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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
55.1.d.a \(1\) \(0.027\) \(\Q\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q-q^{4}-q^{5}+q^{9}-q^{11}+q^{16}+q^{20}+\cdots\)
55.2.a.a \(1\) \(0.439\) \(\Q\) None None \(1\) \(0\) \(1\) \(0\) \(-\) \(q+q^{2}-q^{4}+q^{5}-3q^{8}-3q^{9}+q^{10}+\cdots\)
55.2.a.b \(2\) \(0.439\) \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(-2\) \(-4\) \(-\) \(q+(1+\beta )q^{2}-2\beta q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots\)
55.2.b.a \(4\) \(0.439\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(0\) \(-3\) \(0\) \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(\beta _{1}-\beta _{3})q^{3}+\cdots\)
55.2.e.a \(4\) \(0.439\) \(\Q(i, \sqrt{10})\) None None \(0\) \(-4\) \(-8\) \(0\) \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+3\beta _{2}q^{4}+\cdots\)
55.2.e.b \(4\) \(0.439\) \(\Q(i, \sqrt{11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(-1+\beta _{1}-\beta _{3})q^{3}+2\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
55.2.g.a \(8\) \(0.439\) 8.0.159390625.1 None None \(-4\) \(1\) \(-2\) \(-3\) \(q+(-\beta _{1}-\beta _{2}+\beta _{4})q^{2}+\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots\)
55.2.g.b \(8\) \(0.439\) 8.0.13140625.1 None None \(-2\) \(-5\) \(2\) \(-1\) \(q-\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
55.2.j.a \(16\) \(0.439\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(-2\) \(0\) \(q+(\beta _{1}-\beta _{12}-\beta _{13})q^{2}+(\beta _{5}+\beta _{13}+\cdots)q^{3}+\cdots\)
55.2.l.a \(32\) \(0.439\) None None \(-10\) \(-4\) \(-2\) \(0\)
55.3.c.a \(8\) \(1.499\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(8\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(-4+\beta _{2})q^{4}+\cdots\)
55.3.d.a \(2\) \(1.499\) \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(1\) \(0\) \(q+(1-2\beta )q^{3}-4q^{4}+(2-3\beta )q^{5}-2q^{9}+\cdots\)
55.3.d.b \(2\) \(1.499\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(10\) \(0\) \(q-\beta q^{2}+q^{4}+5q^{5}+2\beta q^{7}+3\beta q^{8}+\cdots\)
55.3.d.c \(2\) \(1.499\) \(\Q(\sqrt{11}) \) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(-10\) \(0\) \(q+\beta q^{2}+7q^{4}-5q^{5}-4\beta q^{7}+3\beta q^{8}+\cdots\)
55.3.d.d \(4\) \(1.499\) \(\Q(\sqrt{5}, \sqrt{-21})\) None None \(0\) \(0\) \(-8\) \(0\) \(q-\beta _{2}q^{2}-\beta _{1}q^{3}+q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots\)
55.3.f.a \(20\) \(1.499\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(-4\) \(-2\) \(-8\) \(0\) \(q-\beta _{5}q^{2}-\beta _{4}q^{3}+(-2\beta _{8}-\beta _{16})q^{4}+\cdots\)
55.3.h.a \(40\) \(1.499\) None None \(0\) \(0\) \(2\) \(0\)
55.3.i.a \(4\) \(1.499\) \(\Q(\zeta_{10})\) None None \(-5\) \(4\) \(-5\) \(15\) \(q+(-2\zeta_{10}+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(4+\cdots)q^{3}+\cdots\)
55.3.i.b \(4\) \(1.499\) \(\Q(\zeta_{10})\) None None \(5\) \(-6\) \(5\) \(30\) \(q+(2+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-4+3\zeta_{10}+\cdots)q^{3}+\cdots\)
55.3.i.c \(12\) \(1.499\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-5\) \(7\) \(15\) \(-40\) \(q+(\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}+\beta _{7}-\beta _{11})q^{2}+\cdots\)
55.3.i.d \(12\) \(1.499\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(5\) \(-13\) \(-15\) \(-5\) \(q+(1+\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}-\beta _{10})q^{2}+\cdots\)
55.3.k.a \(80\) \(1.499\) None None \(-6\) \(-8\) \(-2\) \(-40\)
55.4.a.a \(1\) \(3.245\) \(\Q\) None None \(1\) \(-3\) \(-5\) \(-9\) \(-\) \(q+q^{2}-3q^{3}-7q^{4}-5q^{5}-3q^{6}+\cdots\)
55.4.a.b \(2\) \(3.245\) \(\Q(\sqrt{17}) \) None None \(-7\) \(-3\) \(10\) \(-25\) \(-\) \(q+(-3-\beta )q^{2}+(-1-\beta )q^{3}+(5+7\beta )q^{4}+\cdots\)
55.4.a.c \(3\) \(3.245\) 3.3.568.1 None None \(5\) \(-3\) \(-15\) \(-15\) \(+\) \(q+(1+\beta _{1}-\beta _{2})q^{2}+(-2-3\beta _{2})q^{3}+\cdots\)
55.4.a.d \(4\) \(3.245\) 4.4.1539480.1 None None \(1\) \(9\) \(20\) \(9\) \(+\) \(q+\beta _{1}q^{2}+(2-\beta _{2})q^{3}+(5+\beta _{1}+\beta _{3})q^{4}+\cdots\)
55.4.b.a \(6\) \(3.245\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{5})q^{3}+(1+\beta _{3})q^{4}+\cdots\)
55.4.b.b \(10\) \(3.245\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(14\) \(0\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-6+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
55.4.e.a \(4\) \(3.245\) \(\Q(i, \sqrt{11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(16\) \(0\) \(0\) \(q+(4+4\beta _{1}+\beta _{2}+\beta _{3})q^{3}-8\beta _{1}q^{4}+\cdots\)
55.4.e.b \(28\) \(3.245\) None None \(0\) \(-16\) \(12\) \(0\)
55.4.g.a \(24\) \(3.245\) None None \(2\) \(-8\) \(30\) \(-53\)
55.4.g.b \(24\) \(3.245\) None None \(6\) \(4\) \(-30\) \(81\)
55.4.j.a \(64\) \(3.245\) None None \(0\) \(0\) \(-15\) \(0\)
55.4.l.a \(128\) \(3.245\) None None \(-10\) \(-10\) \(-22\) \(10\)
55.5.c.a \(16\) \(5.685\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(-16\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-1+\beta _{5})q^{3}+(-9+\beta _{2}+\cdots)q^{4}+\cdots\)
55.5.d.a \(1\) \(5.685\) \(\Q\) \(\Q(\sqrt{-55}) \) None \(-3\) \(0\) \(25\) \(-78\) \(q-3q^{2}-7q^{4}+5^{2}q^{5}-78q^{7}+69q^{8}+\cdots\)
55.5.d.b \(1\) \(5.685\) \(\Q\) \(\Q(\sqrt{-55}) \) None \(3\) \(0\) \(25\) \(78\) \(q+3q^{2}-7q^{4}+5^{2}q^{5}+78q^{7}-69q^{8}+\cdots\)
55.5.d.c \(2\) \(5.685\) \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(49\) \(0\) \(q+(5-10\beta )q^{3}-2^{4}q^{4}+(26-3\beta )q^{5}+\cdots\)
55.5.d.d \(2\) \(5.685\) \(\Q(\sqrt{55}) \) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(-50\) \(0\) \(q+\beta q^{2}+39q^{4}-5^{2}q^{5}+8\beta q^{7}+23\beta q^{8}+\cdots\)
55.5.d.e \(16\) \(5.685\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(-30\) \(0\) \(q-\beta _{8}q^{2}-\beta _{7}q^{3}+(8-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
55.5.f.a \(40\) \(5.685\) None None \(0\) \(10\) \(-48\) \(0\)
55.5.h.a \(88\) \(5.685\) None None \(0\) \(0\) \(-24\) \(0\)
55.5.i.a \(4\) \(5.685\) \(\Q(\zeta_{10})\) None None \(5\) \(-30\) \(-25\) \(150\) \(q+(2+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-4-9\zeta_{10}+\cdots)q^{3}+\cdots\)
55.5.i.b \(28\) \(5.685\) None None \(-5\) \(43\) \(-175\) \(-90\)
55.5.i.c \(32\) \(5.685\) None None \(0\) \(3\) \(200\) \(-60\)
55.5.k.a \(176\) \(5.685\) None None \(-6\) \(4\) \(-42\) \(244\)
55.6.a.a \(3\) \(8.821\) 3.3.21865.1 None None \(-7\) \(-36\) \(75\) \(-102\) \(+\) \(q+(-2-\beta _{2})q^{2}+(-11-3\beta _{1})q^{3}+\cdots\)
55.6.a.b \(4\) \(8.821\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None None \(-5\) \(0\) \(-100\) \(-90\) \(+\) \(q+(-1-\beta _{1})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(15+\cdots)q^{4}+\cdots\)
55.6.a.c \(5\) \(8.821\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(9\) \(0\) \(125\) \(70\) \(-\) \(q+(2-\beta _{1})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(24-3\beta _{1}+\cdots)q^{4}+\cdots\)
55.6.a.d \(6\) \(8.821\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(3\) \(0\) \(-150\) \(-66\) \(-\) \(q+(1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(20+\cdots)q^{4}+\cdots\)
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