13 |
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Authors: | Ick Sun Eum Dong Hwa Shin |
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Affiliation: | Department of Mathematical Sciences, KAIST, Daejeon 373-1, Republic of Korea |
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Abstract: | We find some modularity criterion for a product of Klein forms of the congruence subgroup Γ1(N) (Theorem 2.6) and, as its application, construct a basis of the space of modular forms for Γ1(13) of weight 2 (Example 3.4). In the process we face with an interesting property about the coefficients of certain theta function from a quadratic form and prove it conditionally by applying Hecke operators (Proposition 4.3). |
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Keywords: | Modular forms Klein forms Dedekind eta-function |
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