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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
54.2.a.a \(1\) \(0.431\) \(\Q\) None \(-1\) \(0\) \(3\) \(-1\) \(-\) \(q-q^{2}+q^{4}+3q^{5}-q^{7}-q^{8}-3q^{10}+\cdots\)
54.2.a.b \(1\) \(0.431\) \(\Q\) None \(1\) \(0\) \(-3\) \(-1\) \(-\) \(q+q^{2}+q^{4}-3q^{5}-q^{7}+q^{8}-3q^{10}+\cdots\)
54.2.c.a \(2\) \(0.431\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(-2\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{7}+\cdots\)
54.2.e.a \(6\) \(0.431\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(-3\) \(3\) \(q+\zeta_{18}q^{2}+(-\zeta_{18}^{2}+2\zeta_{18}^{5})q^{3}+\cdots\)
54.2.e.b \(12\) \(0.431\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-3\) \(-3\) \(q+(-\beta _{4}+\beta _{6})q^{2}-\beta _{11}q^{3}+\beta _{3}q^{4}+\cdots\)
54.3.b.a \(2\) \(1.471\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(10\) \(q+\beta q^{2}-2q^{4}+6\beta q^{5}+5q^{7}-2\beta q^{8}+\cdots\)
54.3.d.a \(4\) \(1.471\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(18\) \(2\) \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(6-3\beta _{2})q^{5}+(1+\cdots)q^{7}+\cdots\)
54.3.f.a \(36\) \(1.471\) None \(0\) \(0\) \(18\) \(0\)
54.4.a.a \(1\) \(3.186\) \(\Q\) None \(-2\) \(0\) \(-12\) \(-7\) \(-\) \(q-2q^{2}+4q^{4}-12q^{5}-7q^{7}-8q^{8}+\cdots\)
54.4.a.b \(1\) \(3.186\) \(\Q\) None \(-2\) \(0\) \(-3\) \(29\) \(+\) \(q-2q^{2}+4q^{4}-3q^{5}+29q^{7}-8q^{8}+\cdots\)
54.4.a.c \(1\) \(3.186\) \(\Q\) None \(2\) \(0\) \(3\) \(29\) \(+\) \(q+2q^{2}+4q^{4}+3q^{5}+29q^{7}+8q^{8}+\cdots\)
54.4.a.d \(1\) \(3.186\) \(\Q\) None \(2\) \(0\) \(12\) \(-7\) \(+\) \(q+2q^{2}+4q^{4}+12q^{5}-7q^{7}+8q^{8}+\cdots\)
54.4.c.a \(2\) \(3.186\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-9\) \(31\) \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-9\zeta_{6}q^{5}+\cdots\)
54.4.c.b \(4\) \(3.186\) \(\Q(\sqrt{-3}, \sqrt{-35})\) None \(-4\) \(0\) \(-9\) \(-19\) \(q+2\beta _{1}q^{2}+(-4-4\beta _{1})q^{4}+(-4-4\beta _{1}+\cdots)q^{5}+\cdots\)
54.4.e.a \(24\) \(3.186\) None \(0\) \(0\) \(-12\) \(-33\)
54.4.e.b \(30\) \(3.186\) None \(0\) \(0\) \(-12\) \(33\)
54.5.b.a \(2\) \(5.582\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-146\) \(q+\beta q^{2}-8q^{4}-12\beta q^{5}-73q^{7}-8\beta q^{8}+\cdots\)
54.5.b.b \(4\) \(5.582\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(68\) \(q+\zeta_{8}^{2}q^{2}-8q^{4}+(\zeta_{8}-3\zeta_{8}^{2})q^{5}+\cdots\)
54.5.d.a \(8\) \(5.582\) 8.0.\(\cdots\).4 None \(0\) \(0\) \(-18\) \(-26\) \(q+\beta _{1}q^{2}+8\beta _{2}q^{4}+(-3-\beta _{1}+3\beta _{2}+\cdots)q^{5}+\cdots\)
54.5.f.a \(72\) \(5.582\) None \(0\) \(0\) \(-18\) \(0\)
54.6.a.a \(1\) \(8.661\) \(\Q\) None \(-4\) \(0\) \(-33\) \(59\) \(-\) \(q-4q^{2}+2^{4}q^{4}-33q^{5}+59q^{7}-2^{6}q^{8}+\cdots\)
54.6.a.b \(1\) \(8.661\) \(\Q\) None \(-4\) \(0\) \(-24\) \(77\) \(+\) \(q-4q^{2}+2^{4}q^{4}-24q^{5}+77q^{7}-2^{6}q^{8}+\cdots\)
54.6.a.c \(1\) \(8.661\) \(\Q\) None \(-4\) \(0\) \(84\) \(-193\) \(-\) \(q-4q^{2}+2^{4}q^{4}+84q^{5}-193q^{7}+\cdots\)
54.6.a.d \(1\) \(8.661\) \(\Q\) None \(4\) \(0\) \(-84\) \(-193\) \(+\) \(q+4q^{2}+2^{4}q^{4}-84q^{5}-193q^{7}+\cdots\)
54.6.a.e \(1\) \(8.661\) \(\Q\) None \(4\) \(0\) \(24\) \(77\) \(-\) \(q+4q^{2}+2^{4}q^{4}+24q^{5}+77q^{7}+2^{6}q^{8}+\cdots\)
54.6.a.f \(1\) \(8.661\) \(\Q\) None \(4\) \(0\) \(33\) \(59\) \(-\) \(q+4q^{2}+2^{4}q^{4}+33q^{5}+59q^{7}+2^{6}q^{8}+\cdots\)
54.6.c.a \(4\) \(8.661\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-8\) \(0\) \(54\) \(74\) \(q+(-4+4\beta _{1})q^{2}-2^{4}\beta _{1}q^{4}+(3^{3}\beta _{1}+\cdots)q^{5}+\cdots\)
54.6.c.b \(6\) \(8.661\) 6.0.\(\cdots\).3 None \(12\) \(0\) \(54\) \(-132\) \(q+4\beta _{1}q^{2}+(-2^{4}+2^{4}\beta _{1})q^{4}+(18+\cdots)q^{5}+\cdots\)
54.6.e.a \(42\) \(8.661\) None \(0\) \(0\) \(87\) \(-15\)
54.6.e.b \(48\) \(8.661\) None \(0\) \(0\) \(87\) \(15\)
54.7.b.a \(2\) \(12.423\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-410\) \(q+\beta q^{2}-2^{5}q^{4}+6\beta q^{5}-205q^{7}+\cdots\)
54.7.b.b \(2\) \(12.423\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(778\) \(q+2\beta q^{2}-2^{5}q^{4}-15\beta q^{5}+389q^{7}+\cdots\)
54.7.b.c \(4\) \(12.423\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(836\) \(q+\zeta_{8}^{2}q^{2}-2^{5}q^{4}+(5\zeta_{8}+15\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
54.7.d.a \(12\) \(12.423\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-432\) \(240\) \(q+\beta _{3}q^{2}-2^{5}\beta _{2}q^{4}+(-48-24\beta _{2}+\cdots)q^{5}+\cdots\)
54.7.f.a \(108\) \(12.423\) None \(0\) \(0\) \(-432\) \(0\)
54.8.a.a \(1\) \(16.869\) \(\Q\) None \(-8\) \(0\) \(-120\) \(377\) \(-\) \(q-8q^{2}+2^{6}q^{4}-120q^{5}+377q^{7}+\cdots\)
54.8.a.b \(1\) \(16.869\) \(\Q\) None \(-8\) \(0\) \(105\) \(-937\) \(-\) \(q-8q^{2}+2^{6}q^{4}+105q^{5}-937q^{7}+\cdots\)
54.8.a.c \(1\) \(16.869\) \(\Q\) None \(-8\) \(0\) \(312\) \(323\) \(+\) \(q-8q^{2}+2^{6}q^{4}+312q^{5}+323q^{7}+\cdots\)
54.8.a.d \(1\) \(16.869\) \(\Q\) None \(8\) \(0\) \(-312\) \(323\) \(-\) \(q+8q^{2}+2^{6}q^{4}-312q^{5}+323q^{7}+\cdots\)
54.8.a.e \(1\) \(16.869\) \(\Q\) None \(8\) \(0\) \(-105\) \(-937\) \(-\) \(q+8q^{2}+2^{6}q^{4}-105q^{5}-937q^{7}+\cdots\)
54.8.a.f \(1\) \(16.869\) \(\Q\) None \(8\) \(0\) \(120\) \(377\) \(+\) \(q+8q^{2}+2^{6}q^{4}+120q^{5}+377q^{7}+\cdots\)
54.8.a.g \(2\) \(16.869\) \(\Q(\sqrt{329}) \) None \(-16\) \(0\) \(48\) \(880\) \(+\) \(q-8q^{2}+2^{6}q^{4}+(24+\beta )q^{5}+(440+\cdots)q^{7}+\cdots\)
54.8.a.h \(2\) \(16.869\) \(\Q(\sqrt{329}) \) None \(16\) \(0\) \(-48\) \(880\) \(+\) \(q+8q^{2}+2^{6}q^{4}+(-24-\beta )q^{5}+(440+\cdots)q^{7}+\cdots\)
54.8.c.a \(6\) \(16.869\) 6.0.\(\cdots\).1 None \(24\) \(0\) \(-54\) \(210\) \(q+8\beta _{1}q^{2}+(-2^{6}+2^{6}\beta _{1})q^{4}+(-18+\cdots)q^{5}+\cdots\)
54.8.c.b \(8\) \(16.869\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(-32\) \(0\) \(-54\) \(-44\) \(q-8\beta _{1}q^{2}+(-2^{6}+2^{6}\beta _{1})q^{4}+(-14+\cdots)q^{5}+\cdots\)
54.8.e.a \(60\) \(16.869\) None \(0\) \(0\) \(213\) \(1677\)
54.8.e.b \(66\) \(16.869\) None \(0\) \(0\) \(213\) \(-1677\)
54.9.b.a \(2\) \(21.998\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-4130\) \(q+\beta q^{2}-2^{7}q^{4}+60\beta q^{5}-2065q^{7}+\cdots\)
54.9.b.b \(4\) \(21.998\) \(\Q(\sqrt{-2}, \sqrt{79})\) None \(0\) \(0\) \(0\) \(164\) \(q+\beta _{1}q^{2}-2^{7}q^{4}+(-21\beta _{1}+\beta _{2})q^{5}+\cdots\)
54.9.b.c \(4\) \(21.998\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(308\) \(q-2\zeta_{8}^{2}q^{2}-2^{7}q^{4}+(-11\zeta_{8}+51\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
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