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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
468.1.e.a \(1\) \(0.234\) \(\Q\) \(\Q(\sqrt{-39}) \), \(\Q(\sqrt{-13}) \) \(\Q(\sqrt{3}) \) \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+2q^{11}-q^{13}+q^{16}+\cdots\)
468.1.e.b \(1\) \(0.234\) \(\Q\) \(\Q(\sqrt{-39}) \), \(\Q(\sqrt{-13}) \) \(\Q(\sqrt{3}) \) \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}-2q^{11}-q^{13}+q^{16}+\cdots\)
468.1.e.c \(2\) \(0.234\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-39}) \) \(\Q(\sqrt{39}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{5}+iq^{8}+2q^{10}+\cdots\)
468.1.o.a \(4\) \(0.234\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{8}+q^{13}+\cdots\)
468.1.q.a \(4\) \(0.234\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots\)
468.1.r.a \(4\) \(0.234\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(-2\) \(q-\beta _{3}q^{5}+(-1+\beta _{2})q^{7}+(\beta _{1}-\beta _{3})q^{11}+\cdots\)
468.1.v.a \(4\) \(0.234\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{4}q^{5}+\cdots\)
468.1.y.a \(4\) \(0.234\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{3}q^{3}-q^{4}-\zeta_{12}^{4}q^{5}+\cdots\)
468.1.z.a \(2\) \(0.234\) \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{13}) \) \(0\) \(1\) \(0\) \(0\) \(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{13}+(-\zeta_{6}+\cdots)q^{17}+\cdots\)
468.1.br.a \(2\) \(0.234\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None \(1\) \(0\) \(2\) \(0\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{5}-q^{8}+\zeta_{6}q^{10}+\cdots\)
468.1.bx.a \(8\) \(0.234\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}-\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
468.1.cd.a \(4\) \(0.234\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{7}-\zeta_{12}q^{13}+(\zeta_{12}+\cdots)q^{19}+\cdots\)
468.2.a.a \(1\) \(3.737\) \(\Q\) None None \(0\) \(0\) \(-4\) \(4\) \(-\) \(q-4q^{5}+4q^{7}+4q^{11}-q^{13}+8q^{23}+\cdots\)
468.2.a.b \(1\) \(3.737\) \(\Q\) None None \(0\) \(0\) \(-2\) \(-2\) \(+\) \(q-2q^{5}-2q^{7}+2q^{11}-q^{13}-6q^{17}+\cdots\)
468.2.a.c \(1\) \(3.737\) \(\Q\) None None \(0\) \(0\) \(0\) \(2\) \(-\) \(q+2q^{7}+q^{13}+6q^{17}+2q^{19}-5q^{25}+\cdots\)
468.2.a.d \(1\) \(3.737\) \(\Q\) None None \(0\) \(0\) \(4\) \(-2\) \(-\) \(q+4q^{5}-2q^{7}+4q^{11}+q^{13}-2q^{17}+\cdots\)
468.2.a.e \(1\) \(3.737\) \(\Q\) None None \(0\) \(0\) \(4\) \(4\) \(-\) \(q+4q^{5}+4q^{7}-4q^{11}-q^{13}-8q^{23}+\cdots\)
468.2.b.a \(2\) \(3.737\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{5}-\zeta_{6}q^{11}+(-1+\zeta_{6})q^{13}+\cdots\)
468.2.b.b \(2\) \(3.737\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{7}+(-1-\zeta_{6})q^{13}-\zeta_{6}q^{19}+\cdots\)
468.2.b.c \(2\) \(3.737\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{5}-2iq^{7}-3iq^{11}+(3+i)q^{13}+\cdots\)
468.2.c.a \(4\) \(3.737\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}+2q^{4}-2\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+\cdots\)
468.2.c.b \(8\) \(3.737\) 8.0.157351936.1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{4})q^{4}-\beta _{5}q^{5}+\cdots\)
468.2.c.c \(12\) \(3.737\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{3}+\beta _{10})q^{5}+(\beta _{6}+\cdots)q^{7}+\cdots\)
468.2.h.a \(4\) \(3.737\) \(\Q(\sqrt{-2}, \sqrt{13})\) \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(0\) \(-4\) \(q-\beta _{2}q^{2}-2q^{4}+(-1-\beta _{3})q^{7}+2\beta _{2}q^{8}+\cdots\)
468.2.h.b \(4\) \(3.737\) \(\Q(\sqrt{-2}, \sqrt{13})\) \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{2}q^{2}-2q^{4}+(1+\beta _{3})q^{7}+2\beta _{2}q^{8}+\cdots\)
468.2.h.c \(4\) \(3.737\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{2}+2q^{4}-\zeta_{8}^{2}q^{5}-2\zeta_{8}^{2}q^{8}+\cdots\)
468.2.h.d \(16\) \(3.737\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{2}+(-\beta _{3}-\beta _{8})q^{4}+(-\beta _{6}-\beta _{12}+\cdots)q^{5}+\cdots\)
468.2.i.a \(2\) \(3.737\) \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(0\) \(-2\) \(q+(2-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots\)
468.2.i.b \(10\) \(3.737\) 10.0.\(\cdots\).1 None None \(0\) \(-3\) \(7\) \(2\) \(q-\beta _{1}q^{3}+(2-\beta _{1}-\beta _{2}+2\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
468.2.i.c \(12\) \(3.737\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(-1\) \(0\) \(q+(-\beta _{5}-\beta _{7})q^{3}+\beta _{1}q^{5}+(\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
468.2.j.a \(28\) \(3.737\) None None \(0\) \(0\) \(0\) \(2\)
468.2.k.a \(28\) \(3.737\) None None \(0\) \(0\) \(0\) \(-4\)
468.2.l.a \(2\) \(3.737\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-4\) \(-1\) \(q-2q^{5}-\zeta_{6}q^{7}+(-5+5\zeta_{6})q^{11}+\cdots\)
468.2.l.b \(2\) \(3.737\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-4\) \(-1\) \(q-2q^{5}-\zeta_{6}q^{7}+(2-2\zeta_{6})q^{11}+(4+\cdots)q^{13}+\cdots\)
468.2.l.c \(2\) \(3.737\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-5\) \(q-5\zeta_{6}q^{7}+(-4+\zeta_{6})q^{13}-8\zeta_{6}q^{19}+\cdots\)
468.2.l.d \(2\) \(3.737\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(6\) \(4\) \(q+3q^{5}+4\zeta_{6}q^{7}+(-3-\zeta_{6})q^{13}+\cdots\)
468.2.l.e \(4\) \(3.737\) \(\Q(\sqrt{-3}, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{3}q^{5}+(2+2\beta _{2})q^{7}+(-2\beta _{1}-2\beta _{3})q^{11}+\cdots\)
468.2.n.a \(2\) \(3.737\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(-6\) \(0\) \(q+(-1-i)q^{2}+2iq^{4}+(-3-3i)q^{5}+\cdots\)
468.2.n.b \(2\) \(3.737\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(-4\) \(0\) \(q+(-1+i)q^{2}-2iq^{4}+(-2-2i)q^{5}+\cdots\)
468.2.n.c \(2\) \(3.737\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(6\) \(0\) \(q+(-1-i)q^{2}+2iq^{4}+(3+3i)q^{5}+\cdots\)
468.2.n.d \(2\) \(3.737\) \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(-4\) \(0\) \(q+(1-i)q^{2}-2iq^{4}+(-2-2i)q^{5}+\cdots\)
468.2.n.e \(2\) \(3.737\) \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(2\) \(-4\) \(q+(1+i)q^{2}+2iq^{4}+(1+i)q^{5}+(-2+\cdots)q^{7}+\cdots\)
468.2.n.f \(2\) \(3.737\) \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(2\) \(4\) \(q+(1+i)q^{2}+2iq^{4}+(1+i)q^{5}+(2+\cdots)q^{7}+\cdots\)
468.2.n.g \(2\) \(3.737\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(6\) \(0\) \(q+(1+i)q^{2}+2iq^{4}+(3+3i)q^{5}+(-2+\cdots)q^{8}+\cdots\)
468.2.n.h \(8\) \(3.737\) 8.0.157351936.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
468.2.n.i \(8\) \(3.737\) 8.0.18939904.2 None None \(4\) \(0\) \(0\) \(0\) \(q+(1-\beta _{2}+\beta _{5}-\beta _{7})q^{2}+(-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
468.2.n.j \(10\) \(3.737\) 10.0.\(\cdots\).1 None None \(-4\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+(-\beta _{5}-\beta _{7})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
468.2.n.k \(10\) \(3.737\) 10.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(\beta _{7}+\beta _{8})q^{4}+(-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
468.2.n.l \(16\) \(3.737\) 16.0.\(\cdots\).7 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{11}q^{2}+\beta _{7}q^{4}-\beta _{2}q^{5}+(\beta _{7}-\beta _{9}+\cdots)q^{7}+\cdots\)
468.2.p.a \(12\) \(3.737\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{8}q^{5}-\beta _{4}q^{7}+(\beta _{6}+\beta _{9})q^{11}+(-1+\cdots)q^{13}+\cdots\)
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