Spells Known and Prepared. You determine what spells you know and can prepare for each class individually, as if you were a single-classed member of
that class. - PHB, p164
An Arcane Trickster 3/Conjurer 2 knows the following:
Three cantrips from the Wizard list
Six 1st-level Wizard spells (gained at level 1)
Two 1st-level Wizard spells (gained at level 2)
Anything he's found scrolls for.
Note that because you consider the classes individually when determining spells known, the character could not select 2nd-level spells at level 2, even though the character may have the slots (as described below).
The character can prepare (Conjurer Level)+(INT Mod) spells from the Wizard list as a Conjurer.
From Arcane Trickster
Mage Hand plus two cantrips from the Wizard list.
Three 1st-level Wizard spells, two of which must be enchantment or illusion.
All of the spells gained from Arcane Trickster are considered prepared at all times.
Spell Slots. You determine your available spell slots by adding together all your levels in the bard, cleric, druid, sorcerer, and wizard classes, half your levels (rounded down) in the paladin and ranger classes, and a third of your fighter or rogue levels (rounded down) if you have the Eldritch Knight or the Arcane Trickster feature. Use this total to determine your spell slots by consulting the Multiclass Spellcaster table. - ibid
The only part of multi-classing where the two classes have anything to do with each other is in determining spell slots, as quoted above. In the case of an Arcane Trickster 3/Conjurer 2, the character has the spell slots of a third level caster, because (3/3)+2=3. This means the character has four 1st-level and two 2nd-level slots.
If the character has a spell that can be cast in a higher level slot for added effect, the character can do so. Even spells without an added benefit can be cast from a higher level slot, they just don't do any more than they would out of the slot they normally use. Either way, the character doesn't know any 2nd-level spells despite having slots for them.