SCHOOL OF HIGH MAGIC
Starting at second level you gain the ability to more efficiently draw greater power out of your spells. At the beginning of each day you may select a number of spells from those you have prepared equal to half of your proficiency bonus rounded down. Each spell you select must gain the benefit from being cast at a higher level, must be 4th level or lower, and you cannot choose the same spell more than once.
When you cast one of those chosen spells you may expend a spell slot equal to its original level but it counts as being cast at one level higher, and gains the appropriate benefit. Each spell you chose for High Preparations can only be cast once this way until you choose new spells after a long rest.
PRODIGIOUS SPELL SCRIBE
Starting at second level you have an aptitude for understanding complex magical formulas. If you come across a spell scroll and the spell it details is one level higher then you have the ability to cast you may copy it into your spell book for half the original time and cost (This does not mean you may prepare or cast the spell).
In addition, when copying a spell of 6th level or higher the amount of time needed and the cost is always cut in half. This effect is not cumulative. For example copying a 6th level spell into your spell book while you are level 11 the cost is only cut in half, not quartered.
Starting at 6th level you gain the ability to more precisely guide and control your elevated magics. When you up-cast a spell at a higher level you may use a bonus action to roll 1d4. You may add the result to the attack roll of the spell or half that result (Rounded up) to increase the spell save DC if one is required. You may use this ability a number of times equal to your intelligence modifier, and you regain all uses after a long rest.
At level 10 your mastery of the high magics is astonishing. You gain expertise in the Arcana skill, and may use your reaction to add your proficiency bonus to any saving throw that a spell would require you to make if you are not already proficient in the required saving throw.
At level 14 you have mastered the ability to reclaim the magical energies used in the failed or interrupted attempts at a high level spell. When you cast a spell of 6th level or higher and the spell misses its target, the target succeeds on the saving throw causing the spell to have no effect, or lose concentration on the spell during the same round in which you cast it you may regain one spell slot that is one level lower then the spell you cast. You may not exceed the total number of spell slots per level as detailed by the Wizard Level Table in the Player's Handbook. The effect of Expanded Conservation can only be used a number of times equal to half your proficiency bonus rounded down.