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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
43.2.a.a \(1\) \(0.343\) \(\Q\) None \(-2\) \(-2\) \(-4\) \(0\) \(+\) \(q-2q^{2}-2q^{3}+2q^{4}-4q^{5}+4q^{6}+\cdots\)
43.2.a.b \(2\) \(0.343\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(4\) \(-4\) \(-\) \(q+\beta q^{2}-\beta q^{3}+(2-\beta )q^{5}-2q^{6}+(-2+\cdots)q^{7}+\cdots\)
43.2.c.a \(2\) \(0.343\) \(\Q(\sqrt{-3}) \) None \(2\) \(-1\) \(1\) \(-3\) \(q+q^{2}+(-1+\zeta_{6})q^{3}-q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
43.2.c.b \(4\) \(0.343\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-6\) \(3\) \(2\) \(4\) \(q+(-2-\beta _{2})q^{2}+(1+\beta _{1}+\beta _{3})q^{3}+\cdots\)
43.2.e.a \(6\) \(0.343\) \(\Q(\zeta_{14})\) None \(-5\) \(2\) \(-3\) \(0\) \(q+(-\zeta_{14}+\zeta_{14}^{2}-\zeta_{14}^{3}+\zeta_{14}^{4}+\cdots)q^{2}+\cdots\)
43.2.e.b \(6\) \(0.343\) \(\Q(\zeta_{14})\) None \(3\) \(-3\) \(2\) \(-16\) \(q+(\zeta_{14}+\zeta_{14}^{3}+\zeta_{14}^{5})q^{2}+(-1+\zeta_{14}+\cdots)q^{3}+\cdots\)
43.2.g.a \(36\) \(0.343\) None \(-10\) \(-16\) \(-17\) \(6\)
43.3.b.a \(1\) \(1.172\) \(\Q\) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) \(q+4q^{4}+9q^{9}-21q^{11}-17q^{13}+\cdots\)
43.3.b.b \(6\) \(1.172\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-2+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
43.3.d.a \(12\) \(1.172\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-3\) \(9\) \(q+(\beta _{1}-\beta _{2})q^{2}+\beta _{3}q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots\)
43.3.f.a \(42\) \(1.172\) None \(-7\) \(-7\) \(-7\) \(0\)
43.3.h.a \(72\) \(1.172\) None \(-14\) \(-14\) \(-11\) \(-30\)
43.4.a.a \(4\) \(2.537\) 4.4.45868.1 None \(-4\) \(-11\) \(-27\) \(-20\) \(-\) \(q+(-1+\beta _{3})q^{2}+(-3+\beta _{2}-\beta _{3})q^{3}+\cdots\)
43.4.a.b \(6\) \(2.537\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(6\) \(7\) \(43\) \(8\) \(+\) \(q+(1-\beta _{1})q^{2}+(1-\beta _{3})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots\)
43.4.c.a \(20\) \(2.537\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-2\) \(-5\) \(-19\) \(-51\) \(q+\beta _{5}q^{2}+(-\beta _{4}-\beta _{6})q^{3}+(4+\beta _{2}+\cdots)q^{4}+\cdots\)
43.4.e.a \(60\) \(2.537\) None \(-9\) \(-3\) \(-23\) \(96\)
43.4.g.a \(120\) \(2.537\) None \(-12\) \(-9\) \(5\) \(-54\)
43.5.b.a \(1\) \(4.445\) \(\Q\) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) \(q+2^{4}q^{4}+3^{4}q^{9}+199q^{11}-7^{2}q^{13}+\cdots\)
43.5.b.b \(12\) \(4.445\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-8+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
43.5.d.a \(28\) \(4.445\) None \(0\) \(6\) \(-3\) \(129\)
43.5.f.a \(78\) \(4.445\) None \(-7\) \(-7\) \(-7\) \(0\)
43.5.h.a \(168\) \(4.445\) None \(-14\) \(-20\) \(-11\) \(-150\)
43.6.a.a \(8\) \(6.897\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-12\) \(-26\) \(-212\) \(-136\) \(+\) \(q+(-2+\beta _{1})q^{2}+(-2-\beta _{1}+\beta _{4}-\beta _{7})q^{3}+\cdots\)
43.6.a.b \(10\) \(6.897\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(8\) \(28\) \(138\) \(60\) \(-\) \(q+(1-\beta _{1})q^{2}+(3+\beta _{6})q^{3}+(21-\beta _{1}+\cdots)q^{4}+\cdots\)
43.6.c.a \(34\) \(6.897\) None \(-14\) \(-14\) \(71\) \(225\)
43.6.e.a \(108\) \(6.897\) None \(-3\) \(-9\) \(67\) \(-624\)
43.6.g.a \(204\) \(6.897\) None \(0\) \(0\) \(-85\) \(454\)
43.7.b.a \(1\) \(9.892\) \(\Q\) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) \(q+2^{6}q^{4}+3^{6}q^{9}-1638q^{11}+3706q^{13}+\cdots\)
43.7.b.b \(20\) \(9.892\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-40+\beta _{2})q^{4}+\cdots\)
43.7.d.a \(42\) \(9.892\) None \(0\) \(-3\) \(-3\) \(-147\)
43.7.f.a \(126\) \(9.892\) None \(-7\) \(-7\) \(-7\) \(0\)
43.7.h.a \(252\) \(9.892\) None \(-14\) \(-11\) \(-11\) \(126\)
43.8.a.a \(11\) \(13.433\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-24\) \(-68\) \(-752\) \(-12\) \(-\) \(q+(-2-\beta _{1})q^{2}+(-6-\beta _{5})q^{3}+(54+\cdots)q^{4}+\cdots\)
43.8.a.b \(13\) \(13.433\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(16\) \(94\) \(998\) \(1360\) \(+\) \(q+(1+\beta _{1})q^{2}+(7+\beta _{3})q^{3}+(71+2\beta _{1}+\cdots)q^{4}+\cdots\)
43.8.c.a \(50\) \(13.433\) None \(26\) \(-2\) \(-249\) \(-687\)
43.8.e.a \(144\) \(13.433\) None \(1\) \(-33\) \(-253\) \(3440\)
43.8.g.a \(300\) \(13.433\) None \(-40\) \(-12\) \(235\) \(-4122\)
43.9.b.a \(1\) \(17.517\) \(\Q\) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) \(q+2^{8}q^{4}+3^{8}q^{9}+10319q^{11}-54721q^{13}+\cdots\)
43.9.b.b \(28\) \(17.517\) None \(0\) \(0\) \(0\) \(0\)
43.9.d.a \(56\) \(17.517\) None \(0\) \(-84\) \(-3\) \(-5031\)
43.9.f.a \(174\) \(17.517\) None \(-7\) \(-7\) \(-7\) \(0\)
43.9.h.a \(336\) \(17.517\) None \(-14\) \(70\) \(-11\) \(5010\)
43.10.a.a \(15\) \(22.147\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-32\) \(-317\) \(-4717\) \(-9680\) \(+\) \(q+(-2-\beta _{1})q^{2}+(-21-\beta _{2})q^{3}+(6^{3}+\cdots)q^{4}+\cdots\)
43.10.a.b \(17\) \(22.147\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(48\) \(169\) \(4033\) \(-76\) \(-\) \(q+(3-\beta _{1})q^{2}+(10-\beta _{3})q^{3}+(267-4\beta _{1}+\cdots)q^{4}+\cdots\)
43.10.c.a \(64\) \(22.147\) None \(-70\) \(307\) \(681\) \(957\)
43.10.e.a \(192\) \(22.147\) None \(-23\) \(141\) \(677\) \(-23872\)
43.10.g.a \(384\) \(22.147\) None \(56\) \(-321\) \(-695\) \(32650\)
43.11.b.a \(1\) \(27.320\) \(\Q\) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) \(q+2^{10}q^{4}+3^{10}q^{9}-18501q^{11}+\cdots\)
43.11.b.b \(34\) \(27.320\) None \(0\) \(0\) \(0\) \(0\)
43.11.d.a \(72\) \(27.320\) None \(0\) \(-246\) \(-3\) \(31377\)
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