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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
177.2.a.a \(2\) \(1.413\) \(\Q(\sqrt{5}) \) None \(-3\) \(2\) \(-6\) \(-7\) \(+\) \(q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}-3q^{5}+\cdots\)
177.2.a.b \(2\) \(1.413\) \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(0\) \(-7\) \(+\) \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots\)
177.2.a.c \(2\) \(1.413\) \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(2\) \(1\) \(-\) \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
177.2.a.d \(3\) \(1.413\) 3.3.229.1 None \(0\) \(-3\) \(-2\) \(9\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
177.2.d.a \(6\) \(1.413\) 6.0.19298288.1 None \(-4\) \(-1\) \(0\) \(0\) \(q+(-1+\beta _{1}+\beta _{2}+\beta _{5})q^{2}-\beta _{1}q^{3}+\cdots\)
177.2.d.b \(6\) \(1.413\) 6.0.149721291.1 \(\Q(\sqrt{-59}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-2q^{4}+(\beta _{2}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
177.2.d.c \(6\) \(1.413\) 6.0.19298288.1 None \(4\) \(-1\) \(0\) \(0\) \(q+(1-\beta _{1}-\beta _{2}-\beta _{5})q^{2}-\beta _{1}q^{3}+(2+\cdots)q^{4}+\cdots\)
177.2.e.a \(140\) \(1.413\) None \(-1\) \(-5\) \(-2\) \(-2\)
177.2.e.b \(140\) \(1.413\) None \(1\) \(5\) \(2\) \(-2\)
177.2.f.a \(504\) \(1.413\) None \(0\) \(-27\) \(0\) \(-58\)
177.3.b.a \(38\) \(4.823\) None \(0\) \(0\) \(0\) \(-12\)
177.3.c.a \(20\) \(4.823\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(-8\) \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(-2+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots\)
177.3.g.a \(560\) \(4.823\) None \(0\) \(0\) \(0\) \(8\)
177.3.h.a \(1064\) \(4.823\) None \(0\) \(-29\) \(0\) \(-46\)
177.4.a.a \(7\) \(10.443\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-8\) \(21\) \(-28\) \(-59\) \(-\) \(q+(-1-\beta _{1})q^{2}+3q^{3}+(3+2\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
177.4.a.b \(7\) \(10.443\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-21\) \(-2\) \(-59\) \(-\) \(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
177.4.a.c \(8\) \(10.443\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(2\) \(-24\) \(-12\) \(53\) \(+\) \(q+\beta _{1}q^{2}-3q^{3}+(5+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
177.4.a.d \(8\) \(10.443\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(6\) \(24\) \(42\) \(53\) \(+\) \(q+(1-\beta _{1})q^{2}+3q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
177.4.d.a \(2\) \(10.443\) \(\Q(\sqrt{-59}) \) \(\Q(\sqrt{-59}) \) \(0\) \(7\) \(0\) \(58\) \(q+(4-\beta )q^{3}-8q^{4}+(-1+2\beta )q^{5}+\cdots\)
177.4.d.b \(4\) \(10.443\) \(\Q(\sqrt{-3}, \sqrt{-59})\) \(\Q(\sqrt{-59}) \) \(0\) \(-7\) \(0\) \(-58\) \(q+(-2-\beta _{2}-\beta _{3})q^{3}-8q^{4}+(4\beta _{1}+\cdots)q^{5}+\cdots\)
177.4.d.c \(52\) \(10.443\) None \(0\) \(-8\) \(0\) \(-16\)
177.4.e.a \(420\) \(10.443\) None \(-2\) \(45\) \(14\) \(6\)
177.4.e.b \(420\) \(10.443\) None \(2\) \(-45\) \(-14\) \(6\)
177.4.f.a \(1624\) \(10.443\) None \(0\) \(-21\) \(0\) \(-42\)
177.5.b.a \(78\) \(18.296\) None \(0\) \(0\) \(0\) \(76\)
177.5.c.a \(40\) \(18.296\) None \(0\) \(0\) \(0\) \(80\)
177.6.a.a \(11\) \(28.388\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-6\) \(99\) \(-192\) \(-371\) \(+\) \(q+(-1+\beta _{1})q^{2}+9q^{3}+(14-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
177.6.a.b \(12\) \(28.388\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(-108\) \(36\) \(-411\) \(+\) \(q-\beta _{1}q^{2}-9q^{3}+(17+\beta _{2})q^{4}+(3+\beta _{1}+\cdots)q^{5}+\cdots\)
177.6.a.c \(12\) \(28.388\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(22\) \(108\) \(158\) \(413\) \(-\) \(q+(2-\beta _{1})q^{2}+9q^{3}+(17-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
177.6.a.d \(13\) \(28.388\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(-117\) \(-14\) \(373\) \(-\) \(q+\beta _{1}q^{2}-9q^{3}+(19+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
177.6.d.a \(6\) \(28.388\) 6.0.149721291.1 \(\Q(\sqrt{-59}) \) \(0\) \(0\) \(0\) \(0\) \(q+(4\beta _{2}+3\beta _{3}-3\beta _{4})q^{3}-2^{5}q^{4}+(21\beta _{1}+\cdots)q^{5}+\cdots\)
177.6.d.b \(92\) \(28.388\) None \(0\) \(22\) \(0\) \(-80\)
177.7.c.a \(60\) \(40.720\) None \(0\) \(0\) \(0\) \(-408\)
177.8.a.a \(16\) \(55.292\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-6\) \(-432\) \(-68\) \(-2343\) \(-\) \(q-\beta _{1}q^{2}-3^{3}q^{3}+(61+\beta _{2})q^{4}+(-5+\cdots)q^{5}+\cdots\)
177.8.a.b \(17\) \(55.292\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(-32\) \(459\) \(-1072\) \(-2407\) \(-\) \(q+(-2+\beta _{1})q^{2}+3^{3}q^{3}+(69-3\beta _{1}+\cdots)q^{4}+\cdots\)
177.8.a.c \(17\) \(55.292\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(2\) \(-459\) \(-318\) \(3145\) \(+\) \(q+\beta _{1}q^{2}-3^{3}q^{3}+(68+\beta _{1}+\beta _{2})q^{4}+\cdots\)
177.8.a.d \(18\) \(55.292\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(24\) \(486\) \(678\) \(3081\) \(+\) \(q+(1+\beta _{1})q^{2}+3^{3}q^{3}+(75+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
177.9.c.a \(80\) \(72.106\) None \(0\) \(0\) \(0\) \(160\)
177.10.a.a \(21\) \(91.161\) None \(-66\) \(1701\) \(-2964\) \(-30775\) \(+\)
177.10.a.b \(21\) \(91.161\) None \(20\) \(-1701\) \(2058\) \(-17167\) \(+\)
177.10.a.c \(22\) \(91.161\) None \(36\) \(-1782\) \(808\) \(21249\) \(-\)
177.10.a.d \(22\) \(91.161\) None \(46\) \(1782\) \(5786\) \(7641\) \(-\)
177.11.c.a \(100\) \(112.458\) None \(0\) \(0\) \(0\) \(18392\)
177.12.a.a \(26\) \(135.997\) None \(-78\) \(-6318\) \(3808\) \(-98819\) \(-\)
177.12.a.b \(27\) \(135.997\) None \(-128\) \(6561\) \(-17188\) \(-126579\) \(-\)
177.12.a.c \(27\) \(135.997\) None \(-46\) \(-6561\) \(-2442\) \(170093\) \(+\)
177.12.a.d \(28\) \(135.997\) None \(96\) \(6804\) \(26562\) \(142333\) \(+\)
177.14.a.a \(30\) \(189.799\) None \(-138\) \(21870\) \(-137742\) \(-879443\) \(+\)
177.14.a.b \(31\) \(189.799\) None \(-52\) \(-22599\) \(33486\) \(-1135539\) \(+\)
177.14.a.c \(31\) \(189.799\) None \(310\) \(22599\) \(81008\) \(1002941\) \(-\)
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