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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
560.1.p.a \(1\) \(0.279\) \(\Q\) \(\Q(\sqrt{-35}) \) None \(0\) \(-1\) \(-1\) \(1\) \(q-q^{3}-q^{5}+q^{7}+q^{11}+q^{13}+q^{15}+\cdots\)
560.1.p.b \(1\) \(0.279\) \(\Q\) \(\Q(\sqrt{-35}) \) None \(0\) \(1\) \(1\) \(-1\) \(q+q^{3}+q^{5}-q^{7}+q^{11}-q^{13}+q^{15}+\cdots\)
560.1.bt.a \(4\) \(0.279\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{3}+\zeta_{12}^{2}q^{5}+\cdots\)
560.2.a.a \(1\) \(4.472\) \(\Q\) None None \(0\) \(-3\) \(-1\) \(1\) \(+\) \(q-3q^{3}-q^{5}+q^{7}+6q^{9}+5q^{11}+\cdots\)
560.2.a.b \(1\) \(4.472\) \(\Q\) None None \(0\) \(-1\) \(-1\) \(-1\) \(-\) \(q-q^{3}-q^{5}-q^{7}-2q^{9}+3q^{11}+5q^{13}+\cdots\)
560.2.a.c \(1\) \(4.472\) \(\Q\) None None \(0\) \(-1\) \(1\) \(-1\) \(+\) \(q-q^{3}+q^{5}-q^{7}-2q^{9}-3q^{11}-q^{13}+\cdots\)
560.2.a.d \(1\) \(4.472\) \(\Q\) None None \(0\) \(0\) \(-1\) \(1\) \(+\) \(q-q^{5}+q^{7}-3q^{9}-4q^{11}-6q^{13}+\cdots\)
560.2.a.e \(1\) \(4.472\) \(\Q\) None None \(0\) \(1\) \(-1\) \(1\) \(-\) \(q+q^{3}-q^{5}+q^{7}-2q^{9}+5q^{11}+q^{13}+\cdots\)
560.2.a.f \(1\) \(4.472\) \(\Q\) None None \(0\) \(3\) \(1\) \(-1\) \(-\) \(q+3q^{3}+q^{5}-q^{7}+6q^{9}+5q^{11}+\cdots\)
560.2.a.g \(2\) \(4.472\) \(\Q(\sqrt{17}) \) None None \(0\) \(-1\) \(2\) \(-2\) \(-\) \(q-\beta q^{3}+q^{5}-q^{7}+(1+\beta )q^{9}+\beta q^{11}+\cdots\)
560.2.a.h \(2\) \(4.472\) \(\Q(\sqrt{33}) \) None None \(0\) \(1\) \(-2\) \(2\) \(-\) \(q+\beta q^{3}-q^{5}+q^{7}+(5+\beta )q^{9}+(-4+\cdots)q^{11}+\cdots\)
560.2.a.i \(2\) \(4.472\) \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(2\) \(2\) \(-\) \(q+\beta q^{3}+q^{5}+q^{7}+(1+\beta )q^{9}-\beta q^{11}+\cdots\)
560.2.e.a \(4\) \(4.472\) \(\Q(\sqrt{5}, \sqrt{-7})\) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}-4q^{9}+\beta _{3}q^{11}+\cdots\)
560.2.e.b \(4\) \(4.472\) \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+\beta _{3}q^{5}+(\beta _{1}-2\beta _{2})q^{7}+q^{9}+\cdots\)
560.2.e.c \(8\) \(4.472\) 8.0.121550625.1 \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{3}-\beta _{2}q^{5}+(\beta _{1}-\beta _{6})q^{7}+(-3+\cdots)q^{9}+\cdots\)
560.2.e.d \(8\) \(4.472\) 8.0.\(\cdots\).5 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{3}+\beta _{4}q^{5}+\beta _{1}q^{7}+q^{9}+2\beta _{3}q^{11}+\cdots\)
560.2.g.a \(2\) \(4.472\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-4\) \(0\) \(q+3iq^{3}+(-2-i)q^{5}-iq^{7}-6q^{9}+\cdots\)
560.2.g.b \(2\) \(4.472\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{3}+(-2-i)q^{5}+iq^{7}+2q^{9}+\cdots\)
560.2.g.c \(2\) \(4.472\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) \(q+(1+2i)q^{5}-iq^{7}+3q^{9}-4iq^{13}+\cdots\)
560.2.g.d \(2\) \(4.472\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) \(q+iq^{3}+(2+i)q^{5}+iq^{7}+2q^{9}+q^{11}+\cdots\)
560.2.g.e \(4\) \(4.472\) \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(4\) \(0\) \(q+(\beta _{1}+\beta _{3})q^{3}+(1+\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+\cdots\)
560.2.g.f \(6\) \(4.472\) 6.0.5161984.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{3}+(\beta _{2}+\beta _{5})q^{5}+\beta _{4}q^{7}+(-1+\cdots)q^{9}+\cdots\)
560.2.k.a \(8\) \(4.472\) 8.0.303595776.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{3}+\beta _{4}q^{5}+(-\beta _{1}+\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots\)
560.2.k.b \(8\) \(4.472\) 8.0.\(\cdots\).7 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{3}+\beta _{3}q^{5}+(\beta _{4}-\beta _{6})q^{7}+(1+\cdots)q^{9}+\cdots\)
560.2.q.a \(2\) \(4.472\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(1\) \(-1\) \(q+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
560.2.q.b \(2\) \(4.472\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(-1\) \(4\) \(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
560.2.q.c \(2\) \(4.472\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(1\) \(-4\) \(q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
560.2.q.d \(2\) \(4.472\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(1\) \(4\) \(q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
560.2.q.e \(2\) \(4.472\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(1\) \(-1\) \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
560.2.q.f \(2\) \(4.472\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(1\) \(-5\) \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
560.2.q.g \(2\) \(4.472\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(1\) \(1\) \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
560.2.q.h \(2\) \(4.472\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(1\) \(5\) \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
560.2.q.i \(2\) \(4.472\) \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(1\) \(-1\) \(q+(3-3\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
560.2.q.j \(4\) \(4.472\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(-2\) \(-2\) \(2\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
560.2.q.k \(4\) \(4.472\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(2\) \(-2\) \(-2\) \(q+(1+\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
560.2.q.l \(6\) \(4.472\) 6.0.11337408.1 None None \(0\) \(0\) \(-3\) \(-6\) \(q+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}-\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)
560.2.r.a \(184\) \(4.472\) None None \(-4\) \(0\) \(0\) \(0\)
560.2.t.a \(144\) \(4.472\) None None \(0\) \(0\) \(0\) \(0\)
560.2.x.a \(12\) \(4.472\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{4}-\beta _{8})q^{3}+(-\beta _{6}+\beta _{9})q^{5}+\cdots\)
560.2.x.b \(24\) \(4.472\) None None \(0\) \(0\) \(0\) \(0\)
560.2.bb.a \(2\) \(4.472\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(-2\) \(-2\) \(2\) \(q+(-1-i)q^{2}+(-1-i)q^{3}+2iq^{4}+\cdots\)
560.2.bb.b \(2\) \(4.472\) \(\Q(\sqrt{-1}) \) None None \(2\) \(2\) \(4\) \(-2\) \(q+(1+i)q^{2}+(1+i)q^{3}+2iq^{4}+(2+\cdots)q^{5}+\cdots\)
560.2.bb.c \(70\) \(4.472\) None None \(-2\) \(-2\) \(-4\) \(-70\)
560.2.bb.d \(70\) \(4.472\) None None \(2\) \(2\) \(2\) \(70\)
560.2.bc.a \(128\) \(4.472\) None None \(0\) \(0\) \(0\) \(0\)
560.2.bd.a \(44\) \(4.472\) None None \(0\) \(0\) \(0\) \(0\)
560.2.bd.b \(52\) \(4.472\) None None \(0\) \(0\) \(0\) \(0\)
560.2.be.a \(184\) \(4.472\) None None \(0\) \(0\) \(0\) \(0\)
560.2.bj.a \(4\) \(4.472\) \(\Q(i, \sqrt{10})\) None None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{1}q^{3}+\beta _{1}q^{5}+(-1-\beta _{2}+\beta _{3})q^{7}+\cdots\)
560.2.bj.b \(8\) \(4.472\) 8.0.\(\cdots\).3 None None \(0\) \(0\) \(0\) \(2\) \(q+\beta _{1}q^{3}+(\beta _{2}-\beta _{6})q^{5}+(-\beta _{4}+\beta _{6}+\cdots)q^{7}+\cdots\)
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