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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
354.2.a.a \(1\) \(2.827\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
354.2.a.b \(1\) \(2.827\) \(\Q\) None \(-1\) \(-1\) \(2\) \(0\) \(-\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
354.2.a.c \(1\) \(2.827\) \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
354.2.a.d \(1\) \(2.827\) \(\Q\) None \(1\) \(-1\) \(-4\) \(-1\) \(+\) \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-q^{7}+\cdots\)
354.2.a.e \(1\) \(2.827\) \(\Q\) None \(1\) \(-1\) \(0\) \(0\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
354.2.a.f \(1\) \(2.827\) \(\Q\) None \(1\) \(-1\) \(4\) \(0\) \(-\) \(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}+q^{8}+\cdots\)
354.2.a.g \(2\) \(2.827\) \(\Q(\sqrt{11}) \) None \(-2\) \(2\) \(2\) \(8\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
354.2.a.h \(3\) \(2.827\) 3.3.316.1 None \(3\) \(3\) \(2\) \(-1\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
354.2.c.a \(10\) \(2.827\) 10.0.\(\cdots\).1 None \(-10\) \(-1\) \(0\) \(-2\) \(q-q^{2}-\beta _{6}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{6}q^{6}+\cdots\)
354.2.c.b \(10\) \(2.827\) 10.0.\(\cdots\).1 None \(10\) \(-1\) \(0\) \(-2\) \(q+q^{2}-\beta _{6}q^{3}+q^{4}-\beta _{3}q^{5}-\beta _{6}q^{6}+\cdots\)
354.2.e.a \(56\) \(2.827\) None \(-2\) \(-2\) \(4\) \(9\)
354.2.e.b \(56\) \(2.827\) None \(2\) \(2\) \(-2\) \(1\)
354.2.e.c \(84\) \(2.827\) None \(-3\) \(3\) \(0\) \(1\)
354.2.e.d \(84\) \(2.827\) None \(3\) \(-3\) \(-2\) \(-7\)
354.2.g.a \(280\) \(2.827\) None \(-10\) \(1\) \(0\) \(2\)
354.2.g.b \(280\) \(2.827\) None \(10\) \(1\) \(0\) \(2\)
354.3.b.a \(40\) \(9.646\) None \(0\) \(0\) \(0\) \(8\)
354.3.d.a \(20\) \(9.646\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(8\) \(q+\beta _{4}q^{2}-\beta _{7}q^{3}-2q^{4}+\beta _{5}q^{5}+\beta _{6}q^{6}+\cdots\)
354.3.f.a \(560\) \(9.646\) None \(0\) \(0\) \(0\) \(-8\)
354.3.h.a \(1120\) \(9.646\) None \(0\) \(0\) \(0\) \(-8\)
354.4.a.a \(2\) \(20.887\) \(\Q(\sqrt{21}) \) None \(-4\) \(6\) \(-12\) \(-23\) \(-\) \(q-2q^{2}+3q^{3}+4q^{4}+(-5-2\beta )q^{5}+\cdots\)
354.4.a.b \(2\) \(20.887\) \(\Q(\sqrt{51}) \) None \(-4\) \(6\) \(26\) \(0\) \(+\) \(q-2q^{2}+3q^{3}+4q^{4}+(13+\beta )q^{5}+\cdots\)
354.4.a.c \(2\) \(20.887\) \(\Q(\sqrt{13}) \) None \(4\) \(6\) \(-20\) \(-23\) \(-\) \(q+2q^{2}+3q^{3}+4q^{4}+(-9-2\beta )q^{5}+\cdots\)
354.4.a.d \(3\) \(20.887\) 3.3.30645.1 None \(-6\) \(-9\) \(-6\) \(6\) \(-\) \(q-2q^{2}-3q^{3}+4q^{4}+(-2-\beta _{1}-2\beta _{2})q^{5}+\cdots\)
354.4.a.e \(3\) \(20.887\) 3.3.45581.1 None \(-6\) \(-9\) \(4\) \(13\) \(+\) \(q-2q^{2}-3q^{3}+4q^{4}+(2-\beta _{1}+\beta _{2})q^{5}+\cdots\)
354.4.a.f \(3\) \(20.887\) 3.3.18989.1 None \(-6\) \(9\) \(-28\) \(26\) \(+\) \(q-2q^{2}+3q^{3}+4q^{4}+(-9+\beta _{1}+\beta _{2})q^{5}+\cdots\)
354.4.a.g \(3\) \(20.887\) 3.3.47277.1 None \(6\) \(-9\) \(-18\) \(6\) \(-\) \(q+2q^{2}-3q^{3}+4q^{4}+(-6+\beta _{1}+\beta _{2})q^{5}+\cdots\)
354.4.a.h \(4\) \(20.887\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(8\) \(-12\) \(22\) \(13\) \(+\) \(q+2q^{2}-3q^{3}+4q^{4}+(5+\beta _{1}-\beta _{3})q^{5}+\cdots\)
354.4.a.i \(6\) \(20.887\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(12\) \(18\) \(20\) \(26\) \(+\) \(q+2q^{2}+3q^{3}+4q^{4}+(3+\beta _{1})q^{5}+\cdots\)
354.4.c.a \(30\) \(20.887\) None \(-60\) \(5\) \(0\) \(6\)
354.4.c.b \(30\) \(20.887\) None \(60\) \(5\) \(0\) \(6\)
354.5.b.a \(76\) \(36.593\) None \(0\) \(0\) \(0\) \(-184\)
354.5.d.a \(40\) \(36.593\) None \(0\) \(0\) \(0\) \(-80\)
354.6.a.a \(1\) \(56.776\) \(\Q\) None \(4\) \(-9\) \(10\) \(144\) \(-\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}+10q^{5}-6^{2}q^{6}+\cdots\)
354.6.a.b \(4\) \(56.776\) 4.4.32832.1 None \(16\) \(36\) \(-104\) \(-162\) \(+\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}+(-5^{2}+2\beta _{1}+\cdots)q^{5}+\cdots\)
354.6.a.c \(5\) \(56.776\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-20\) \(45\) \(-10\) \(-162\) \(+\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots\)
354.6.a.d \(5\) \(56.776\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(20\) \(-45\) \(-24\) \(-103\) \(+\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}+(-5+\beta _{3}+\cdots)q^{5}+\cdots\)
354.6.a.e \(5\) \(56.776\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(20\) \(-45\) \(166\) \(-198\) \(-\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}+(33-\beta _{2})q^{5}+\cdots\)
354.6.a.f \(6\) \(56.776\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-24\) \(-54\) \(-46\) \(-103\) \(+\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}+(-8+\beta _{5})q^{5}+\cdots\)
354.6.a.g \(6\) \(56.776\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-24\) \(-54\) \(4\) \(-54\) \(-\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}+(1-\beta _{5})q^{5}+\cdots\)
354.6.a.h \(8\) \(56.776\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-32\) \(72\) \(40\) \(181\) \(-\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}+(5+\beta _{1})q^{5}+\cdots\)
354.6.a.i \(8\) \(56.776\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(32\) \(72\) \(96\) \(181\) \(-\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}+(12-\beta _{1})q^{5}+\cdots\)
354.6.c.a \(50\) \(56.776\) None \(-200\) \(-13\) \(0\) \(38\)
354.6.c.b \(50\) \(56.776\) None \(200\) \(-13\) \(0\) \(38\)
354.7.d.a \(60\) \(81.439\) None \(0\) \(0\) \(0\) \(408\)
354.8.a.a \(1\) \(110.584\) \(\Q\) None \(8\) \(27\) \(-320\) \(-505\) \(-\) \(q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}-320q^{5}+\cdots\)
354.8.a.b \(5\) \(110.584\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(40\) \(135\) \(164\) \(-76\) \(-\) \(q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(33+\beta _{1}+\cdots)q^{5}+\cdots\)
354.8.a.c \(7\) \(110.584\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-56\) \(189\) \(-158\) \(-581\) \(-\) \(q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(-23-\beta _{2}+\cdots)q^{5}+\cdots\)
354.8.a.d \(8\) \(110.584\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(64\) \(-216\) \(-592\) \(-340\) \(-\) \(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(-74+\beta _{3}+\cdots)q^{5}+\cdots\)
354.8.a.e \(9\) \(110.584\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-72\) \(-243\) \(-230\) \(-340\) \(-\) \(q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(-26+\beta _{3}+\cdots)q^{5}+\cdots\)
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