DH8 CREW DID NOT START DSCNT WHEN CLRED BY THE N90 APCH CTLR.

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WHILE ABOUT 15 DME SW OF LGA AT 7000 FT NY APCH TOLD US WE WERE SUPPOSED TO BE AT 4000 FT. THE CTLR STATED THAT WE HAD BEEN 'CLRED TO 4000 FT 15 MI BACK.' WE BOTH IMMEDIATELY LOOKED AT THE ALT ALERTER WHICH WAS INDICATING 4000 FT AND THEN I ACKNOWLEDGED THE CTLR AS THE CAPT BEGAN AN EXPEDITIOUS DSCNT. I ALSO BEGAN THE ARR CHKLIST. THE CAPT AND I DID NOT DISCUSS THE INCIDENT ANY FURTHER AS OUR WORKLOAD WAS HVY AND WE WERE CLOSE TO THE ARPT. BEFORE HANDING US OFF TO THE NEXT SECTOR THE CTLR THANKED US FOR OUR QUICK DSCNT AND WE CONTINUED WITHOUT PROB TO LAND VISUALLY ON RWY 22. ON THE GND AT LGA WE HAD AN OPPORTUNITY TO DISCUSS OUR DEV. WE HAD BEEN FLYING ON V123 ABOUT 35 NM SW OF LGA AT 7000 FT; ALREADY TALKING TO NY APCH; WHEN WE WERE CLRED DOWN TO 4000 FT AND DIRECT TO LGA. 4000 FT WAS SET IN THE ALT ALERTER AND WE BOTH VERIFIED THE SELECTION. THE CAPT ALSO INITIATED THE TURN DIRECT TO LGA VIA THE AUTOPLT WHICH WAS COUPLED TO THE RNAV. WE NEVER LEFT 7000 FT AND DID NOT REALIZE OUR ERROR UNTIL THE CTLR SPOKE TO US AGAIN 15 MI LATER. I BELIEVE THE PRIMARY CAUSE OF OUR DEV CAN BE ATTRIBUTED TO OUR FAILURE TO OBSERVE A STERILE COCKPIT. WHEN THE CTLR GAVE US OUR DSCNT CLRNC WE WERE IN THE MIDDLE OF A CONVERSATION AND WE CONTINUED TO TALK AFTER RECEIVING THE CLRNC. IF WE HAD FOLLOWED SOP'S WE WOULD HAVE INITIATED STERILE COCKPIT AND THE ARR CHKLIST AFTER BEGINNING OUR DSCNT. THE DISTR OF OUR CONVERSATION KEPT US FROM FULLY COMPLYING WITH THE CTLR'S INSTRUCTIONS. FOR MYSELF; 2 SECONDARY CAUSES WERE A LACK OF SITUATIONAL AWARENESS AND COMPLACENCY. IN MY OPINION THEY WERE BOTH BROUGHT ON BY FATIGUE. I HAD GOTTEN UP AT XA30 IN THE MORNING IN ORDER TO ARRIVE AT THE ARPT FOR A XC35 SHOW TIME. I DID NOT GET A SUFFICIENT AMOUNT OF SLEEP TO REMAIN ALERT AFTER ALMOST 12 HRS OF CONTINUOUS DUTY. THIS WAS ALSO THE 7TH AND LAST LEG OF THE DAY. WE HAD ALREADY FLOWN A LEG UNDER CAVU CONDITIONS EARLIER. MY SITUATIONAL AWARENESS WAS NOT WHAT IT SHOULD HAVE BEEN EVEN THOUGH I HAD THE LGA VOR DME READOUT SHOWING ON MY RMI. NORMALLY; I WOULD HAVE REALIZED THAT AT 15 DME WE SHOULD HAVE BEEN AT A LOWER ALT AND THE ARR CHKLIST SHOULD HAVE BEEN COMPLETED. THE CLOUD LAYER BELOW US ALSO PREVENTED ME FROM 'SEEING' OUR PROX TO LGA. I STRONGLY BELIEVE THAT MY LACK OF REST CONTRIBUTED TO MY POOR PERFORMANCE.