Timeline for Explicit description of zeros of some cusp forms of weight 2 on $\Gamma_0(p)$
Current License: CC BY-SA 3.0
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| Apr 1, 2018 at 20:12 | comment | added | Y. Zhao | @Kimball: I think the condition on the order of zeros provides the uniqueness of such cusp forms because all the different theta functions span the space of weight 2 modular forms on $\Gamma_0(p)$ with Fricke eigenvalue 1(when one limits oneself to the primes given in the table above). I just calculated those example with $\mathbb{Q}(\sqrt{-p})$ having small class numbers, and I did not find a linear combination of more than 2 theta series. I also did not test whether it is a Hecke eigenform or not. | |
| Mar 31, 2018 at 13:08 | comment | added | Kimball | Does this condition on order of zeroes at the cusps give you a unique (up to scaling) cusp form? Is it eigen? Is it ever a linear combination of more than 2 theta series? | |
| Mar 30, 2018 at 21:52 | history | asked | Y. Zhao | CC BY-SA 3.0 |