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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
138.2.a.a \(1\) \(1.102\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(-2\) \(+\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-2q^{7}+\cdots\)
138.2.a.b \(1\) \(1.102\) \(\Q\) None \(-1\) \(1\) \(0\) \(2\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
138.2.a.c \(1\) \(1.102\) \(\Q\) None \(1\) \(-1\) \(2\) \(0\) \(-\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
138.2.a.d \(2\) \(1.102\) \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(-2\) \(0\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(-1+\beta )q^{5}+q^{6}+\cdots\)
138.2.d.a \(8\) \(1.102\) 8.0.\(\cdots\).3 None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{7})q^{3}-q^{4}+\beta _{3}q^{5}+\cdots\)
138.2.e.a \(10\) \(1.102\) \(\Q(\zeta_{22})\) None \(-1\) \(-1\) \(8\) \(8\) \(q-\zeta_{22}q^{2}+\zeta_{22}^{8}q^{3}+\zeta_{22}^{2}q^{4}+(1+\cdots)q^{5}+\cdots\)
138.2.e.b \(10\) \(1.102\) \(\Q(\zeta_{22})\) None \(-1\) \(1\) \(-2\) \(0\) \(q-\zeta_{22}q^{2}-\zeta_{22}^{8}q^{3}+\zeta_{22}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
138.2.e.c \(10\) \(1.102\) \(\Q(\zeta_{22})\) None \(1\) \(-1\) \(0\) \(-2\) \(q+\zeta_{22}q^{2}+\zeta_{22}^{8}q^{3}+\zeta_{22}^{2}q^{4}+(1+\cdots)q^{5}+\cdots\)
138.2.e.d \(10\) \(1.102\) \(\Q(\zeta_{22})\) None \(1\) \(1\) \(2\) \(2\) \(q+\zeta_{22}q^{2}-\zeta_{22}^{8}q^{3}+\zeta_{22}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
138.2.f.a \(80\) \(1.102\) None \(0\) \(4\) \(0\) \(0\)
138.3.b.a \(8\) \(3.760\) 8.0.1358954496.3 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}+\beta _{1}q^{3}+2q^{4}+(-\beta _{2}+2\beta _{3}+\cdots)q^{5}+\cdots\)
138.3.c.a \(16\) \(3.760\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(4\) \(0\) \(0\) \(q-\beta _{3}q^{2}+\beta _{1}q^{3}-2q^{4}-\beta _{7}q^{5}+\beta _{11}q^{6}+\cdots\)
138.3.g.a \(160\) \(3.760\) None \(0\) \(-4\) \(0\) \(0\)
138.3.h.a \(80\) \(3.760\) None \(0\) \(0\) \(0\) \(0\)
138.4.a.a \(1\) \(8.142\) \(\Q\) None \(-2\) \(-3\) \(-10\) \(32\) \(-\) \(q-2q^{2}-3q^{3}+4q^{4}-10q^{5}+6q^{6}+\cdots\)
138.4.a.b \(1\) \(8.142\) \(\Q\) None \(-2\) \(3\) \(2\) \(-32\) \(-\) \(q-2q^{2}+3q^{3}+4q^{4}+2q^{5}-6q^{6}+\cdots\)
138.4.a.c \(1\) \(8.142\) \(\Q\) None \(2\) \(-3\) \(-2\) \(-34\) \(-\) \(q+2q^{2}-3q^{3}+4q^{4}-2q^{5}-6q^{6}+\cdots\)
138.4.a.d \(2\) \(8.142\) \(\Q(\sqrt{277}) \) None \(-4\) \(6\) \(2\) \(28\) \(+\) \(q-2q^{2}+3q^{3}+4q^{4}+(1-\beta )q^{5}-6q^{6}+\cdots\)
138.4.a.e \(2\) \(8.142\) \(\Q(\sqrt{2}) \) None \(4\) \(-6\) \(8\) \(12\) \(+\) \(q+2q^{2}-3q^{3}+4q^{4}+(4+\beta )q^{5}-6q^{6}+\cdots\)
138.4.a.f \(3\) \(8.142\) 3.3.16372.1 None \(6\) \(9\) \(20\) \(10\) \(+\) \(q+2q^{2}+3q^{3}+4q^{4}+(7+\beta _{2})q^{5}+\cdots\)
138.4.d.a \(24\) \(8.142\) None \(0\) \(8\) \(0\) \(0\)
138.4.e.a \(30\) \(8.142\) None \(-6\) \(-9\) \(-20\) \(-10\)
138.4.e.b \(30\) \(8.142\) None \(-6\) \(9\) \(-6\) \(22\)
138.4.e.c \(30\) \(8.142\) None \(6\) \(-9\) \(-4\) \(4\)
138.4.e.d \(30\) \(8.142\) None \(6\) \(9\) \(-2\) \(0\)
138.4.f.a \(240\) \(8.142\) None \(0\) \(-8\) \(0\) \(0\)
138.5.b.a \(16\) \(14.265\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}-\beta _{1}q^{3}+8q^{4}+\beta _{4}q^{5}+\beta _{7}q^{6}+\cdots\)
138.5.c.a \(28\) \(14.265\) None \(0\) \(-8\) \(0\) \(-104\)
138.5.g.a \(320\) \(14.265\) None \(0\) \(20\) \(0\) \(0\)
138.5.h.a \(160\) \(14.265\) None \(0\) \(0\) \(0\) \(0\)
138.6.a.a \(1\) \(22.133\) \(\Q\) None \(-4\) \(-9\) \(-44\) \(-70\) \(-\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}-44q^{5}+6^{2}q^{6}+\cdots\)
138.6.a.b \(1\) \(22.133\) \(\Q\) None \(-4\) \(-9\) \(76\) \(210\) \(-\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}+76q^{5}+6^{2}q^{6}+\cdots\)
138.6.a.c \(1\) \(22.133\) \(\Q\) None \(4\) \(-9\) \(-10\) \(-8\) \(+\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}-10q^{5}-6^{2}q^{6}+\cdots\)
138.6.a.d \(1\) \(22.133\) \(\Q\) None \(4\) \(9\) \(-46\) \(-136\) \(+\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}-46q^{5}+6^{2}q^{6}+\cdots\)
138.6.a.e \(2\) \(22.133\) \(\Q(\sqrt{154}) \) None \(-8\) \(18\) \(-4\) \(-40\) \(+\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}+(-2+3\beta )q^{5}+\cdots\)
138.6.a.f \(2\) \(22.133\) \(\Q(\sqrt{514}) \) None \(8\) \(-18\) \(40\) \(-100\) \(-\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}+(20+3\beta )q^{5}+\cdots\)
138.6.a.g \(3\) \(22.133\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-12\) \(-27\) \(-18\) \(-50\) \(+\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}+(-6-\beta _{2})q^{5}+\cdots\)
138.6.a.h \(3\) \(22.133\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-12\) \(27\) \(-4\) \(-34\) \(-\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
138.6.a.i \(4\) \(22.133\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(16\) \(36\) \(54\) \(348\) \(-\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}+(13-\beta _{1})q^{5}+\cdots\)
138.6.d.a \(40\) \(22.133\) None \(0\) \(-4\) \(0\) \(0\)
138.7.b.a \(24\) \(31.747\) None \(0\) \(0\) \(0\) \(0\)
138.7.c.a \(44\) \(31.747\) None \(0\) \(-20\) \(0\) \(-8\)
138.8.a.a \(1\) \(43.109\) \(\Q\) None \(8\) \(27\) \(-230\) \(106\) \(-\) \(q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}-230q^{5}+\cdots\)
138.8.a.b \(3\) \(43.109\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-24\) \(-81\) \(160\) \(-364\) \(+\) \(q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(55+5\beta _{1}+\cdots)q^{5}+\cdots\)
138.8.a.c \(3\) \(43.109\) 3.3.3351293.1 None \(-24\) \(81\) \(-162\) \(-296\) \(-\) \(q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(-55-5\beta _{1}+\cdots)q^{5}+\cdots\)
138.8.a.d \(3\) \(43.109\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(24\) \(-81\) \(92\) \(-858\) \(-\) \(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(31+\beta _{2})q^{5}+\cdots\)
138.8.a.e \(4\) \(43.109\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-32\) \(-108\) \(-90\) \(-222\) \(-\) \(q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(-23+\beta _{1}+\cdots)q^{5}+\cdots\)
138.8.a.f \(4\) \(43.109\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-32\) \(108\) \(-162\) \(1218\) \(+\) \(q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(-40-\beta _{1}+\cdots)q^{5}+\cdots\)
138.8.a.g \(4\) \(43.109\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(32\) \(-108\) \(342\) \(-30\) \(+\) \(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(85+\beta _{1}+\cdots)q^{5}+\cdots\)
138.8.a.h \(4\) \(43.109\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(32\) \(108\) \(270\) \(2022\) \(+\) \(q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(68-\beta _{1}+\cdots)q^{5}+\cdots\)
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