Pandas: Aggregate variables as a function of a single column

Question

I'm trying to aggregate certain variables in my dataframe as a function of the categories/labels in one column. Example df:

id   side   level   x   y
1    left   up      12  23
1    right  up      32  21
1    left   down    43  54
1    right  down    33  22
2    left   up      99  88
...

I need to aggregate x and y values as a function of either side or level. For example, if I do it as a function of level and drop the side variable, the df should look like this:

id   level   x   y
1    up      44  44
1    down    76  76
2    up      ..  ..
...

Here I aggregate all values of up and down and sum the values across side.

I've tried this approach but the values don't seem correct and I haven't been able to remove repeated values

df['new_x'] = df.groupby('level')['x'].transform('sum')