Identities arising from Hecke transformations of modular forms over \(\mathbb{Q} (\sqrt 2)\) and \(\mathbb{Q} (\sqrt 3)\) (Q2368070)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Identities arising from Hecke transformations of modular forms over \(\mathbb{Q} (\sqrt 2)\) and \(\mathbb{Q} (\sqrt 3)\) |
scientific article |
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Identities arising from Hecke transformations of modular forms over \(\mathbb{Q} (\sqrt 2)\) and \(\mathbb{Q} (\sqrt 3)\) (English)
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22 August 1993
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The author deals with Hecke operators for Hilbert modular forms over \(\mathbb{Q}(\sqrt 2)\) and \(\mathbb{Q}(\sqrt 3)\). There exists a basis consisting of simultaneous eigenforms under all Hecke operators \(T(\tau)\). In certain cases of low weight the author constructs eigenforms \(f\) explicitly by the help of a computer algebra system. A comparison between the Fourier expansions on both sides of \(T(\tau)f=\lambda_ \tau f\) for special values of \(\tau\) leads to a number of identities.
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Eisenstein series
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explicit computation
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eigenforms
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Hecke operators
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Hilbert modular forms
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computer algebra system
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Fourier expansions
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