The first part you tabbed (from E to D string) is an A minor (aeolian mode) in the Key of C maj. (no flats or sharps)
The rest of your tab is an A dorian in the Key of G maj. (since you got a sharp F note)

I guess you made a typing mistake .

If you want a Dorian throghout , change the 8 on the A-string into 9.
If you want the Aeolian , change the 7 on the b-string into 6.

Yes, modes follows formulas and position patterns just like the major , pentatonic etc.

Here are the formulas:
======================
1) Ionian (major) : WWHWWWH
2) Dorian : WHWWWHW
3) Phrygian: HWWWHWW
4) Lydian : WWWHWWH
5) Mixolydian: WWHWWHW
6) Aeolian (minor) : WHWWHWW
7) Locrian : HWWHWWW


For hard rock and metal Aeolian and Phrygian are realy common.