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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
567.1.d.a \(1\) \(0.283\) \(\Q\) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(1\) \(q-q^{2}+q^{7}+q^{8}-q^{11}-q^{14}-q^{16}+\cdots\)
567.1.d.b \(1\) \(0.283\) \(\Q\) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(1\) \(q+q^{2}+q^{7}-q^{8}+q^{11}+q^{14}-q^{16}+\cdots\)
567.1.d.c \(2\) \(0.283\) \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\beta q^{2}+2q^{4}-q^{7}-\beta q^{8}+\beta q^{11}+\cdots\)
567.1.j.a \(2\) \(0.283\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+q^{4}+\zeta_{6}^{2}q^{7}+\zeta_{6}q^{13}+q^{16}-\zeta_{6}q^{19}+\cdots\)
567.1.k.a \(2\) \(0.283\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q-\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{7}+(-1+\zeta_{6}^{2})q^{13}+\cdots\)
567.1.l.a \(2\) \(0.283\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{7}-q^{8}+\zeta_{6}^{2}q^{11}+\cdots\)
567.1.l.b \(2\) \(0.283\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{6}q^{4}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{16}+\zeta_{6}^{2}q^{25}+\cdots\)
567.1.l.c \(2\) \(0.283\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(-1\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{7}+q^{8}-\zeta_{6}^{2}q^{11}+\cdots\)
567.1.l.d \(4\) \(0.283\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(2\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}^{2}+\zeta_{12}^{4}+\cdots)q^{4}+\cdots\)
567.1.n.a \(2\) \(0.283\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-\zeta_{6}q^{4}-\zeta_{6}q^{7}-\zeta_{6}^{2}q^{13}+\zeta_{6}^{2}q^{16}+\cdots\)
567.1.t.a \(2\) \(0.283\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q-q^{4}+\zeta_{6}q^{7}+(1+\zeta_{6})q^{13}+q^{16}+\cdots\)
567.2.a.a \(1\) \(4.528\) \(\Q\) None None \(-1\) \(0\) \(1\) \(-1\) \(+\) \(q-q^{2}-q^{4}+q^{5}-q^{7}+3q^{8}-q^{10}+\cdots\)
567.2.a.b \(1\) \(4.528\) \(\Q\) None None \(1\) \(0\) \(-1\) \(-1\) \(+\) \(q+q^{2}-q^{4}-q^{5}-q^{7}-3q^{8}-q^{10}+\cdots\)
567.2.a.c \(3\) \(4.528\) \(\Q(\zeta_{18})^+\) None None \(-3\) \(0\) \(-3\) \(3\) \(+\) \(q+(-1+\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
567.2.a.d \(3\) \(4.528\) 3.3.321.1 None None \(-1\) \(0\) \(-5\) \(-3\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-2-\beta _{2})q^{5}+\cdots\)
567.2.a.e \(3\) \(4.528\) 3.3.621.1 None None \(0\) \(0\) \(-3\) \(3\) \(-\) \(q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
567.2.a.f \(3\) \(4.528\) 3.3.621.1 None None \(0\) \(0\) \(3\) \(3\) \(-\) \(q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
567.2.a.g \(3\) \(4.528\) 3.3.321.1 None None \(1\) \(0\) \(5\) \(-3\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(2+\beta _{2})q^{5}+\cdots\)
567.2.a.h \(3\) \(4.528\) \(\Q(\zeta_{18})^+\) None None \(3\) \(0\) \(3\) \(3\) \(-\) \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
567.2.a.i \(4\) \(4.528\) \(\Q(\sqrt{3}, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(-4\) \(-\) \(q+\beta _{3}q^{2}-\beta _{2}q^{4}-2\beta _{1}q^{5}-q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots\)
567.2.c.a \(8\) \(4.528\) 8.0.\(\cdots\).3 \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{4}q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots\)
567.2.c.b \(8\) \(4.528\) 8.0.\(\cdots\).6 None None \(0\) \(0\) \(0\) \(-4\) \(q+(-\beta _{3}-\beta _{5})q^{2}-\beta _{1}q^{4}+\beta _{2}q^{5}+\cdots\)
567.2.c.c \(12\) \(4.528\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{2}q^{2}-\beta _{4}q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{6}+\cdots)q^{7}+\cdots\)
567.2.e.a \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(1\) \(-5\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
567.2.e.b \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(-1\) \(-5\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
567.2.e.c \(8\) \(4.528\) 8.0.1767277521.3 None None \(-1\) \(0\) \(-2\) \(1\) \(q+(-\beta _{2}-\beta _{6})q^{2}+(-\beta _{5}+\beta _{7})q^{4}+\cdots\)
567.2.e.d \(8\) \(4.528\) 8.0.1767277521.3 None None \(1\) \(0\) \(2\) \(1\) \(q+(\beta _{2}+\beta _{6})q^{2}+(-\beta _{5}+\beta _{7})q^{4}+(1+\cdots)q^{5}+\cdots\)
567.2.e.e \(10\) \(4.528\) 10.0.\(\cdots\).1 None None \(-2\) \(0\) \(-4\) \(5\) \(q-\beta _{1}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+(-1+\cdots)q^{5}+\cdots\)
567.2.e.f \(10\) \(4.528\) 10.0.\(\cdots\).1 None None \(2\) \(0\) \(4\) \(5\) \(q+\beta _{1}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+(1+\cdots)q^{5}+\cdots\)
567.2.e.g \(16\) \(4.528\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(6\) \(q-\beta _{1}q^{2}+(-\beta _{5}-\beta _{7}-\beta _{8}-\beta _{12}+\cdots)q^{4}+\cdots\)
567.2.f.a \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(-1\) \(1\) \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
567.2.f.b \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(-2\) \(1\) \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots\)
567.2.f.c \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(1\) \(1\) \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
567.2.f.d \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-3\) \(-1\) \(q+2\zeta_{6}q^{4}-3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
567.2.f.e \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(3\) \(-1\) \(q+2\zeta_{6}q^{4}+3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
567.2.f.f \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(-1\) \(1\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
567.2.f.g \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(2\) \(1\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
567.2.f.h \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(1\) \(1\) \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
567.2.f.i \(4\) \(4.528\) \(\Q(\sqrt{-3}, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(2\) \(q+\beta _{1}q^{2}+5\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
567.2.f.j \(4\) \(4.528\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(-2\) \(q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}+(-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
567.2.f.k \(4\) \(4.528\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(-2\) \(q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}+(\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
567.2.f.l \(6\) \(4.528\) 6.0.1156923.1 None None \(0\) \(0\) \(-3\) \(-3\) \(q+\beta _{4}q^{2}+(-\beta _{1}+\beta _{2}-2\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
567.2.f.m \(6\) \(4.528\) 6.0.1156923.1 None None \(0\) \(0\) \(3\) \(-3\) \(q-\beta _{4}q^{2}+(-\beta _{1}+\beta _{2}-2\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
567.2.f.n \(8\) \(4.528\) 8.0.49787136.1 None None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{3}q^{2}+\beta _{4}q^{4}-2\beta _{7}q^{5}+(1-\beta _{5}+\cdots)q^{7}+\cdots\)
567.2.g.a \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(-4\) \(1\) \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-2q^{5}+\cdots\)
567.2.g.b \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(-8\) \(1\) \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-4q^{5}+(2+\cdots)q^{7}+\cdots\)
567.2.g.c \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) \(q+2\zeta_{6}q^{4}+(-3+2\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{13}+\cdots\)
567.2.g.d \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(5\) \(q+2\zeta_{6}q^{4}+(3-\zeta_{6})q^{7}+(7-7\zeta_{6})q^{13}+\cdots\)
567.2.g.e \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(8\) \(1\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+4q^{5}+(2-3\zeta_{6})q^{7}+\cdots\)
567.2.g.f \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(4\) \(1\) \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+2q^{5}+(-1+\cdots)q^{7}+\cdots\)
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