2. If the 2007th degree equation
$$
x^{2007}-4014 x^{2006}+a_{2} 005 x^{2005}+\cdots+a_{1} x+a_{0}=0
$$

has 2007 positive real roots, then, for all possible equations, the maximum value of $\sum_{k=0}^{2005}\left|a_{k}\right|$ is ( ).
(A) $2^{2007}-4014$
(B) $2^{2007}-4015$
(C) $3^{2007}-4014$
(D) $3^{2007}-4015$
2. D.

Let the 2007 positive real roots of the original equation be $x_{1}$, $x_{2}, \cdots, x_{2007}$. We can obtain the identity
$$
\begin{array}{l}
x^{200}-4014 x^{206}+a_{20 \sigma} x^{2 \omega 6}+\cdots+a_{1} x+a_{0} \\
=\left(x-x_{1}\right)\left(x-x_{2}\right) \cdots\left(x-x_{2007}\right) .
\end{array}
$$

By Vieta's formulas, we have
$$
(-1)^{k} a_{2007-k}>0(k=2,3, \cdots, 2007) \text {. }
$$

In the above identity, let $x=-1$, we get
$$
\begin{array}{l}
(-1)^{2007}-4014(-1)^{2006}+ \\
a_{2000}(-1)^{2005}+\cdots+a_{1}(-1)+a_{0} \\
=\left(-1-x_{1}\right)\left(-1-x_{2}\right) \cdots\left(-1-x_{2007}\right),
\end{array}
$$

which is
$$
\begin{array}{c}
1+4014+a_{2000}(-1)^{2}+\cdots+ \\
a_{1}(-1)^{2006}+a_{0}(-1)^{2007} \\
=\left(1+x_{1}\right)\left(1+x_{2}\right) \cdots\left(1+x_{2007}\right) .
\end{array}
$$

By the AM-GM inequality, we have
$$
\begin{array}{l}
\left(1+x_{1}\right)\left(1+x_{2}\right) \cdots\left(1+x_{2007}\right) \\
\leqslant\left(1+\frac{x_{1}+x_{2}+\cdots+x_{2007}}{2007}\right)^{2007}=3^{2007} .
\end{array}
$$

Therefore, $\sum_{k=0}^{2005}\left|a_{k}\right| \leqslant 3^{2007}-4015$.
When $x_{1}=x_{2}=\cdots=x_{2007}=2$, the equality holds.