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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1620.1.f.a \(1\) \(0.808\) \(\Q\) \(\Q(\sqrt{-5}) \) None \(-1\) \(0\) \(-1\) \(-1\) \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
1620.1.f.b \(1\) \(0.808\) \(\Q\) \(\Q(\sqrt{-5}) \) None \(-1\) \(0\) \(1\) \(1\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
1620.1.f.c \(1\) \(0.808\) \(\Q\) \(\Q(\sqrt{-5}) \) None \(1\) \(0\) \(-1\) \(1\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
1620.1.f.d \(1\) \(0.808\) \(\Q\) \(\Q(\sqrt{-5}) \) None \(1\) \(0\) \(1\) \(-1\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
1620.1.f.e \(4\) \(0.808\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{3}q^{2}-q^{4}-\zeta_{12}q^{5}-\zeta_{12}^{3}q^{8}+\cdots\)
1620.1.l.a \(2\) \(0.808\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{5}+(-1+i)q^{7}-q^{11}+(-1+\cdots)q^{17}+\cdots\)
1620.1.l.b \(2\) \(0.808\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-2\) \(q-iq^{5}+(-1+i)q^{7}+q^{11}+(1-i+\cdots)q^{17}+\cdots\)
1620.1.m.a \(8\) \(0.808\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{9}q^{2}-\zeta_{24}^{6}q^{4}-\zeta_{24}q^{5}+\zeta_{24}^{3}q^{8}+\cdots\)
1620.1.p.a \(4\) \(0.808\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{2}-q^{4}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)
1620.1.p.b \(4\) \(0.808\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{15}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)
1620.1.p.c \(4\) \(0.808\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}q^{5}-\zeta_{12}^{3}q^{8}+\cdots\)
1620.1.p.d \(4\) \(0.808\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{5}q^{5}+\cdots\)
1620.1.p.e \(4\) \(0.808\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)
1620.1.v.a \(4\) \(0.808\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(2\) \(q+\zeta_{12}^{5}q^{5}+(-\zeta_{12}-\zeta_{12}^{4})q^{7}+\zeta_{12}^{4}q^{11}+\cdots\)
1620.1.v.b \(4\) \(0.808\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(2\) \(q-\zeta_{12}^{5}q^{5}+(-\zeta_{12}-\zeta_{12}^{4})q^{7}-\zeta_{12}^{4}q^{11}+\cdots\)
1620.1.w.a \(8\) \(0.808\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-\zeta_{24}^{9}q^{5}+\cdots\)
1620.1.w.b \(8\) \(0.808\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-\zeta_{24}q^{5}+\cdots\)
1620.1.w.c \(8\) \(0.808\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-\zeta_{24}^{5}q^{5}+\cdots\)
1620.1.bf.a \(6\) \(0.808\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(-3\) \(q-\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}+\zeta_{18}q^{5}+(\zeta_{18}^{4}+\cdots)q^{7}+\cdots\)
1620.1.bf.b \(6\) \(0.808\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(3\) \(q+\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}+\zeta_{18}q^{5}+(-\zeta_{18}^{4}+\cdots)q^{7}+\cdots\)
1620.1.bp.a \(18\) \(0.808\) \(\Q(\zeta_{54})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{54}^{25}q^{2}-\zeta_{54}^{26}q^{3}-\zeta_{54}^{23}q^{4}+\cdots\)
1620.1.bp.b \(18\) \(0.808\) \(\Q(\zeta_{54})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{54}^{25}q^{2}+\zeta_{54}^{26}q^{3}-\zeta_{54}^{23}q^{4}+\cdots\)
1620.2.a.a \(1\) \(12.936\) \(\Q\) None None \(0\) \(0\) \(-1\) \(-4\) \(-\) \(q-q^{5}-4q^{7}-3q^{11}-4q^{13}+5q^{19}+\cdots\)
1620.2.a.b \(1\) \(12.936\) \(\Q\) None None \(0\) \(0\) \(-1\) \(-1\) \(+\) \(q-q^{5}-q^{7}-4q^{13}+6q^{17}+2q^{19}+\cdots\)
1620.2.a.c \(1\) \(12.936\) \(\Q\) None None \(0\) \(0\) \(-1\) \(2\) \(-\) \(q-q^{5}+2q^{7}+3q^{11}-4q^{13}+6q^{17}+\cdots\)
1620.2.a.d \(1\) \(12.936\) \(\Q\) None None \(0\) \(0\) \(1\) \(-4\) \(+\) \(q+q^{5}-4q^{7}+3q^{11}-4q^{13}+5q^{19}+\cdots\)
1620.2.a.e \(1\) \(12.936\) \(\Q\) None None \(0\) \(0\) \(1\) \(-1\) \(+\) \(q+q^{5}-q^{7}-4q^{13}-6q^{17}+2q^{19}+\cdots\)
1620.2.a.f \(1\) \(12.936\) \(\Q\) None None \(0\) \(0\) \(1\) \(2\) \(+\) \(q+q^{5}+2q^{7}-3q^{11}-4q^{13}-6q^{17}+\cdots\)
1620.2.a.g \(2\) \(12.936\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(-2\) \(-2\) \(+\) \(q-q^{5}+(-1+\beta )q^{7}-\beta q^{11}+(2-2\beta )q^{13}+\cdots\)
1620.2.a.h \(2\) \(12.936\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(2\) \(-2\) \(-\) \(q+q^{5}+(-1+\beta )q^{7}+\beta q^{11}+(2-2\beta )q^{13}+\cdots\)
1620.2.a.i \(3\) \(12.936\) 3.3.564.1 None None \(0\) \(0\) \(-3\) \(3\) \(-\) \(q-q^{5}+(1-\beta _{1})q^{7}-\beta _{2}q^{11}+(2+\beta _{2})q^{13}+\cdots\)
1620.2.a.j \(3\) \(12.936\) 3.3.564.1 None None \(0\) \(0\) \(3\) \(3\) \(-\) \(q+q^{5}+(1-\beta _{1})q^{7}+\beta _{2}q^{11}+(2+\beta _{2})q^{13}+\cdots\)
1620.2.d.a \(2\) \(12.936\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}+iq^{7}+q^{11}-iq^{17}+\cdots\)
1620.2.d.b \(2\) \(12.936\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) \(q+(1+i)q^{5}+iq^{7}-q^{11}+iq^{17}+\cdots\)
1620.2.d.c \(6\) \(12.936\) 6.0.301925376.2 None None \(0\) \(0\) \(-1\) \(0\) \(q+\beta _{3}q^{5}+(\beta _{1}+\beta _{3}-\beta _{4})q^{7}-\beta _{2}q^{11}+\cdots\)
1620.2.d.d \(6\) \(12.936\) 6.0.301925376.2 None None \(0\) \(0\) \(1\) \(0\) \(q-\beta _{3}q^{5}+(\beta _{1}+\beta _{3}-\beta _{4})q^{7}+\beta _{2}q^{11}+\cdots\)
1620.2.d.e \(8\) \(12.936\) 8.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{5}-\beta _{2}q^{7}+(-\beta _{1}+\beta _{4}+\beta _{6}+\cdots)q^{11}+\cdots\)
1620.2.e.a \(48\) \(12.936\) None None \(0\) \(0\) \(0\) \(0\)
1620.2.e.b \(48\) \(12.936\) None None \(0\) \(0\) \(0\) \(0\)
1620.2.i.a \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-2\) \(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
1620.2.i.b \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-2\) \(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
1620.2.i.c \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-2\) \(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
1620.2.i.d \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(1\) \(q-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
1620.2.i.e \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(4\) \(q-\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
1620.2.i.f \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(4\) \(q-\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
1620.2.i.g \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(-2\) \(q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
1620.2.i.h \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(-2\) \(q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
1620.2.i.i \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(-2\) \(q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
1620.2.i.j \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(1\) \(q+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
1620.2.i.k \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(4\) \(q+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
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