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Sep 18, 2011 at 20:45 vote accept Rob Harron
Sep 18, 2011 at 20:42 comment added Rob Harron Ah, yes, for some reason I got myself confused looking at the analytic conductors, but it's clear on the Galois side. Thanks! I'll just add that a proof of the standard bound you mention is available in Murty's paper Congrences between modular forms available at mast.queensu.ca/~murty/congr.dvi .
Sep 18, 2011 at 20:02 comment added Kevin Buzzard Re the discriminant and conductor: if $N$ is the level of $f$ and $f$ is new, then $N$ is the product of $|d|$ ($d$ the discriminant of $K$) and the norm of the conductor of the grossencharacter. This just comes from basic facts about conductors of representations (if I got them right!)
Sep 18, 2011 at 19:41 history answered Kevin Buzzard CC BY-SA 3.0