I tried the code from your question, one command per line, without the 'show' commands.
Your question about free_module
The command M11.free_module() did not produce any error in Sage 6.3.beta6.
Everything worked except the command about newforms.
The error with the method newforms
If you have a quick look at the documentation for the method newforms, which you can access by
sage: M11.newforms?
you will see that the examples all involve spaces of cusp forms.
Indeed the following works.
sage: CuspForms(11).newforms()
[q - 2*q^2 - q^3 + 2*q^4 + q^5 + O(q^6)]
Your first question: why \QQ7 is red?
When you ask show(M11.modular_symbols()), the output is rendered using LaTeX, and the 7-adic field appears in bold as $\mathbf{Q}_7$. Maybe you don't have LaTeX installed, and when you viewed the output the boldface was rendered as red? Where was the output rendered?
Full output of the code you provided
For reference this was the output when running your commands,
slightly reordered.
sage: version() # for reference
'Sage Version 6.3.beta6, Release Date: 2014-07-19'
sage: M11 = ModularForms(11,2,base_ring=Qp(7,10))
sage: M11
Modular Forms space of dimension 2 for Congruence Subgroup Gamma0(11) of weight 2 over 7-adic Field with capped relative precision 10
sage: M11.modular_symbols()
Modular Symbols space of dimension 3 for Gamma_0(11) of weight 2 with sign 0 over 7-adic Field with capped relative precision 10
sage: M11.level()
11
sage: M11.weight()
2
sage: M11.character()
Dirichlet character modulo 11 of conductor 1 mapping 2 |--> 1
sage: M11.dimension()
2
sage: M11.group().order()
+Infinity
sage: M11.group().gens()
(
[1 1] [ 7 -2] [ 8 -3] [-1 0]
[0 1], [11 -3], [11 -4], [ 0 -1]
)
sage: M11.newforms()
[<repr(<sage.modular.modform.element.Newform at 0x1136915a0>) failed: IndexError: list index out of range>]
sage: M11.free_module()
Vector space of dimension 2 over 7-adic Field with capped relative precision 10
sage: M11.hecke_module_of_level(1)
Modular Forms space of dimension 0 for Modular Group SL(2,Z) of weight 2 over 7-adic Field with capped relative precision 10
