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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
69.2.a.a \(1\) \(0.551\) \(\Q\) None \(1\) \(1\) \(0\) \(-2\) \(-\) \(q+q^{2}+q^{3}-q^{4}+q^{6}-2q^{7}-3q^{8}+\cdots\)
69.2.a.b \(2\) \(0.551\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(2\) \(-\) \(q-\beta q^{2}-q^{3}+3q^{4}+(-1+\beta )q^{5}+\cdots\)
69.2.c.a \(6\) \(0.551\) 6.0.8869743.1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-2+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
69.2.e.a \(10\) \(0.551\) \(\Q(\zeta_{22})\) None \(-4\) \(1\) \(5\) \(-8\) \(q+(-1+\zeta_{22}-\zeta_{22}^{2}-\zeta_{22}^{4}-\zeta_{22}^{6}+\cdots)q^{2}+\cdots\)
69.2.e.b \(10\) \(0.551\) \(\Q(\zeta_{22})\) None \(4\) \(1\) \(-3\) \(6\) \(q+(-\zeta_{22}^{4}+\zeta_{22}^{5}-\zeta_{22}^{8}+\zeta_{22}^{9})q^{2}+\cdots\)
69.2.e.c \(20\) \(0.551\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-4\) \(-2\) \(-6\) \(-6\) \(q+(\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+2\beta _{6}+2\beta _{7}+\cdots)q^{2}+\cdots\)
69.2.g.a \(60\) \(0.551\) None \(0\) \(-11\) \(0\) \(-22\)
69.3.b.a \(14\) \(1.880\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(-4\) \(0\) \(-4\) \(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-2+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
69.3.d.a \(8\) \(1.880\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(-4\) \(0\) \(0\) \(0\) \(q+(-\beta _{2}+\beta _{3})q^{2}+\beta _{3}q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
69.3.f.a \(80\) \(1.880\) None \(4\) \(0\) \(0\) \(0\)
69.3.h.a \(140\) \(1.880\) None \(0\) \(-7\) \(0\) \(-18\)
69.4.a.a \(2\) \(4.071\) \(\Q(\sqrt{5}) \) None \(-4\) \(6\) \(-26\) \(-10\) \(-\) \(q+(-2-\beta )q^{2}+3q^{3}+(1+4\beta )q^{4}+\cdots\)
69.4.a.b \(2\) \(4.071\) \(\Q(\sqrt{2}) \) None \(-2\) \(-6\) \(8\) \(-28\) \(-\) \(q+(-1+\beta )q^{2}-3q^{3}+(1-2\beta )q^{4}+\cdots\)
69.4.a.c \(4\) \(4.071\) 4.4.1140200.1 None \(-2\) \(-12\) \(-2\) \(32\) \(+\) \(q+\beta _{1}q^{2}-3q^{3}+(6-\beta _{1}-2\beta _{2})q^{4}+\cdots\)
69.4.a.d \(4\) \(4.071\) 4.4.2009704.1 None \(4\) \(12\) \(4\) \(-14\) \(+\) \(q+(1-\beta _{1})q^{2}+3q^{3}+(7-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
69.4.c.a \(2\) \(4.071\) \(\Q(\sqrt{-23}) \) \(\Q(\sqrt{-23}) \) \(0\) \(4\) \(0\) \(0\) \(q-\beta q^{2}+(2-\beta )q^{3}-15q^{4}+(-23+\cdots)q^{6}+\cdots\)
69.4.c.b \(4\) \(4.071\) \(\Q(\sqrt{-3}, \sqrt{-23})\) \(\Q(\sqrt{-23}) \) \(0\) \(-4\) \(0\) \(0\) \(q+(-1-\beta _{2}-\beta _{3})q^{2}+(-1+2\beta _{1}+\cdots)q^{3}+\cdots\)
69.4.c.c \(16\) \(4.071\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-6\) \(0\) \(0\) \(q-\beta _{11}q^{2}-\beta _{10}q^{3}+(-2+\beta _{1})q^{4}+\cdots\)
69.4.e.a \(60\) \(4.071\) None \(0\) \(-18\) \(22\) \(24\)
69.4.e.b \(60\) \(4.071\) None \(4\) \(18\) \(-6\) \(-4\)
69.4.g.a \(220\) \(4.071\) None \(0\) \(-5\) \(0\) \(-22\)
69.5.b.a \(30\) \(7.133\) None \(0\) \(8\) \(0\) \(-4\)
69.5.d.a \(16\) \(7.133\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(12\) \(0\) \(0\) \(0\) \(q+(1+\beta _{2})q^{2}+\beta _{3}q^{3}+(9+\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots\)
69.5.f.a \(160\) \(7.133\) None \(-12\) \(0\) \(0\) \(0\)
69.5.h.a \(300\) \(7.133\) None \(0\) \(-19\) \(0\) \(-18\)
69.6.a.a \(2\) \(11.066\) \(\Q(\sqrt{29}) \) None \(0\) \(-18\) \(94\) \(-118\) \(-\) \(q-2\beta q^{2}-9q^{3}+84q^{4}+(47-\beta )q^{5}+\cdots\)
69.6.a.b \(3\) \(11.066\) 3.3.5333.1 None \(-8\) \(27\) \(-56\) \(-114\) \(+\) \(q+(-3+\beta _{2})q^{2}+9q^{3}+(9-4\beta _{1}-9\beta _{2})q^{4}+\cdots\)
69.6.a.c \(4\) \(11.066\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(4\) \(-36\) \(-122\) \(62\) \(-\) \(q+(1+\beta _{1})q^{2}-9q^{3}+(-12+4\beta _{1}+\cdots)q^{4}+\cdots\)
69.6.a.d \(4\) \(11.066\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(4\) \(-36\) \(22\) \(-62\) \(+\) \(q+(1-\beta _{1})q^{2}-9q^{3}+(7-\beta _{1}+\beta _{3})q^{4}+\cdots\)
69.6.a.e \(5\) \(11.066\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(8\) \(45\) \(94\) \(272\) \(-\) \(q+(2-\beta _{2})q^{2}+9q^{3}+(24-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
69.6.c.a \(6\) \(11.066\) 6.0.8869743.1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-3\beta _{2}-2\beta _{3}+\beta _{4}+\beta _{5})q^{2}+\cdots\)
69.6.c.b \(32\) \(11.066\) None \(0\) \(0\) \(0\) \(0\)
69.6.e.a \(100\) \(11.066\) None \(-8\) \(90\) \(6\) \(118\)
69.6.e.b \(100\) \(11.066\) None \(12\) \(-90\) \(-50\) \(-78\)
69.6.g.a \(380\) \(11.066\) None \(0\) \(-11\) \(0\) \(-22\)
69.7.b.a \(44\) \(15.874\) None \(0\) \(20\) \(0\) \(568\)
69.7.d.a \(24\) \(15.874\) None \(-20\) \(0\) \(0\) \(0\)
69.7.f.a \(240\) \(15.874\) None \(20\) \(0\) \(0\) \(0\)
69.7.h.a \(460\) \(15.874\) None \(0\) \(23\) \(0\) \(-18\)
69.8.a.a \(5\) \(21.555\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(-135\) \(-266\) \(-496\) \(-\) \(q+\beta _{1}q^{2}-3^{3}q^{3}+(54+2\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
69.8.a.b \(6\) \(21.555\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-8\) \(162\) \(-372\) \(-1104\) \(-\) \(q+(-1-\beta _{1})q^{2}+3^{3}q^{3}+(29+3\beta _{1}+\cdots)q^{4}+\cdots\)
69.8.a.c \(7\) \(21.555\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-189\) \(-516\) \(1018\) \(+\) \(q+\beta _{1}q^{2}-3^{3}q^{3}+(93+\beta _{1}+\beta _{2})q^{4}+\cdots\)
69.8.a.d \(8\) \(21.555\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(24\) \(216\) \(378\) \(126\) \(+\) \(q+(3-\beta _{1})q^{2}+3^{3}q^{3}+(70-4\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
69.8.c.a \(6\) \(21.555\) 6.0.8869743.1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) \(q+(-2\beta _{1}-6\beta _{2}+3\beta _{3}+2\beta _{4}+2\beta _{5})q^{2}+\cdots\)
69.8.c.b \(48\) \(21.555\) None \(0\) \(24\) \(0\) \(0\)
69.8.e.a \(140\) \(21.555\) None \(-16\) \(-378\) \(-6\) \(978\)
69.8.e.b \(140\) \(21.555\) None \(-12\) \(378\) \(2\) \(-394\)
69.8.g.a \(540\) \(21.555\) None \(0\) \(-35\) \(0\) \(-22\)
69.9.b.a \(58\) \(28.109\) None \(0\) \(-112\) \(0\) \(6996\)
69.9.d.a \(32\) \(28.109\) None \(12\) \(0\) \(0\) \(0\)
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