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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
483.2.a.a \(1\) \(3.857\) \(\Q\) None \(2\) \(1\) \(0\) \(1\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}+q^{7}+q^{9}+\cdots\)
483.2.a.b \(1\) \(3.857\) \(\Q\) None \(2\) \(1\) \(4\) \(-1\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}+4q^{5}+2q^{6}+\cdots\)
483.2.a.c \(2\) \(3.857\) \(\Q(\sqrt{5}) \) None \(-3\) \(2\) \(-5\) \(2\) \(+\) \(q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+(-2+\cdots)q^{5}+\cdots\)
483.2.a.d \(2\) \(3.857\) \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(1\) \(-2\) \(+\) \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-\beta )q^{5}+\cdots\)
483.2.a.e \(2\) \(3.857\) \(\Q(\sqrt{5}) \) None \(-1\) \(2\) \(5\) \(2\) \(-\) \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(3-\beta )q^{5}+\cdots\)
483.2.a.f \(2\) \(3.857\) \(\Q(\sqrt{13}) \) None \(-1\) \(2\) \(-5\) \(-2\) \(+\) \(q-\beta q^{2}+q^{3}+(1+\beta )q^{4}+(-3+\beta )q^{5}+\cdots\)
483.2.a.g \(2\) \(3.857\) \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(-3\) \(2\) \(+\) \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
483.2.a.h \(3\) \(3.857\) 3.3.837.1 None \(0\) \(3\) \(3\) \(-3\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
483.2.a.i \(4\) \(3.857\) 4.4.24197.1 None \(0\) \(-4\) \(5\) \(4\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots\)
483.2.a.j \(4\) \(3.857\) 4.4.15317.1 None \(2\) \(-4\) \(5\) \(-4\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)
483.2.d.a \(4\) \(3.857\) \(\Q(i, \sqrt{5})\) None \(0\) \(-2\) \(-6\) \(6\) \(q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
483.2.d.b \(4\) \(3.857\) \(\Q(i, \sqrt{5})\) None \(0\) \(2\) \(6\) \(6\) \(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
483.2.d.c \(8\) \(3.857\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(-8\) \(q-\zeta_{16}^{4}q^{2}+(\zeta_{16}+\zeta_{16}^{5}+\zeta_{16}^{7})q^{3}+\cdots\)
483.2.d.d \(44\) \(3.857\) None \(0\) \(0\) \(0\) \(-8\)
483.2.e.a \(48\) \(3.857\) None \(0\) \(-4\) \(0\) \(0\)
483.2.h.a \(8\) \(3.857\) 8.0.342102016.5 None \(-8\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta _{1}q^{3}-q^{4}+(\beta _{4}-\beta _{5})q^{5}+\cdots\)
483.2.h.b \(12\) \(3.857\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{8}q^{2}-\beta _{5}q^{3}+(1-\beta _{7})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
483.2.h.c \(12\) \(3.857\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(4\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+\beta _{9}q^{3}+(3+\beta _{7})q^{4}-\beta _{5}q^{5}+\cdots\)
483.2.i.a \(2\) \(3.857\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(1\) \(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots\)
483.2.i.b \(2\) \(3.857\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(5\) \(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(2+\zeta_{6})q^{7}+\cdots\)
483.2.i.c \(2\) \(3.857\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(-5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
483.2.i.d \(2\) \(3.857\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(3\) \(-1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
483.2.i.e \(4\) \(3.857\) \(\Q(\sqrt{-3}, \sqrt{17})\) None \(1\) \(-2\) \(1\) \(10\) \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots\)
483.2.i.f \(12\) \(3.857\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(1\) \(6\) \(-3\) \(-2\) \(q+(-\beta _{1}-\beta _{5})q^{2}+\beta _{7}q^{3}+(1+\beta _{4}+\cdots)q^{4}+\cdots\)
483.2.i.g \(16\) \(3.857\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-1\) \(-8\) \(-5\) \(-2\) \(q+(\beta _{1}-\beta _{5})q^{2}+(-1-\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots\)
483.2.i.h \(20\) \(3.857\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-3\) \(10\) \(5\) \(0\) \(q+(\beta _{1}+\beta _{4})q^{2}-\beta _{9}q^{3}+(-\beta _{1}-\beta _{8}+\cdots)q^{4}+\cdots\)
483.2.j.a \(64\) \(3.857\) None \(4\) \(0\) \(0\) \(0\)
483.2.m.a \(120\) \(3.857\) None \(0\) \(-2\) \(0\) \(0\)
483.2.n.a \(116\) \(3.857\) None \(0\) \(0\) \(0\) \(-10\)
483.2.q.a \(10\) \(3.857\) \(\Q(\zeta_{22})\) None \(4\) \(-1\) \(1\) \(-1\) \(q+(-\zeta_{22}^{2}+\zeta_{22}^{3}+\zeta_{22}^{5}-\zeta_{22}^{6}+\cdots)q^{2}+\cdots\)
483.2.q.b \(10\) \(3.857\) \(\Q(\zeta_{22})\) None \(5\) \(-1\) \(-5\) \(-1\) \(q+(\zeta_{22}-\zeta_{22}^{2}-\zeta_{22}^{4}-\zeta_{22}^{6}+\zeta_{22}^{7}+\cdots)q^{2}+\cdots\)
483.2.q.c \(20\) \(3.857\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-4\) \(-2\) \(-1\) \(-2\) \(q+(-\beta _{2}-\beta _{6})q^{2}+\beta _{12}q^{3}+(-\beta _{5}+\cdots)q^{4}+\cdots\)
483.2.q.d \(60\) \(3.857\) None \(-1\) \(6\) \(-13\) \(-6\)
483.2.q.e \(60\) \(3.857\) None \(-1\) \(6\) \(5\) \(6\)
483.2.q.f \(80\) \(3.857\) None \(1\) \(-8\) \(13\) \(8\)
483.2.r.a \(320\) \(3.857\) None \(4\) \(0\) \(0\) \(0\)
483.2.u.a \(480\) \(3.857\) None \(0\) \(4\) \(0\) \(0\)
483.2.v.a \(600\) \(3.857\) None \(0\) \(0\) \(0\) \(-18\)
483.2.y.a \(320\) \(3.857\) None \(2\) \(-16\) \(-2\) \(2\)
483.2.y.b \(320\) \(3.857\) None \(2\) \(16\) \(-2\) \(2\)
483.2.bb.a \(1200\) \(3.857\) None \(0\) \(-27\) \(0\) \(-36\)
483.2.bc.a \(1200\) \(3.857\) None \(0\) \(-9\) \(0\) \(-44\)
483.2.bf.a \(640\) \(3.857\) None \(-4\) \(0\) \(0\) \(0\)
483.3.b.a \(88\) \(13.161\) None \(0\) \(8\) \(0\) \(0\)
483.3.f.a \(48\) \(13.161\) None \(4\) \(0\) \(0\) \(0\)
483.3.g.a \(60\) \(13.161\) None \(0\) \(0\) \(0\) \(-16\)
483.4.a.a \(3\) \(28.498\) 3.3.3877.1 None \(-4\) \(9\) \(2\) \(-21\) \(-\) \(q+(-1-\beta _{1})q^{2}+3q^{3}+(1+4\beta _{1}+\beta _{2})q^{4}+\cdots\)
483.4.a.b \(4\) \(28.498\) 4.4.8184789.1 None \(2\) \(12\) \(-23\) \(-28\) \(-\) \(q+(1+\beta _{1})q^{2}+3q^{3}+(3+\beta _{1})q^{4}+(-6+\cdots)q^{5}+\cdots\)
483.4.a.c \(7\) \(28.498\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-6\) \(21\) \(-41\) \(49\) \(-\) \(q+(-1+\beta _{1})q^{2}+3q^{3}+(3-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
483.4.a.d \(7\) \(28.498\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-2\) \(-21\) \(-11\) \(-49\) \(-\) \(q-\beta _{1}q^{2}-3q^{3}+(3+\beta _{4}+\beta _{5})q^{4}+\cdots\)
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