Congruences modulo prime powers of Hecke eigenvalues in level 11

We continue the study of strong, weak, and $dc$-weak eigenforms introduced by Chen, Kiming, and Wiese. We completely determine all systems of Hecke eigenvalues of level $1$ modulo $128$, showing there are finitely many. This extends results of Hatada and can be considered as evidence for the more general conjecture formulated by the author together with Kiming and Wiese on finiteness of systems of Hecke eigenvalues modulo prime powers at any fixed level. We also discuss the finiteness of systems of Hecke eigenvalues of level $1$ modulo $9$, reducing the question to the finiteness of a single eigenvalue. Furthermore, we answer the question of comparing weak and $dc$-weak eigenforms and provide the first known examples of non-weak $dc$-weak eigenforms.Comment: 28 pages; Minor revisio

dCAPS procedures for the detection of the wild type isoleucine and mutant threonine amino acid residues at ACCase codon position 1781: (4a) <i>Nsi</i>I restricted (134 bp) correspond to the I1781 allele and unrestricted fragments (165 bp) correspond to either T1781 or L1781 alleles.

<p>(4b) <i>Nde</i>I restricted fragments (132 bp) correspond to the mutant threonine allele while the undigested band (169 bp) corresponds to either the wild type isoleucine or leucine alleles. Heterozygous plants show one each of the restricted and unrestricted PCR fragments in the two assays.</p

Efficacy of clethodim on different 2088 ACCase genotypes and plant growth stages. Genotypes compared using Wilcoxon rank sum test.

<p>Efficacy of clethodim on different 2088 ACCase genotypes and plant growth stages. Genotypes compared using Wilcoxon rank sum test.</p

Estimated GR₅₀ values for 10 ACCase inhibiting herbicides and different 2088 ACCase genotypes.

<p>Estimated GR₅₀ values for 10 ACCase inhibiting herbicides and different 2088 ACCase genotypes.</p

Herbicide rates used in whole plant dose response assays.

<p>CC2088-STD1: wild type homozygous 2088 genotype from standard sensitive population.</p><p>CC2088-RG3: wild type homozygous 2088 genotype from population RG3.</p><p>RR2088-RG3: mutant homozygous 2088 genotype from population RG3.</p

Pinoxaden whole plant dose response tests on four plant groups.

<p>Homozygous wild type STD1-II1781 from the standard sensitive population; homozygous wild type BG2-II1781; heterozygous mutant type BG2-IT1781 and heterozygous mutant type BG2-IL1781 from population BG2.</p

CAPS procedure for the detection of a thymine to cysteine change (C2088R mutation) at nucleotide position 6262 in <i>Lolium</i> spp.

<p>The <i>Hha</i> I digested fragment (126 bp) correspond to the resistant R2088 allele and the <i>Hha</i> 1 undigested fragment (161 bp) correspond to the C2088 allele. Heterozygous plants display both the 126 bp and 161 resistant and sensitive alleles respectively. Lanes 1 and 10: DNA ladder, lanes 2, 3 and 4: homozygous mutant RR2088, lanes 4, 5, 6: heterozygous CR2088 plants, lanes 7, 8, 9: homozygous wild CC2088 plants.</p

Correlation between cycloxydim phenotypes and combined genotypes at ACCase codon positions 1781 and 2027.

<p>Correlation between cycloxydim phenotypes and combined genotypes at ACCase codon positions 1781 and 2027.</p

Cycloxydim whole plant dose response tests on four plant groups.

<p>Homozygous wild type STD1-II1781 from the standard sensitive population; homozygous wild type BG2-II1781; heterozygous mutant type BG2-IT1781 and heterozygous mutant type BG2-IL1781 from population BG2.</p

Estimated resistance factors for 10 ACCase herbicides and different 2088 ACCase genotypes.

<p>Estimated resistance factors for 10 ACCase herbicides and different 2088 ACCase genotypes.</p