NOTES ON ATKIN–LEHNER THEORY FOR DRINFELD MODULAR FORMS
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 h...
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| Veröffentlicht in: | Bulletin of the Australian Mathematical Society 2023-08, Vol.108 (1), p.50-68 |
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| container_title | Bulletin of the Australian Mathematical Society |
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| creator | DALAL, TARUN KUMAR, NARASIMHA |
| description | 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
$(k,l)=(2,1)$
. |
| doi_str_mv | 10.1017/S000497272200123X |
| format | Article |
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$S_{k,l}(\Gamma _0(T))$
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
$(k,l)=(2,1)$
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$S_{k,l}(\Gamma _0(T))$
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
$(k,l)=(2,1)$
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$S_{k,l}(\Gamma _0(T))$
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
$(k,l)=(2,1)$
.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/S000497272200123X</doi><tpages>19</tpages><orcidid>https://orcid.org/0000-0003-4164-4737</orcidid><orcidid>https://orcid.org/0000-0002-6754-338X</orcidid></addata></record> |
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| language | eng |
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| subjects | Linear algebra |
| title | NOTES ON ATKIN–LEHNER THEORY FOR DRINFELD MODULAR FORMS |
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