Hi ,sorry for the delayed reply
The architecture is s390x and the OS is SLES 12 SP3 
(however test_gdb fails on SLES 11 SP4 too)
Python was installed using https://www.python.org/ftp/python/2.7.15/Python-2.7.15.tar.xz
The whole output of `./python -Werror -m test -v test_gdb` is as below:

4e227cf6c7ae">test@4e227cf6c7ae:~/Python-2.7.15> sudo ./python -Werror -m test -v test_gdb
== CPython 2.7.15 (default, Jun 25 2018, 05:10:18) [GCC 4.8.5]
==   Linux-4.15.0-22-generic-s390x-with-SuSE-12-s390x big-endian
==   /home/test/Python-2.7.15/build/test_python_21830
== CPU count: 2
Run tests sequentially
0:00:00 load avg: 4.32 [1/1] test_gdb
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test_NULL_instance_dict (test.test_gdb.PrettyPrintTests)
Ensure that a PyInstanceObject with with a NULL in_dict is handled ... skipped 'Python was compiled with optimizations'
test_NULL_ob_type (test.test_gdb.PrettyPrintTests)
Ensure that a PyObject* with NULL ob_type is handled gracefully ... skipped 'Python was compiled with optimizations'
test_NULL_ptr (test.test_gdb.PrettyPrintTests)
Ensure that a NULL PyObject* is handled gracefully ... skipped 'Python was compiled with optimizations'
test_builtin_function (test.test_gdb.PrettyPrintTests) ... skipped 'Python was compiled with optimizations'
test_builtin_method (test.test_gdb.PrettyPrintTests) ... skipped 'Python was compiled with optimizations'
test_builtins_help (test.test_gdb.PrettyPrintTests)
Ensure that the new-style class _Helper in site.py can be handled ... skipped 'Python was compiled with optimizations'
test_classic_class (test.test_gdb.PrettyPrintTests)
Verify the pretty-printing of classic class instances ... skipped 'Python was compiled with optimizations'
test_corrupt_ob_type (test.test_gdb.PrettyPrintTests)
Ensure that a PyObject* with a corrupt ob_type is handled gracefully ... skipped 'Python was compiled with optimizations'
test_corrupt_tp_flags (test.test_gdb.PrettyPrintTests)
Ensure that a PyObject* with a type with corrupt tp_flags is handled ... skipped 'Python was compiled with optimizations'
test_corrupt_tp_name (test.test_gdb.PrettyPrintTests)
Ensure that a PyObject* with a type with corrupt tp_name is handled ... skipped 'Python was compiled with optimizations'
test_dicts (test.test_gdb.PrettyPrintTests)
Verify the pretty-printing of dictionaries ... skipped 'Python was compiled with optimizations'
test_exceptions (test.test_gdb.PrettyPrintTests) ... skipped 'Python was compiled with optimizations'
test_frames (test.test_gdb.PrettyPrintTests) ... skipped 'Python was compiled with optimizations'
test_frozensets (test.test_gdb.PrettyPrintTests)
Verify the pretty-printing of frozensets ... skipped 'Python was compiled with optimizations'
test_getting_backtrace (test.test_gdb.PrettyPrintTests) ... skipped 'Python was compiled with optimizations'
test_int (test.test_gdb.PrettyPrintTests)
Verify the pretty-printing of various "int" values ... skipped 'Python was compiled with optimizations'
test_lists (test.test_gdb.PrettyPrintTests)
Verify the pretty-printing of lists ... skipped 'Python was compiled with optimizations'
test_long (test.test_gdb.PrettyPrintTests)
Verify the pretty-printing of various "long" values ... skipped 'Python was compiled with optimizations'
test_modern_class (test.test_gdb.PrettyPrintTests)
Verify the pretty-printing of new-style class instances ... skipped 'Python was compiled with optimizations'
test_selfreferential_dict (test.test_gdb.PrettyPrintTests)
Ensure that a reference loop involving a dict doesn't lead proxyval ... skipped 'Python was compiled with optimizations'
test_selfreferential_list (test.test_gdb.PrettyPrintTests)
Ensure that a reference loop involving a list doesn't lead proxyval ... skipped 'Python was compiled with optimizations'
test_selfreferential_new_style_instance (test.test_gdb.PrettyPrintTests) ... skipped 'Python was compiled with optimizations'
test_selfreferential_old_style_instance (test.test_gdb.PrettyPrintTests) ... skipped 'Python was compiled with optimizations'
test_sets (test.test_gdb.PrettyPrintTests)
Verify the pretty-printing of sets ... skipped 'Python was compiled with optimizations'
test_singletons (test.test_gdb.PrettyPrintTests)
Verify the pretty-printing of True, False and None ... skipped 'Python was compiled with optimizations'
test_strings (test.test_gdb.PrettyPrintTests)
Verify the pretty-printing of strings ... skipped 'Python was compiled with optimizations'
test_subclassing_list (test.test_gdb.PrettyPrintTests)
Verify the pretty-printing of an instance of a list subclass ... skipped 'Python was compiled with optimizations'
test_subclassing_tuple (test.test_gdb.PrettyPrintTests)
Verify the pretty-printing of an instance of a tuple subclass ... skipped 'Python was compiled with optimizations'
test_truncation (test.test_gdb.PrettyPrintTests)
Verify that very long output is truncated ... skipped 'Python was compiled with optimizations'
test_tuples (test.test_gdb.PrettyPrintTests)
Verify the pretty-printing of tuples ... skipped 'Python was compiled with optimizations'
test_unicode (test.test_gdb.PrettyPrintTests)
Verify the pretty-printing of unicode values ... skipped 'Python was compiled with optimizations'
test_basic_command (test.test_gdb.PyListTests)
Verify that the "py-list" command works ... skipped 'Python was compiled with optimizations'
test_one_abs_arg (test.test_gdb.PyListTests)
Verify the "py-list" command with one absolute argument ... skipped 'Python was compiled with optimizations'
test_two_abs_args (test.test_gdb.PyListTests)
Verify the "py-list" command with two absolute arguments ... skipped 'Python was compiled with optimizations'
test_down_at_bottom (test.test_gdb.StackNavigationTests)
Verify handling of "py-down" at the bottom of the stack ... FAIL
test_pyup_command (test.test_gdb.StackNavigationTests)
Verify that the "py-up" command works ... skipped 'Python was compiled with optimizations'
test_up_at_top (test.test_gdb.StackNavigationTests)
Verify handling of "py-up" at the top of the stack ... skipped 'Python was compiled with optimizations'
test_up_then_down (test.test_gdb.StackNavigationTests)
Verify "py-up" followed by "py-down" ... skipped 'Python was compiled with optimizations'
test_bt (test.test_gdb.PyBtTests)
Verify that the "py-bt" command works ... skipped 'Python was compiled with optimizations'
test_bt_full (test.test_gdb.PyBtTests)
Verify that the "py-bt-full" command works ... skipped 'Python was compiled with optimizations'
test_gc (test.test_gdb.PyBtTests)
Verify that "py-bt" indicates if a thread is garbage-collecting ... skipped 'Python was compiled with optimizations'
test_pycfunction (test.test_gdb.PyBtTests)
Verify that "py-bt" displays invocations of PyCFunction instances ... skipped 'Python was compiled with optimizations'
test_threads (test.test_gdb.PyBtTests)
Verify that "py-bt" indicates threads that are waiting for the GIL ... skipped 'Python was compiled with optimizations'
test_basic_command (test.test_gdb.PyPrintTests)
Verify that the "py-print" command works ... skipped 'Python was compiled with optimizations'
test_print_after_up (test.test_gdb.PyPrintTests) ... skipped 'Python was compiled with optimizations'
test_printing_builtin (test.test_gdb.PyPrintTests) ... skipped 'Python was compiled with optimizations'
test_printing_global (test.test_gdb.PyPrintTests) ... skipped 'Python was compiled with optimizations'
test_basic_command (test.test_gdb.PyLocalsTests) ... skipped 'Python was compiled with optimizations'
test_locals_after_up (test.test_gdb.PyLocalsTests) ... skipped 'Python was compiled with optimizations'

======================================================================
FAIL: test_down_at_bottom (test.test_gdb.StackNavigationTests)
Verify handling of "py-down" at the bottom of the stack
----------------------------------------------------------------------
Traceback (most recent call last):
  File "/home/test/Python-2.7.15/Lib/test/test_gdb.py", line 708, in test_down_at_bottom
    cmds_after_breakpoint=['py-down'])
  File "/home/test/Python-2.7.15/Lib/test/test_gdb.py", line 221, in get_stack_trace
    self.assertEqual(unexpected_errlines, [])
AssertionError: Lists differ: ['Could not trace the inferior... != []

First list contains 4 additional elements.
First extra element 0:
'Could not trace the inferior process.'

+ []
- ['Could not trace the inferior process.',
-  'Error: ptrace: Operation not permittedDuring startup program exited with code 127.',
-  "Python Exception <class 'gdb.error'> No frame is currently selected.: ",
-  'Error occurred in Python command: No frame is currently selected.']

----------------------------------------------------------------------
Ran 49 tests in 0.455s

FAILED (failures=1, skipped=48)
test test_gdb failed -- Traceback (most recent call last):
  File "/home/test/Python-2.7.15/Lib/test/test_gdb.py", line 708, in test_down_at_bottom
    cmds_after_breakpoint=['py-down'])
  File "/home/test/Python-2.7.15/Lib/test/test_gdb.py", line 221, in get_stack_trace
    self.assertEqual(unexpected_errlines, [])
AssertionError: Lists differ: ['Could not trace the inferior... != []

First list contains 4 additional elements.
First extra element 0:
'Could not trace the inferior process.'

+ []
- ['Could not trace the inferior process.',
-  'Error: ptrace: Operation not permittedDuring startup program exited with code 127.',
-  "Python Exception <class 'gdb.error'> No frame is currently selected.: ",
-  'Error occurred in Python command: No frame is currently selected.']

1 test failed:
    test_gdb

Total duration: 2 sec
Tests result: FAILURE