Welcome!
First off, these are generally quite nice scores, with strengths across many domains. Secondly, there are many possible reasons why disparities within indices might exist; anything we might suggest here is a suggestion only. As to your specific data set:
The difference between digit span and picture span may be related to differences in the nature of the tasks. DS is an auditory memory task with three components: a verbatim (forward) rote memory task, and two mental manipulation tasks (backward and sequencing). It also uses symbolic content, and has no delay in response time. In contrast, PS is a visual memory task with one condition: verbatim (forward) rote memory. It uses concrete-familiar content, and has up to a five second delay before the response. While most people perform similarly on the subtests, some people do not. For example, people with a strong bias toward either auditory or visual processing may do better on the analogous working memory task. People with subtle attentional weaknesses, but good working memory (and such do exist), may do better on DS, due to the contribution of the two mental manipulation conditions. Individuals who prefer meaningful, semantic learning over abstraction in isolation may do better with PS, using concrete-familiar content, rather than symbolic content. Also, PS is the second-to-last task, and sometimes students are just tired by the time they get to it.
Coding and Symbol Search also usually track together, but not always. Fast visual processors with slow fine-motor skills often do better on SS than Cd. Sometimes individuals with more retentive symbolic memory blaze through Cd because they quickly memorize the key, and are able to complete the majority of the subtest without having to reference the key at the top of the page, which speeds up performance. The targets change with each line for SS, which doesn't allow them to leverage this strength in the same way. I sometimes see differences between the two subtests associated with weaknesses in visual scanning, as SS requires a great deal of that. And then, I have to add that SS is the last subtest administered, so, again, fatigue may be a factor.
It seems to me the two most likely explanations for the differences are 1) fatigue lowering the last two subtest scores; and 2) strengths in symbolic memory amplifying performance in the context of otherwise age-appropriate working memory and processing speed. #2 would be consistent with the achievement finding of exceptional mathematics performance. Also in support of #2 is the relatively lower performance in VSI, on two timed tasks, suggesting that processing speed may be closer to average in other cases, in addition to symbol search. #1 is consistent with your note that she was stressed and tired at the time, and is one of the simplest solutions. And then we have solution #3, which is both, and solution #4, which is neither.
Your best source of information on the likelihood of any of these proposed explanations would be the observations and clinical notes in the examiner's written evaluation. Or, failing that, asking the examiner for oral reports.
