id sid tid token lemma pos c821gh96f72 1 1 we we PRON c821gh96f72 1 2 prove prove VERB c821gh96f72 1 3 the the DET c821gh96f72 1 4 existence existence NOUN c821gh96f72 1 5 of of ADP c821gh96f72 1 6 congruences congruence NOUN c821gh96f72 1 7 between between ADP c821gh96f72 1 8 ordinary ordinary ADJ c821gh96f72 1 9 symplectic symplectic ADJ c821gh96f72 1 10 galois galois NOUN c821gh96f72 1 11 representations representation NOUN c821gh96f72 1 12 in in ADP c821gh96f72 1 13 two two NUM c821gh96f72 1 14 different different ADJ c821gh96f72 1 15 settings setting NOUN c821gh96f72 1 16 . . PUNCT c821gh96f72 2 1 first first ADV c821gh96f72 2 2 , , PUNCT c821gh96f72 2 3 we we PRON c821gh96f72 2 4 calculate calculate VERB c821gh96f72 2 5 lower low ADJ c821gh96f72 2 6 bounds bound NOUN c821gh96f72 2 7 on on ADP c821gh96f72 2 8 the the DET c821gh96f72 2 9 degree degree NOUN c821gh96f72 2 10 of of ADP c821gh96f72 2 11 the the DET c821gh96f72 2 12 weight weight NOUN c821gh96f72 2 13 space space NOUN c821gh96f72 2 14 map map NOUN c821gh96f72 2 15 for for ADP c821gh96f72 2 16 hida hida ADJ c821gh96f72 2 17 families family NOUN c821gh96f72 2 18 given give VERB c821gh96f72 2 19 assumptions assumption NOUN c821gh96f72 2 20 on on ADP c821gh96f72 2 21 the the DET c821gh96f72 2 22 p p NOUN c821gh96f72 2 23 - - PUNCT c821gh96f72 2 24 adic adic ADJ c821gh96f72 2 25 l l NOUN c821gh96f72 2 26 - - PUNCT c821gh96f72 2 27 invariant invariant ADJ c821gh96f72 2 28 ( ( PUNCT c821gh96f72 2 29 or or CCONJ c821gh96f72 2 30 the the DET c821gh96f72 2 31 adjoint adjoint ADJ c821gh96f72 2 32 l l NOUN c821gh96f72 2 33 - - PUNCT c821gh96f72 2 34 invariant invariant ADJ c821gh96f72 2 35 ) ) PUNCT c821gh96f72 2 36 of of ADP c821gh96f72 2 37 a a DET c821gh96f72 2 38 weight weight NOUN c821gh96f72 2 39 ( ( PUNCT c821gh96f72 2 40 3,3 3,3 NOUN c821gh96f72 2 41 ) ) PUNCT c821gh96f72 2 42 automorphic automorphic ADJ c821gh96f72 2 43 representation representation NOUN c821gh96f72 2 44 on on ADP c821gh96f72 2 45 the the DET c821gh96f72 2 46 hida hida PROPN c821gh96f72 2 47 family family NOUN c821gh96f72 2 48 when when SCONJ c821gh96f72 2 49 such such DET c821gh96f72 2 50 an an DET c821gh96f72 2 51 l l NOUN c821gh96f72 2 52 - - PUNCT c821gh96f72 2 53 invariant invariant ADJ c821gh96f72 2 54 is be AUX c821gh96f72 2 55 defined define VERB c821gh96f72 2 56 using use VERB c821gh96f72 2 57 theorems theorem NOUN c821gh96f72 2 58 of of ADP c821gh96f72 2 59 giovanni giovanni PROPN c821gh96f72 2 60 rosso rosso PROPN c821gh96f72 2 61 . . PUNCT c821gh96f72 3 1 second second ADV c821gh96f72 3 2 , , PUNCT c821gh96f72 3 3 we we PRON c821gh96f72 3 4 set set VERB c821gh96f72 3 5 up up ADP c821gh96f72 3 6 a a DET c821gh96f72 3 7 galois galois NOUN c821gh96f72 3 8 deformation deformation NOUN c821gh96f72 3 9 problem problem NOUN c821gh96f72 3 10 for for ADP c821gh96f72 3 11 a a DET c821gh96f72 3 12 fixed fix VERB c821gh96f72 3 13 absolutely absolutely ADV c821gh96f72 3 14 irreducible irreducible ADJ c821gh96f72 3 15 galois galois NOUN c821gh96f72 3 16 representation representation NOUN c821gh96f72 3 17 which which PRON c821gh96f72 3 18 is be AUX c821gh96f72 3 19 odd odd ADJ c821gh96f72 3 20 , , PUNCT c821gh96f72 3 21 ordinary ordinary ADJ c821gh96f72 3 22 and and CCONJ c821gh96f72 3 23 indecomposable indecomposable ADJ c821gh96f72 3 24 at at ADP c821gh96f72 3 25 p p PROPN c821gh96f72 3 26 , , PUNCT c821gh96f72 3 27 and and CCONJ c821gh96f72 3 28 unramified unramifie VERB c821gh96f72 3 29 everywhere everywhere ADV c821gh96f72 3 30 else else ADV c821gh96f72 3 31 . . PUNCT c821gh96f72 4 1 under under ADP c821gh96f72 4 2 a a DET c821gh96f72 4 3 mild mild ADJ c821gh96f72 4 4 local local ADJ c821gh96f72 4 5 hypothesis hypothesis NOUN c821gh96f72 4 6 , , PUNCT c821gh96f72 4 7 we we PRON c821gh96f72 4 8 prove prove VERB c821gh96f72 4 9 the the DET c821gh96f72 4 10 existence existence NOUN c821gh96f72 4 11 of of ADP c821gh96f72 4 12 at at ADV c821gh96f72 4 13 least least ADV c821gh96f72 4 14 two two NUM c821gh96f72 4 15 characteristic characteristic ADJ c821gh96f72 4 16 zero zero NUM c821gh96f72 4 17 lifts lift NOUN c821gh96f72 4 18 of of ADP c821gh96f72 4 19 our our PRON c821gh96f72 4 20 fixed fix VERB c821gh96f72 4 21 galois galois NOUN c821gh96f72 4 22 representation representation NOUN c821gh96f72 4 23 . . PUNCT