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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
74.2.a.a \(2\) \(0.591\) \(\Q(\sqrt{13}) \) None \(-2\) \(3\) \(-1\) \(2\) \(-\) \(q-q^{2}+(1+\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
74.2.a.b \(2\) \(0.591\) \(\Q(\sqrt{5}) \) None \(2\) \(-1\) \(1\) \(-2\) \(-\) \(q+q^{2}-\beta q^{3}+q^{4}+(-1+3\beta )q^{5}+\cdots\)
74.2.b.a \(4\) \(0.591\) \(\Q(i, \sqrt{21})\) None \(0\) \(-2\) \(0\) \(-8\) \(q+\beta _{2}q^{2}+(-1+\beta _{3})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
74.2.c.a \(2\) \(0.591\) \(\Q(\sqrt{-3}) \) None \(1\) \(-2\) \(1\) \(0\) \(q+(1-\zeta_{6})q^{2}-2\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
74.2.c.b \(2\) \(0.591\) \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(-3\) \(4\) \(q+(1-\zeta_{6})q^{2}+2\zeta_{6}q^{3}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots\)
74.2.c.c \(6\) \(0.591\) 6.0.4406832.1 None \(-3\) \(0\) \(-1\) \(0\) \(q+(-1-\beta _{3})q^{2}+(\beta _{2}+\beta _{4})q^{3}+\beta _{3}q^{4}+\cdots\)
74.2.e.a \(4\) \(0.591\) \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(-6\) \(-8\) \(q+\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
74.2.e.b \(4\) \(0.591\) \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(6\) \(4\) \(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
74.2.f.a \(6\) \(0.591\) \(\Q(\zeta_{18})\) None \(0\) \(-3\) \(3\) \(6\) \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(-\zeta_{18}-\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
74.2.f.b \(12\) \(0.591\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-3\) \(-6\) \(6\) \(q+(\beta _{4}-\beta _{7})q^{2}+(-1+\beta _{1}-\beta _{8})q^{3}+\cdots\)
74.2.h.a \(12\) \(0.591\) \(\Q(\zeta_{36})\) None \(0\) \(6\) \(0\) \(-12\) \(q+\zeta_{36}q^{2}+(1-\zeta_{36}^{4}-\zeta_{36}^{6})q^{3}+\cdots\)
74.3.d.a \(2\) \(2.016\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-12\) \(10\) \(q+(1+i)q^{2}+iq^{3}+2iq^{4}+(-6+6i)q^{5}+\cdots\)
74.3.d.b \(2\) \(2.016\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(6\) \(-8\) \(q+(1+i)q^{2}+4iq^{3}+2iq^{4}+(3-3i)q^{5}+\cdots\)
74.3.d.c \(2\) \(2.016\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(6\) \(6\) \(q+(1+i)q^{2}-3iq^{3}+2iq^{4}+(3-3i)q^{5}+\cdots\)
74.3.d.d \(4\) \(2.016\) \(\Q(i, \sqrt{65})\) None \(-4\) \(0\) \(-6\) \(-8\) \(q+(-1+\beta _{1})q^{2}-\beta _{1}q^{3}-2\beta _{1}q^{4}+\cdots\)
74.3.g.a \(8\) \(2.016\) 8.0.303595776.1 None \(4\) \(0\) \(12\) \(8\) \(q+(-\beta _{4}+\beta _{5})q^{2}+(2\beta _{1}-\beta _{5}-\beta _{7})q^{3}+\cdots\)
74.3.g.b \(12\) \(2.016\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-6\) \(0\) \(0\) \(-8\) \(q+(\beta _{4}-\beta _{7})q^{2}-\beta _{3}q^{3}+2\beta _{6}q^{4}+(1+\cdots)q^{5}+\cdots\)
74.3.i.a \(36\) \(2.016\) None \(0\) \(0\) \(-6\) \(0\)
74.3.i.b \(48\) \(2.016\) None \(0\) \(0\) \(0\) \(0\)
74.4.a.a \(1\) \(4.366\) \(\Q\) None \(-2\) \(-5\) \(12\) \(-7\) \(-\) \(q-2q^{2}-5q^{3}+4q^{4}+12q^{5}+10q^{6}+\cdots\)
74.4.a.b \(1\) \(4.366\) \(\Q\) None \(2\) \(-5\) \(-14\) \(-19\) \(-\) \(q+2q^{2}-5q^{3}+4q^{4}-14q^{5}-10q^{6}+\cdots\)
74.4.a.c \(3\) \(4.366\) 3.3.15629.1 None \(-6\) \(4\) \(7\) \(7\) \(+\) \(q-2q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+4q^{4}+(2+\cdots)q^{5}+\cdots\)
74.4.a.d \(4\) \(4.366\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(8\) \(4\) \(21\) \(23\) \(+\) \(q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(5+\beta _{2}+\cdots)q^{5}+\cdots\)
74.4.b.a \(10\) \(4.366\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(14\) \(0\) \(-4\) \(q-\beta _{5}q^{2}+(1-\beta _{2})q^{3}-4q^{4}+(2\beta _{5}+\cdots)q^{5}+\cdots\)
74.4.c.a \(8\) \(4.366\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(-5\) \(-10\) \(3\) \(q+(2-2\beta _{2})q^{2}+(-\beta _{1}-\beta _{2})q^{3}-4\beta _{2}q^{4}+\cdots\)
74.4.c.b \(10\) \(4.366\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-10\) \(-5\) \(-1\) \(-1\) \(q+2\beta _{3}q^{2}+(-1+\beta _{1}-\beta _{3})q^{3}+(-4+\cdots)q^{4}+\cdots\)
74.4.e.a \(20\) \(4.366\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(-2\) \(-18\) \(-2\) \(q+\beta _{11}q^{2}+\beta _{14}q^{3}+4\beta _{6}q^{4}+(-1+\cdots)q^{5}+\cdots\)
74.4.f.a \(24\) \(4.366\) None \(0\) \(6\) \(-9\) \(-75\)
74.4.f.b \(30\) \(4.366\) None \(0\) \(6\) \(-6\) \(-75\)
74.4.h.a \(60\) \(4.366\) None \(0\) \(-12\) \(18\) \(150\)
74.5.d.a \(14\) \(7.649\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(-28\) \(0\) \(-12\) \(48\) \(q+(-2+2\beta _{5})q^{2}+(\beta _{1}+\beta _{5})q^{3}-8\beta _{5}q^{4}+\cdots\)
74.5.d.b \(14\) \(7.649\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(28\) \(0\) \(36\) \(-48\) \(q+(2+2\beta _{5})q^{2}+(\beta _{1}-\beta _{5})q^{3}+8\beta _{5}q^{4}+\cdots\)
74.5.g.a \(28\) \(7.649\) None \(-28\) \(0\) \(42\) \(48\)
74.5.g.b \(28\) \(7.649\) None \(28\) \(0\) \(-102\) \(-48\)
74.5.i.a \(72\) \(7.649\) None \(0\) \(0\) \(-78\) \(0\)
74.5.i.b \(72\) \(7.649\) None \(0\) \(0\) \(114\) \(0\)
74.6.a.a \(1\) \(11.868\) \(\Q\) None \(4\) \(-15\) \(4\) \(15\) \(+\) \(q+4q^{2}-15q^{3}+2^{4}q^{4}+4q^{5}-60q^{6}+\cdots\)
74.6.a.b \(1\) \(11.868\) \(\Q\) None \(4\) \(7\) \(-84\) \(-139\) \(+\) \(q+4q^{2}+7q^{3}+2^{4}q^{4}-84q^{5}+28q^{6}+\cdots\)
74.6.a.c \(3\) \(11.868\) 3.3.324233.1 None \(-12\) \(-8\) \(-42\) \(84\) \(+\) \(q-4q^{2}+(-3+\beta _{1}-\beta _{2})q^{3}+2^{4}q^{4}+\cdots\)
74.6.a.d \(5\) \(11.868\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-20\) \(19\) \(-67\) \(182\) \(-\) \(q-4q^{2}+(4+\beta _{2})q^{3}+2^{4}q^{4}+(-14+\cdots)q^{5}+\cdots\)
74.6.a.e \(5\) \(11.868\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(20\) \(19\) \(95\) \(170\) \(-\) \(q+4q^{2}+(4-\beta _{1})q^{3}+2^{4}q^{4}+(19+\beta _{2}+\cdots)q^{5}+\cdots\)
74.6.b.a \(14\) \(11.868\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(14\) \(0\) \(-312\) \(q-\beta _{9}q^{2}+(1+\beta _{2})q^{3}-2^{4}q^{4}+(\beta _{9}+\cdots)q^{5}+\cdots\)
74.6.c.a \(14\) \(11.868\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-28\) \(-8\) \(57\) \(188\) \(q+(-4+4\beta _{3})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+\cdots\)
74.6.c.b \(16\) \(11.868\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(32\) \(-8\) \(70\) \(-32\) \(q+(4+4\beta _{3})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+2^{4}\beta _{3}q^{4}+\cdots\)
74.6.e.a \(28\) \(11.868\) None \(0\) \(-20\) \(-90\) \(-156\)
74.6.f.a \(48\) \(11.868\) None \(0\) \(-3\) \(-72\) \(114\)
74.6.f.b \(54\) \(11.868\) None \(0\) \(-3\) \(39\) \(114\)
74.6.h.a \(96\) \(11.868\) None \(0\) \(6\) \(90\) \(-228\)
74.7.d.a \(18\) \(17.024\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(72\) \(0\) \(294\) \(-104\) \(q+(4-4\beta _{6})q^{2}+(\beta _{1}-4\beta _{6})q^{3}-2^{5}\beta _{6}q^{4}+\cdots\)
74.7.d.b \(20\) \(17.024\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-80\) \(0\) \(60\) \(104\) \(q+(-4-4\beta _{6})q^{2}+(-\beta _{1}+3\beta _{6})q^{3}+\cdots\)
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