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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
392.1.g.a \(1\) \(0.196\) \(\Q\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{14}) \) \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}-q^{9}-2q^{11}+q^{16}+\cdots\)
392.1.g.b \(2\) \(0.196\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}-q^{8}+q^{9}+\cdots\)
392.1.j.a \(2\) \(0.196\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{2}) \) \(1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{8}+\zeta_{6}q^{9}-\zeta_{6}q^{16}+\cdots\)
392.1.k.a \(2\) \(0.196\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{14}) \) \(-1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{8}+\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\cdots\)
392.1.k.b \(4\) \(0.196\) \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(2\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\beta _{3}q^{6}+\cdots\)
392.2.a.a \(1\) \(3.130\) \(\Q\) None None \(0\) \(-3\) \(1\) \(0\) \(+\) \(q-3q^{3}+q^{5}+6q^{9}-q^{11}-2q^{13}+\cdots\)
392.2.a.b \(1\) \(3.130\) \(\Q\) None None \(0\) \(-2\) \(4\) \(0\) \(-\) \(q-2q^{3}+4q^{5}+q^{9}-8q^{15}+2q^{17}+\cdots\)
392.2.a.c \(1\) \(3.130\) \(\Q\) None None \(0\) \(-1\) \(-1\) \(0\) \(+\) \(q-q^{3}-q^{5}-2q^{9}+3q^{11}-6q^{13}+\cdots\)
392.2.a.d \(1\) \(3.130\) \(\Q\) None None \(0\) \(0\) \(-2\) \(0\) \(+\) \(q-2q^{5}-3q^{9}-4q^{11}-2q^{13}+6q^{17}+\cdots\)
392.2.a.e \(1\) \(3.130\) \(\Q\) None None \(0\) \(1\) \(1\) \(0\) \(-\) \(q+q^{3}+q^{5}-2q^{9}+3q^{11}+6q^{13}+\cdots\)
392.2.a.f \(1\) \(3.130\) \(\Q\) None None \(0\) \(3\) \(-1\) \(0\) \(-\) \(q+3q^{3}-q^{5}+6q^{9}-q^{11}+2q^{13}+\cdots\)
392.2.a.g \(2\) \(3.130\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta q^{3}+2\beta q^{5}-q^{9}+6q^{11}-4\beta q^{13}+\cdots\)
392.2.a.h \(2\) \(3.130\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta q^{3}+\beta q^{5}+5q^{9}-4q^{11}-\beta q^{13}+\cdots\)
392.2.b.a \(2\) \(3.130\) \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(0\) \(q-\beta q^{2}+(-2+\beta )q^{4}+(2+\beta )q^{8}+3q^{9}+\cdots\)
392.2.b.b \(2\) \(3.130\) \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{2}-\beta q^{3}-2q^{4}+\beta q^{5}+2q^{6}+\cdots\)
392.2.b.c \(4\) \(3.130\) 4.0.2312.1 None None \(-1\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
392.2.b.d \(4\) \(3.130\) 4.0.7168.1 \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+\beta _{1}q^{3}+2q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
392.2.b.e \(6\) \(3.130\) 6.0.1142512.1 None None \(2\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+\beta _{3}q^{3}-\beta _{2}q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
392.2.b.f \(6\) \(3.130\) 6.0.1142512.1 None None \(2\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}-\beta _{3}q^{3}-\beta _{2}q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
392.2.b.g \(12\) \(3.130\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(-2\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}-\beta _{9}q^{3}-\beta _{1}q^{4}+(\beta _{7}-\beta _{8}+\cdots)q^{5}+\cdots\)
392.2.e.a \(4\) \(3.130\) 4.0.2048.2 \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-\beta _{3}q^{3}+2q^{4}-\beta _{1}q^{6}-2\beta _{2}q^{8}+\cdots\)
392.2.e.b \(4\) \(3.130\) 4.0.2048.2 \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+2q^{4}+(-\beta _{1}+\beta _{3})q^{6}+\cdots\)
392.2.e.c \(8\) \(3.130\) 8.0.339738624.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}+(\beta _{4}+\beta _{7})q^{3}+(-1+\beta _{6}+\cdots)q^{4}+\cdots\)
392.2.e.d \(8\) \(3.130\) 8.0.\(\cdots\).10 None None \(4\) \(0\) \(0\) \(0\) \(q+(1-\beta _{5})q^{2}-\beta _{2}q^{3}+(\beta _{3}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)
392.2.e.e \(12\) \(3.130\) 12.0.\(\cdots\).2 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}-\beta _{10}q^{3}+\beta _{1}q^{4}-\beta _{9}q^{5}+\cdots\)
392.2.i.a \(2\) \(3.130\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(4\) \(0\) \(q+(-2+2\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
392.2.i.b \(2\) \(3.130\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-1\) \(0\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots\)
392.2.i.c \(2\) \(3.130\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-2\) \(0\) \(q-2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+\cdots\)
392.2.i.d \(2\) \(3.130\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(2\) \(0\) \(q+2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+\cdots\)
392.2.i.e \(2\) \(3.130\) \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(-4\) \(0\) \(q+(2-2\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}-8q^{15}+\cdots\)
392.2.i.f \(2\) \(3.130\) \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(-1\) \(0\) \(q+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{5}-6\zeta_{6}q^{9}+(1+\cdots)q^{11}+\cdots\)
392.2.i.g \(4\) \(3.130\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+5\beta _{2}q^{9}+\cdots\)
392.2.i.h \(4\) \(3.130\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(-2\beta _{1}-2\beta _{3})q^{5}-\beta _{2}q^{9}+\cdots\)
392.2.m.a \(4\) \(3.130\) \(\Q(\sqrt{-3}, \sqrt{-7})\) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(-3+\beta _{1}+\cdots)q^{8}+\cdots\)
392.2.m.b \(8\) \(3.130\) 8.0.339738624.1 \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{2}+\beta _{3}q^{3}+(-2-2\beta _{4})q^{4}+\cdots\)
392.2.m.c \(8\) \(3.130\) 8.0.339738624.1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}+(-\beta _{3}+\beta _{5}-\beta _{7})q^{3}+(-2+\cdots)q^{4}+\cdots\)
392.2.m.d \(8\) \(3.130\) 8.0.339738624.1 \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}-\beta _{1}q^{3}+(-2-2\beta _{4})q^{4}+\cdots\)
392.2.m.e \(8\) \(3.130\) 8.0.339738624.1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+2q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots\)
392.2.m.f \(8\) \(3.130\) \(\Q(\zeta_{24})\) None None \(4\) \(0\) \(0\) \(0\) \(q+(1+\zeta_{24}-\zeta_{24}^{2})q^{2}+(-\zeta_{24}^{4}+\zeta_{24}^{7})q^{3}+\cdots\)
392.2.m.g \(12\) \(3.130\) 12.0.\(\cdots\).2 None None \(0\) \(6\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{8})q^{2}+(1+\beta _{10})q^{3}+(\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
392.2.m.h \(16\) \(3.130\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(-4\) \(0\) \(0\) \(0\) \(q+(\beta _{5}+\beta _{14})q^{2}-\beta _{15}q^{3}+(1+\beta _{5}+\cdots)q^{4}+\cdots\)
392.2.p.a \(4\) \(3.130\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots\)
392.2.p.b \(4\) \(3.130\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+2\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots\)
392.2.p.c \(4\) \(3.130\) \(\Q(\sqrt{-3}, \sqrt{-7})\) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(3-\beta _{1}+\cdots)q^{8}+\cdots\)
392.2.p.d \(8\) \(3.130\) 8.0.\(\cdots\).10 \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}-\beta _{6}q^{3}+(-2+2\beta _{2})q^{4}+\cdots\)
392.2.p.e \(8\) \(3.130\) 8.0.432972864.2 None None \(1\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{6})q^{2}+(\beta _{5}+\beta _{6})q^{3}+\beta _{5}q^{4}+\cdots\)
392.2.p.f \(8\) \(3.130\) 8.0.432972864.2 None None \(1\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{6})q^{2}+(-\beta _{5}-\beta _{6})q^{3}+\cdots\)
392.2.p.g \(12\) \(3.130\) 12.0.\(\cdots\).1 None None \(-2\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{5})q^{2}-\beta _{6}q^{3}-\beta _{3}q^{4}+\cdots\)
392.2.p.h \(24\) \(3.130\) None None \(2\) \(0\) \(0\) \(0\)
392.2.q.a \(42\) \(3.130\) None None \(0\) \(-7\) \(-2\) \(1\)
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