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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
387.1.b.a \(1\) \(0.193\) \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-43}) \) \(\Q(\sqrt{129}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{4}-2q^{13}+q^{16}+q^{25}-2q^{31}+\cdots\)
387.1.w.a \(6\) \(0.193\) \(\Q(\zeta_{14})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{14}q^{4}+(-\zeta_{14}^{2}-\zeta_{14}^{5})q^{7}+(-\zeta_{14}^{4}+\cdots)q^{13}+\cdots\)
387.2.a.a \(1\) \(3.090\) \(\Q\) None None \(-1\) \(0\) \(-2\) \(0\) \(-\) \(q-q^{2}-q^{4}-2q^{5}+3q^{8}+2q^{10}+\cdots\)
387.2.a.b \(1\) \(3.090\) \(\Q\) None None \(-1\) \(0\) \(1\) \(-3\) \(+\) \(q-q^{2}-q^{4}+q^{5}-3q^{7}+3q^{8}-q^{10}+\cdots\)
387.2.a.c \(1\) \(3.090\) \(\Q\) None None \(0\) \(0\) \(2\) \(-2\) \(-\) \(q-2q^{4}+2q^{5}-2q^{7}+5q^{11}+3q^{13}+\cdots\)
387.2.a.d \(1\) \(3.090\) \(\Q\) None None \(1\) \(0\) \(-1\) \(-3\) \(+\) \(q+q^{2}-q^{4}-q^{5}-3q^{7}-3q^{8}-q^{10}+\cdots\)
387.2.a.e \(1\) \(3.090\) \(\Q\) None None \(2\) \(0\) \(4\) \(0\) \(-\) \(q+2q^{2}+2q^{4}+4q^{5}+8q^{10}-3q^{11}+\cdots\)
387.2.a.f \(2\) \(3.090\) \(\Q(\sqrt{2}) \) None None \(-2\) \(0\) \(-2\) \(2\) \(+\) \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
387.2.a.g \(2\) \(3.090\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(4\) \(-\) \(q-2q^{4}+2\beta q^{5}+2q^{7}-3\beta q^{11}+5q^{13}+\cdots\)
387.2.a.h \(2\) \(3.090\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(-4\) \(-4\) \(+\) \(q+\beta q^{2}+(-2-\beta )q^{5}+(-2-\beta )q^{7}+\cdots\)
387.2.a.i \(3\) \(3.090\) 3.3.568.1 None None \(2\) \(0\) \(4\) \(4\) \(-\) \(q+(1-\beta _{1})q^{2}+(3+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
387.2.a.j \(4\) \(3.090\) \(\Q(\sqrt{5}, \sqrt{13})\) None None \(0\) \(0\) \(0\) \(-2\) \(-\) \(q+(\beta _{1}+\beta _{3})q^{2}+3q^{4}+\beta _{1}q^{5}+(-1+\cdots)q^{7}+\cdots\)
387.2.d.a \(4\) \(3.090\) \(\Q(\sqrt{-2}, \sqrt{43})\) \(\Q(\sqrt{-43}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2q^{4}+\beta _{1}q^{11}+\beta _{3}q^{13}+4q^{16}+\cdots\)
387.2.d.b \(12\) \(3.090\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+(2+\beta _{3}+\beta _{6})q^{4}+\beta _{1}q^{5}+\cdots\)
387.2.e.a \(84\) \(3.090\) None None \(0\) \(-5\) \(5\) \(3\)
387.2.f.a \(2\) \(3.090\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(-3\) \(-2\) \(3\) \(q+(-1+\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
387.2.f.b \(4\) \(3.090\) \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(-1\) \(6\) \(-4\) \(7\) \(q-\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\)
387.2.f.c \(38\) \(3.090\) None None \(-4\) \(-7\) \(-9\) \(-7\)
387.2.f.d \(40\) \(3.090\) None None \(6\) \(2\) \(17\) \(-3\)
387.2.g.a \(84\) \(3.090\) None None \(0\) \(1\) \(-10\) \(-6\)
387.2.h.a \(2\) \(3.090\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(-1\) \(-3\) \(q-q^{2}-q^{4}+(-1+\zeta_{6})q^{5}-3\zeta_{6}q^{7}+\cdots\)
387.2.h.b \(2\) \(3.090\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q-2q^{4}+\zeta_{6}q^{7}+7\zeta_{6}q^{13}+4q^{16}+\cdots\)
387.2.h.c \(2\) \(3.090\) \(\Q(\sqrt{-3}) \) None None \(4\) \(0\) \(2\) \(-3\) \(q+2q^{2}+2q^{4}+(2-2\zeta_{6})q^{5}-3\zeta_{6}q^{7}+\cdots\)
387.2.h.d \(4\) \(3.090\) \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(6\) \(0\) \(-2\) \(4\) \(q+(1-\beta _{2})q^{2}-3\beta _{2}q^{4}-2\beta _{1}q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
387.2.h.e \(6\) \(3.090\) 6.0.64827.1 None None \(-2\) \(0\) \(-1\) \(5\) \(q-\beta _{2}q^{2}+(-1+\beta _{2}-\beta _{3})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
387.2.h.f \(6\) \(3.090\) 6.0.1783323.2 None None \(2\) \(0\) \(3\) \(-3\) \(q-\beta _{2}q^{2}+(1+\beta _{3})q^{4}+(\beta _{3}+\beta _{4}-\beta _{5})q^{5}+\cdots\)
387.2.h.g \(12\) \(3.090\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(2\) \(q+(-\beta _{1}-\beta _{6})q^{2}+(2+\beta _{2}+\beta _{4}+\beta _{7}+\cdots)q^{4}+\cdots\)
387.2.k.a \(84\) \(3.090\) None None \(0\) \(-3\) \(-3\) \(-3\)
387.2.l.a \(84\) \(3.090\) None None \(0\) \(0\) \(0\) \(0\)
387.2.m.a \(84\) \(3.090\) None None \(0\) \(-3\) \(-6\) \(0\)
387.2.t.a \(28\) \(3.090\) None None \(0\) \(0\) \(0\) \(6\)
387.2.u.a \(6\) \(3.090\) \(\Q(\zeta_{14})\) None None \(-3\) \(0\) \(-2\) \(-16\) \(q+(-\zeta_{14}-\zeta_{14}^{3}-\zeta_{14}^{5})q^{2}+(-1+\cdots)q^{4}+\cdots\)
387.2.u.b \(6\) \(3.090\) \(\Q(\zeta_{14})\) None None \(5\) \(0\) \(-10\) \(0\) \(q+(\zeta_{14}-\zeta_{14}^{2}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots\)
387.2.u.c \(6\) \(3.090\) \(\Q(\zeta_{14})\) None None \(5\) \(0\) \(3\) \(0\) \(q+(\zeta_{14}-\zeta_{14}^{2}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots\)
387.2.u.d \(12\) \(3.090\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-3\) \(0\) \(10\) \(14\) \(q+(-1+\beta _{2}+\beta _{6}+\beta _{7}+\beta _{8}-\beta _{9}+\cdots)q^{2}+\cdots\)
387.2.u.e \(30\) \(3.090\) None None \(2\) \(0\) \(4\) \(2\)
387.2.u.f \(48\) \(3.090\) None None \(0\) \(0\) \(0\) \(-24\)
387.2.v.a \(96\) \(3.090\) None None \(0\) \(0\) \(0\) \(0\)
387.2.y.a \(12\) \(3.090\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-2\zeta_{21}^{3}q^{4}+(1+3\zeta_{21}-\zeta_{21}^{2}+\zeta_{21}^{3}+\cdots)q^{7}+\cdots\)
387.2.y.b \(36\) \(3.090\) None None \(-2\) \(0\) \(-3\) \(-11\)
387.2.y.c \(36\) \(3.090\) None None \(10\) \(0\) \(17\) \(6\)
387.2.y.d \(48\) \(3.090\) None None \(-2\) \(0\) \(-1\) \(-16\)
387.2.y.e \(72\) \(3.090\) None None \(0\) \(0\) \(0\) \(26\)
387.2.z.a \(504\) \(3.090\) None None \(-7\) \(-15\) \(3\) \(-8\)
387.2.ba.a \(504\) \(3.090\) None None \(-7\) \(-12\) \(-9\) \(-14\)
387.2.bb.a \(504\) \(3.090\) None None \(-7\) \(-9\) \(-12\) \(4\)
387.2.bc.a \(168\) \(3.090\) None None \(0\) \(0\) \(0\) \(-6\)
387.2.bj.a \(504\) \(3.090\) None None \(-21\) \(-11\) \(-15\) \(0\)
387.2.bk.a \(504\) \(3.090\) None None \(-21\) \(-14\) \(-21\) \(0\)
387.2.bl.a \(504\) \(3.090\) None None \(-21\) \(-11\) \(-18\) \(-18\)
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