diff --git a/pandas/io/formats/style_render.py b/pandas/io/formats/style_render.py
index ecfe3de10c829..2f5428f78edfc 100644
--- a/pandas/io/formats/style_render.py
+++ b/pandas/io/formats/style_render.py
@@ -50,6 +50,8 @@
 jinja2 = import_optional_dependency("jinja2", extra="DataFrame.style requires jinja2.")
 from markupsafe import escape as escape_html  # markupsafe is jinja2 dependency
 
+_DOLLAR_PATTERN = re.compile(r"\$.*?\$")
+
 BaseFormatter = Union[str, Callable]
 ExtFormatter = Union[BaseFormatter, dict[Any, Optional[BaseFormatter]]]
 CSSPair = tuple[str, Union[str, float]]
@@ -71,7 +73,11 @@ class StylerRenderer:
     Base class to process rendering a Styler with a specified jinja2 template.
     """
 
-    loader = jinja2.PackageLoader("pandas", "io/formats/templates")
+    import os
+
+    loader = jinja2.FileSystemLoader(
+        os.path.join(os.path.dirname(__file__), "templates")
+    )
     env = jinja2.Environment(loader=loader, trim_blocks=True)
     template_html = env.get_template("html.tpl")
     template_html_table = env.get_template("html_table.tpl")
@@ -834,10 +840,7 @@ def _generate_body_row(
 
             data_element = _element(
                 "td",
-                (
-                    f"{self.css['data']} {self.css['row']}{r} "
-                    f"{self.css['col']}{c}{cls}"
-                ),
+                (f"{self.css['data']} {self.css['row']}{r} {self.css['col']}{c}{cls}"),
                 value,
                 data_element_visible,
                 attributes="",
@@ -956,7 +959,7 @@ def concatenated_visible_rows(obj):
                     idx_len = d["index_lengths"].get((lvl, r), None)
                     if idx_len is not None:  # i.e. not a sparsified entry
                         d["clines"][rn + idx_len].append(
-                            f"\\cline{{{lvln+1}-{len(visible_index_levels)+data_len}}}"
+                            f"\\cline{{{lvln + 1}-{len(visible_index_levels) + data_len}}}"
                         )
 
     def format(
@@ -1211,7 +1214,7 @@ def format(
         data = self.data.loc[subset]
 
         if not isinstance(formatter, dict):
-            formatter = {col: formatter for col in data.columns}
+            formatter = dict.fromkeys(data.columns, formatter)
 
         cis = self.columns.get_indexer_for(data.columns)
         ris = self.index.get_indexer_for(data.index)
@@ -1397,7 +1400,7 @@ def format_index(
             return self  # clear the formatter / revert to default and avoid looping
 
         if not isinstance(formatter, dict):
-            formatter = {level: formatter for level in levels_}
+            formatter = dict.fromkeys(levels_, formatter)
         else:
             formatter = {
                 obj._get_level_number(level): formatter_
@@ -1540,7 +1543,7 @@ def relabel_index(
 
         >>> df = pd.DataFrame({"samples": np.random.rand(10)})
         >>> styler = df.loc[np.random.randint(0, 10, 3)].style
-        >>> styler.relabel_index([f"sample{i+1} ({{}})" for i in range(3)])
+        >>> styler.relabel_index([f"sample{i + 1} ({{}})" for i in range(3)])
         ... # doctest: +SKIP
                          samples
         sample1 (5)     0.315811
@@ -1694,7 +1697,7 @@ def format_index_names(
             return self  # clear the formatter / revert to default and avoid looping
 
         if not isinstance(formatter, dict):
-            formatter = {level: formatter for level in levels_}
+            formatter = dict.fromkeys(levels_, formatter)
         else:
             formatter = {
                 obj._get_level_number(level): formatter_
@@ -2503,7 +2506,7 @@ def color(value, user_arg, command, comm_arg):
         if value[0] == "#" and len(value) == 7:  # color is hex code
             return command, f"[HTML]{{{value[1:].upper()}}}{arg}"
         if value[0] == "#" and len(value) == 4:  # color is short hex code
-            val = f"{value[1].upper()*2}{value[2].upper()*2}{value[3].upper()*2}"
+            val = f"{value[1].upper() * 2}{value[2].upper() * 2}{value[3].upper() * 2}"
             return command, f"[HTML]{{{val}}}{arg}"
         elif value[:3] == "rgb":  # color is rgb or rgba
             r = re.findall("(?<=\\()[0-9\\s%]+(?=,)", value)[0].strip()
@@ -2579,7 +2582,7 @@ def _escape_latex(s: str) -> str:
 
 
 def _math_mode_with_dollar(s: str) -> str:
-    r"""
+    """
     All characters in LaTeX math mode are preserved.
 
     The substrings in LaTeX math mode, which start with
@@ -2597,17 +2600,18 @@ def _math_mode_with_dollar(s: str) -> str:
         Escaped string
     """
     s = s.replace(r"\$", r"rt8§=§7wz")
-    pattern = re.compile(r"\$.*?\$")
     pos = 0
-    ps = pattern.search(s, pos)
     res = []
-    while ps:
-        res.append(_escape_latex(s[pos : ps.span()[0]]))
-        res.append(ps.group())
-        pos = ps.span()[1]
-        ps = pattern.search(s, pos)
-
-    res.append(_escape_latex(s[pos : len(s)]))
+    matches = list(_DOLLAR_PATTERN.finditer(s))
+    # Pre-calculate slices to avoid repeated function calls
+    for m in matches:
+        start, end = m.span()
+        if pos < start:
+            res.append(_escape_latex(s[pos:start]))
+        res.append(m.group())
+        pos = end
+    if pos < len(s):
+        res.append(_escape_latex(s[pos : len(s)]))
     return "".join(res).replace(r"rt8§=§7wz", r"\$")