How much stardust is needed to power up a pokemon?

Stardust cost per Pokemon "level" (Powering up increases level by 1, stardust increases every 4 "levels."):
Levels 1 to 20:

200 stardust, 1 candy
400 stardust, 1 candy
600 stardust, 1 candy
800 stardust, 1 candy
1000 stardust, 1 candy

Levels 21 to 40:

1300 stardust, 2 candy
1600 stardust, 2 candy
1900 stardust, 2 candy
2200 stardust, 2 candy
2500 stardust, 2 candy

Level 41 to 43:

3000 stardust, 3 candy

source

Note: Pokémon you catch are not necessarily at "level" 1. For example, I caught a 701 CP Pinsir and it is roughly "level" 13

Here is some data: https://www.reddit.com/r/TheSilphRoad/comments/4sa4p5/stardust_costs_increase_every_4_power_ups/

I don't believe stardust changes with trainer level, only with how much you've powered up the pokemon. That being said the higher trainer you are the more CP you get from evolving so it is best to wait on evolving your pokemon until you have a higher trainer level which will save you candy and stardust.

Based on a data dump of an earlier version of the game, the upgrade costs are the following, but these have probably not changed in recent updates. They are per level, and a level requires 2 power ups (this is often denoted as half levels, so each power up increases the Pokemon's level by 0.5).

A Pokemon's CP depends on 3 things:

• Its level (not your Trainer level)
• Its Individual values, of which there are 3 and which are different for each individual Pokemon
• Its base stats, which are different for each species

The formula for a Pokemon's current CP is

(Attack * Defense^0.5 * Stamina^0.5 * CP_Multiplier^2) / 10

In order to determine the upgrade cost per CP, you have to use this formula to calculate the Pokemon's CP at each level. The table below includes example CP values for an average Snorlax (Base Stats 180/180/320, IVs 7/7/7)

Level Stardust Candies Ex. CP
    1      200       1     41
    2      200       1    128
    3      400       1    215
    4      400       1    302
    5      600       1    390
    6      600       1    477
    7      800       1    564
    8      800       1    651
    9     1000       1    738
   10     1000       1    825
   11     1300       2    908
   12     1300       2    990
   13     1600       2   1073
   14     1600       2   1155
   15     1900       2   1238
   16     1900       2   1320
   17     2200       2   1403
   18     2200       2   1485
   19     2500       2   1568
   20     2500       2   1650
   21     3000       3   1733
   22     3000       3   1815
   23     3500       3   1898
   24     3500       3   1980
   25     4000       3   2063
   26     4000       4   2146
   27     4500       4   2228
   28     4500       4   2311
   29     5000       4   2393
   30     5000       4   2476
   31     6000       6   2517
   32     6000       6   2558
   33     7000       8   2599
   34     7000       8   2641
   35     8000      10   2682
   36     8000      10   2723
   37     9000      12   2764
   38     9000      12   2806
   39    10000      15   2847
   40    10000      15   2888

As you can see, there are always 2 levels with the same cost, so the cost changes every 4 power ups.

According to the same data dump, a Pokemon's level can be up to 2 higher than the Trainer level, but no higher than 40 (which is also the maximum Trainer level).