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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
384.1.h.a \(1\) \(0.192\) \(\Q\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{3}) \) \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{9}+2q^{11}-q^{25}-q^{27}+\cdots\)
384.1.h.b \(1\) \(0.192\) \(\Q\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{3}) \) \(0\) \(1\) \(0\) \(0\) \(q+q^{3}+q^{9}-2q^{11}-q^{25}+q^{27}+\cdots\)
384.2.a.a \(1\) \(3.066\) \(\Q\) None None \(0\) \(-1\) \(-4\) \(2\) \(-\) \(q-q^{3}-4q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots\)
384.2.a.b \(1\) \(3.066\) \(\Q\) None None \(0\) \(-1\) \(0\) \(-2\) \(+\) \(q-q^{3}-2q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
384.2.a.c \(1\) \(3.066\) \(\Q\) None None \(0\) \(-1\) \(0\) \(2\) \(-\) \(q-q^{3}+2q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
384.2.a.d \(1\) \(3.066\) \(\Q\) None None \(0\) \(-1\) \(4\) \(-2\) \(-\) \(q-q^{3}+4q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots\)
384.2.a.e \(1\) \(3.066\) \(\Q\) None None \(0\) \(1\) \(-4\) \(-2\) \(+\) \(q+q^{3}-4q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots\)
384.2.a.f \(1\) \(3.066\) \(\Q\) None None \(0\) \(1\) \(0\) \(-2\) \(-\) \(q+q^{3}-2q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
384.2.a.g \(1\) \(3.066\) \(\Q\) None None \(0\) \(1\) \(0\) \(2\) \(-\) \(q+q^{3}+2q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
384.2.a.h \(1\) \(3.066\) \(\Q\) None None \(0\) \(1\) \(4\) \(2\) \(-\) \(q+q^{3}+4q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots\)
384.2.c.a \(4\) \(3.066\) \(\Q(i, \sqrt{5})\) None None \(0\) \(-2\) \(0\) \(0\) \(q+(-1+\beta _{3})q^{3}+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
384.2.c.b \(4\) \(3.066\) \(\Q(i, \sqrt{5})\) None None \(0\) \(-2\) \(0\) \(0\) \(q+(-1+\beta _{3})q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
384.2.c.c \(4\) \(3.066\) \(\Q(i, \sqrt{5})\) None None \(0\) \(2\) \(0\) \(0\) \(q+(1+\beta _{1})q^{3}+(\beta _{1}+\beta _{3})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
384.2.c.d \(4\) \(3.066\) \(\Q(i, \sqrt{5})\) None None \(0\) \(2\) \(0\) \(0\) \(q+(1+\beta _{1})q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
384.2.d.a \(2\) \(3.066\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-8\) \(q+iq^{3}-4q^{7}-q^{9}+4iq^{11}+4iq^{13}+\cdots\)
384.2.d.b \(2\) \(3.066\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(8\) \(q+iq^{3}+4q^{7}-q^{9}+4iq^{11}-4iq^{13}+\cdots\)
384.2.d.c \(4\) \(3.066\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}+\zeta_{8}^{3}q^{7}-q^{9}+\cdots\)
384.2.f.a \(4\) \(3.066\) \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}-3q^{9}-2\beta _{2}q^{11}+\cdots\)
384.2.f.b \(4\) \(3.066\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+(\zeta_{8}+\zeta_{8}^{2})q^{5}-\zeta_{8}^{3}q^{7}+\cdots\)
384.2.f.c \(4\) \(3.066\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+(1-\zeta_{8}^{2})q^{9}+(-2\zeta_{8}+\zeta_{8}^{3})q^{11}+\cdots\)
384.2.f.d \(4\) \(3.066\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+(-\zeta_{8}-\zeta_{8}^{2})q^{5}+\zeta_{8}^{3}q^{7}+\cdots\)
384.2.j.a \(8\) \(3.066\) 8.0.18939904.2 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+(\beta _{3}-\beta _{5})q^{5}+(\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{7}+\cdots\)
384.2.j.b \(8\) \(3.066\) 8.0.18939904.2 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}+(-\beta _{2}+\beta _{6})q^{5}+(\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\)
384.2.k.a \(12\) \(3.066\) 12.0.\(\cdots\).2 None None \(0\) \(-2\) \(0\) \(8\) \(q+\beta _{4}q^{3}+\beta _{6}q^{5}+(1-\beta _{11})q^{7}+(-\beta _{3}+\cdots)q^{9}+\cdots\)
384.2.k.b \(12\) \(3.066\) 12.0.\(\cdots\).2 None None \(0\) \(2\) \(0\) \(-8\) \(q-\beta _{10}q^{3}-\beta _{7}q^{5}+(-1+\beta _{11})q^{7}+\cdots\)
384.2.n.a \(32\) \(3.066\) None None \(0\) \(0\) \(0\) \(0\)
384.2.o.a \(56\) \(3.066\) None None \(0\) \(4\) \(0\) \(8\)
384.2.v.a \(512\) \(3.066\) None None \(0\) \(0\) \(0\) \(0\)
384.2.w.a \(992\) \(3.066\) None None \(0\) \(-16\) \(0\) \(-32\)
384.3.b.a \(4\) \(10.463\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}+\zeta_{12}^{3}q^{5}+\zeta_{12}^{2}q^{7}+3q^{9}+\cdots\)
384.3.b.b \(4\) \(10.463\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+3q^{9}+\cdots\)
384.3.b.c \(8\) \(10.463\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{2}q^{3}+(-\zeta_{24}^{3}+\zeta_{24}^{5})q^{5}+\cdots\)
384.3.e.a \(8\) \(10.463\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(-4\) \(0\) \(-8\) \(q-\beta _{1}q^{3}+\beta _{3}q^{5}+(-1-\beta _{2})q^{7}+(\beta _{2}+\cdots)q^{9}+\cdots\)
384.3.e.b \(8\) \(10.463\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(-4\) \(0\) \(8\) \(q-\beta _{1}q^{3}+\beta _{2}q^{5}+(1+\beta _{3})q^{7}+(\beta _{3}+\cdots)q^{9}+\cdots\)
384.3.e.c \(8\) \(10.463\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(4\) \(0\) \(-8\) \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-1-\beta _{3})q^{7}+(\beta _{3}+\cdots)q^{9}+\cdots\)
384.3.e.d \(8\) \(10.463\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(4\) \(0\) \(8\) \(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(1+\beta _{2})q^{7}+(\beta _{2}+\cdots)q^{9}+\cdots\)
384.3.g.a \(8\) \(10.463\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(-16\) \(0\) \(q-\zeta_{24}q^{3}+(-2+\zeta_{24}^{3})q^{5}+(-\zeta_{24}^{2}+\cdots)q^{7}+\cdots\)
384.3.g.b \(8\) \(10.463\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(16\) \(0\) \(q+\zeta_{24}q^{3}+(2-\zeta_{24}^{3})q^{5}+(-\zeta_{24}^{2}+\cdots)q^{7}+\cdots\)
384.3.h.a \(2\) \(10.463\) \(\Q(\sqrt{6}) \) \(\Q(\sqrt{-6}) \) None \(0\) \(-6\) \(0\) \(0\) \(q-3q^{3}+\beta q^{5}+\beta q^{7}+9q^{9}-10q^{11}+\cdots\)
384.3.h.b \(2\) \(10.463\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(-1+\beta )q^{3}+(-7-2\beta )q^{9}-14q^{11}+\cdots\)
384.3.h.c \(2\) \(10.463\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(1+\beta )q^{3}+(-7+2\beta )q^{9}+14q^{11}+\cdots\)
384.3.h.d \(2\) \(10.463\) \(\Q(\sqrt{6}) \) \(\Q(\sqrt{-6}) \) None \(0\) \(6\) \(0\) \(0\) \(q+3q^{3}+\beta q^{5}-\beta q^{7}+9q^{9}+10q^{11}+\cdots\)
384.3.h.e \(4\) \(10.463\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(-16\) \(0\) \(q+\beta _{3}q^{3}-4q^{5}+(-2\beta _{1}-2\beta _{3})q^{7}+\cdots\)
384.3.h.f \(4\) \(10.463\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(16\) \(0\) \(q-\beta _{1}q^{3}+4q^{5}+(-2\beta _{1}-2\beta _{3})q^{7}+\cdots\)
384.3.h.g \(16\) \(10.463\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{8}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}+(-1-\beta _{5}+\cdots)q^{9}+\cdots\)
384.3.i.a \(8\) \(10.463\) 8.0.629407744.1 None None \(0\) \(-4\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(3\beta _{4}-\beta _{6}-\beta _{7})q^{5}+\cdots\)
384.3.i.b \(8\) \(10.463\) 8.0.629407744.1 None None \(0\) \(4\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(3\beta _{4}-\beta _{6}+\cdots)q^{5}+\cdots\)
384.3.i.c \(20\) \(10.463\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(-6\) \(0\) \(0\) \(q-\beta _{5}q^{3}+(\beta _{8}-\beta _{9}-\beta _{10})q^{5}-\beta _{6}q^{7}+\cdots\)
384.3.i.d \(20\) \(10.463\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(6\) \(0\) \(0\) \(q+\beta _{5}q^{3}+(\beta _{8}-\beta _{9}-\beta _{10})q^{5}+\beta _{6}q^{7}+\cdots\)
384.3.l.a \(16\) \(10.463\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+\beta _{9}q^{5}-\beta _{5}q^{7}-3\beta _{4}q^{9}+\cdots\)
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