I have this problem, too. BSOD occures every time in 5-10 minutes after boot (or resuming from hibernation). Every single time, it happens once after boot, then it works without any problem hours, at least.
I have tried anything possible; upgrading/downgrading drivers (GPU, NIC, etc), swapping and testing memory and HD, etc. Nothing seems to help. I really wouldn’t like to uninstall avast, but I see no other option if I can’t find solution for the problem 
This all started on January 16. I think, there was some Microsoft updates happening the day before, maybe it’s somehow related. If I recall correctly, I have seen some user reporting the similar problem with another AV software since then.
However, here is a crash analyze, based on the dump file:
Crash Dump Analysis provided by OSR Open Systems Resources, Inc. (http://www.osr.com)
Online Crash Dump Analysis Service
See http://www.osronline.com for more information
Windows 7 Kernel Version 7601 (Service Pack 1) MP (8 procs) Free x64
Product: WinNt, suite: TerminalServer SingleUserTS
Built by: 7601.18700.amd64fre.win7sp1_gdr.141211-1742
Machine Name:
Kernel base = 0xfffff80003052000 PsLoadedModuleList = 0xfffff80003295890
Debug session time: Mon Jan 26 05:27:45.337 2015 (UTC - 5:00)
System Uptime: 0 days 0:08:21.242
IRQL_GT_ZERO_AT_SYSTEM_SERVICE (4a)
Returning to usermode from a system call at an IRQL > PASSIVE_LEVEL.
Arguments:
Arg1: 0000000075492e09, Address of system function (system call routine)
Arg2: 0000000000000002, Current IRQL
Arg3: 0000000000000000, 0
Arg4: fffff88007a30ca0, 0
Debugging Details:
TRIAGER: Could not open triage file : e:\dump_analysis\program\triage\modclass.ini, error 2
PROCESS_NAME: AvastSvc.exe
BUGCHECK_STR: RAISED_IRQL_FAULT
FAULTING_IP:
+0
00000000`75492e09 ?? ???
CUSTOMER_CRASH_COUNT: 1
DEFAULT_BUCKET_ID: WIN7_DRIVER_FAULT
CURRENT_IRQL: 2
LAST_CONTROL_TRANSFER: from fffff800030c8429 to fffff800030c8e80
STACK_TEXT:
fffff88007a30a68 fffff800030c8429 : 000000000000004a 0000000075492e09 0000000000000002 0000000000000000 : nt!KeBugCheckEx
fffff88007a30a70 fffff800030c8360 : ffffffff00000004 c720000129605867 fffffa8000000000 0000098000000000 : nt!KiBugCheckDispatch+0x69
fffff88007a30bb0 0000000075492e09 : 0000000000000000 0000000000000000 0000000000000000 0000000000000000 : nt!KiSystemServiceExit+0x245
000000000eb5f098 0000000000000000 : 0000000000000000 0000000000000000 0000000000000000 0000000000000000 : 0x75492e09
STACK_COMMAND: kb
FOLLOWUP_IP:
nt!KiSystemServiceExit+245
fffff800`030c8360 4883ec50 sub rsp,50h
SYMBOL_STACK_INDEX: 2
SYMBOL_NAME: nt!KiSystemServiceExit+245
FOLLOWUP_NAME: MachineOwner
MODULE_NAME: nt
IMAGE_NAME: ntkrnlmp.exe
DEBUG_FLR_IMAGE_TIMESTAMP: 548a6e28
FAILURE_BUCKET_ID: X64_RAISED_IRQL_FAULT_AvastSvc.exe_nt!KiSystemServiceExit+245
BUCKET_ID: X64_RAISED_IRQL_FAULT_AvastSvc.exe_nt!KiSystemServiceExit+245