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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1336.1.e.a \(1\) \(0.667\) \(\Q\) \(\Q(\sqrt{-167}) \), \(\Q(\sqrt{-334}) \) \(\Q(\sqrt{2}) \) \(-1\) \(0\) \(0\) \(2\) \(q-q^{2}+q^{4}+2q^{7}-q^{8}+q^{9}-2q^{14}+\cdots\)
1336.1.e.b \(1\) \(0.667\) \(\Q\) \(\Q(\sqrt{-334}) \) None \(1\) \(0\) \(-1\) \(-1\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}+q^{9}+\cdots\)
1336.1.e.c \(1\) \(0.667\) \(\Q\) \(\Q(\sqrt{-334}) \) None \(1\) \(0\) \(1\) \(-1\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{9}+\cdots\)
1336.1.e.d \(2\) \(0.667\) \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-334}) \) None \(-2\) \(0\) \(0\) \(-2\) \(q-q^{2}+q^{4}-\beta q^{5}-q^{7}-q^{8}+q^{9}+\cdots\)
1336.1.e.e \(10\) \(0.667\) \(\Q(\zeta_{22})\) \(\Q(\sqrt{-167}) \) None \(1\) \(0\) \(0\) \(-2\) \(q-\zeta_{22}^{6}q^{2}+(\zeta_{22}^{2}+\zeta_{22}^{9})q^{3}-\zeta_{22}q^{4}+\cdots\)
1336.2.a.a \(2\) \(10.668\) \(\Q(\sqrt{5}) \) None None \(0\) \(3\) \(0\) \(-7\) \(+\) \(q+(1+\beta )q^{3}+(1-2\beta )q^{5}+(-4+\beta )q^{7}+\cdots\)
1336.2.a.b \(7\) \(10.668\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(0\) \(-6\) \(0\) \(-1\) \(+\) \(q+(-1+\beta _{1})q^{3}+(-\beta _{4}+\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1336.2.a.c \(9\) \(10.668\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(0\) \(-1\) \(-8\) \(2\) \(+\) \(q-\beta _{1}q^{3}+(-1-\beta _{2}-\beta _{8})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1336.2.a.d \(12\) \(10.668\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(-1\) \(8\) \(-4\) \(-\) \(q-\beta _{1}q^{3}+(1-\beta _{9})q^{5}+\beta _{11}q^{7}+(2+\cdots)q^{9}+\cdots\)
1336.2.a.e \(12\) \(10.668\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(5\) \(-2\) \(10\) \(-\) \(q+\beta _{1}q^{3}+\beta _{9}q^{5}+(1+\beta _{11})q^{7}+(2+\cdots)q^{9}+\cdots\)
1336.3.g.a \(84\) \(36.403\) None None \(0\) \(0\) \(0\) \(0\)
1336.4.a.a \(29\) \(78.827\) None None \(0\) \(-9\) \(12\) \(-82\) \(-\)
1336.4.a.b \(30\) \(78.827\) None None \(0\) \(1\) \(-40\) \(16\) \(-\)
1336.4.a.c \(32\) \(78.827\) None None \(0\) \(15\) \(2\) \(44\) \(+\)
1336.4.a.d \(33\) \(78.827\) None None \(0\) \(1\) \(40\) \(-26\) \(+\)
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