Basis of eigenforms

The following is a table of representatives for the Galois conjugacy classes of eigenforms in $S_2(\Gamma_0(389))$:

	Generator	q-expansion
A1	-	${q - {2}q^{2} - {2}q^{3} + {2}q^{4} - {3}q^{5} + {4}q^{6} - {5}q^{7} + q^{9} + {6}q^{10} + \cdots }$
A2	$\alpha^2-2=0$	${q + {\alpha}q^{2}+({\alpha- {2}})q^{3} - q^{5}+({{-2}\alpha+ {2}})q^{6}+ \cdots}$
A3	$\beta^3 - 4\beta - 2=0$	${q + {\beta}q^{2} - {\beta}q^{3}+({\beta^{2} - {2}})q^{4}+({-\beta^{2} + 1})q^{5} - {\beta^{2}}q^{6} +\cdots}$
A6	$\gamma^6+3\gamma^5-2\gamma^4-8\gamma^3$	${q + {\gamma}q^{2}+({\gamma^{5} + {3}\gamma^{4} - {2}\gamma^{3} - {8}\gamma^{2} + \gamma + {2}})q^{3}+\cdots}$
	$+2\gamma^2+4\gamma-1=0$
A20		(see the field K20 of Section 3)