Abstract
It is known that a modular form on can be expressed as a rational function in , and . By using known theorems and calculating the order of vanishing, we can compute the eta-quotients for a given level. Using this count, knowing how many eta-quotients are linearly independent, and using the dimension formula, we can figure out a subspace spanned by the eta-quotients. In this paper, we primarily focus on the case where the level is , a prime. In this case, we will show an explicit count for the number of eta-quotients of level and show that they are linearly independent.
Citation
Allison Arnold-Roksandich. Kevin James. Rodney Keaton. "Counting eta-quotients of prime level." Involve 11 (5) 827 - 844, 2018. https://doi.org/10.2140/involve.2018.11.827
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