Weakly holomorphic modular forms in prime power levels of genus zero

Let $M_k^\sharp(N)$ be the space of weight $k$, level $N$ weakly holomorphic modular forms with poles only at the cusp at $\infty$. We explicitly construct a canonical basis for $M_k^\sharp(N)$ for $N\in\{8,9,16,25\}$, and show that many of the Fourier coefficients of the basis elements in $M_0^\sharp(N)$ are divisible by high powers of the prime dividing the level $N$. Additionally, we show that these basis elements satisfy a Zagier duality property, and extend Griffin's results on congruences in level 1 to levels 2, 3, 4, 5, 7, 8, 9, 16, and 25

FIGURE 6 in A new species of lizard of the L. wiegmannii group (Iguania: Liolaemidae) from the Uruguayan Savanna

FIGURE 6. Relation between the measurements of the parietal head scales (left and right) and the mental scale between species of the genus Liolaemus, group wiegmannii and Liolaemus sp. nov. living nearby. Right parietal scale (SPR); Left parietal scale (SPL) and length and width of the mental scale (PMS). All measurements were divided by head width (HW) (the same letters mean significant differences between species)

FIGURE 4 in A new species of lizard of the L. wiegmannii group (Iguania: Liolaemidae) from the Uruguayan Savanna

FIGURE 4. Phylogenetic relationships of Liolaemus gardeli relative to other members of the Liolaemus wiegmannii group. Numbers above and below branches represent bootstrap values (>50%) of Maximum Likelihood (ML) and Maximum Parsimony (MP), respectively. Thicker branches have posterior probability values (PP)> 0.9