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NOTES ON ATKIN–LEHNER THEORY FOR DRINFELD MODULAR FORMS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 108 / Issue 1 / August 2023
- Published online by Cambridge University Press:
- 15 November 2022, pp. 50-68
- Print publication:
- August 2023
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- Article
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We settle a part of the conjecture by Bandini and Valentino [‘On the structure and slopes of Drinfeld cusp forms’, Exp. Math. 31(2) (2022), 637–651] for
$S_{k,l}(\Gamma _0(T))$ when 
$\mathrm {dim}\ S_{k,l}(\mathrm {GL}_2(A))\leq 2$. We frame and check the conjecture for primes 
$\mathfrak {p}$ and higher levels 
$\mathfrak {p}\mathfrak {m}$, and show that a part of the conjecture for level 
$\mathfrak {p} \mathfrak {m}$ does not hold if 
$\mathfrak {m}\ne A$ and 
$(k,l)=(2,1)$.
