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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
35.2.a.a \(1\) \(0.279\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(-\) \(q+q^{3}-2q^{4}-q^{5}+q^{7}-2q^{9}-3q^{11}+\cdots\)
35.2.a.b \(2\) \(0.279\) \(\Q(\sqrt{17}) \) None \(-1\) \(-1\) \(2\) \(-2\) \(-\) \(q-\beta q^{2}+(-1+\beta )q^{3}+(2+\beta )q^{4}+q^{5}+\cdots\)
35.2.b.a \(2\) \(0.279\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+2iq^{2}-iq^{3}-2q^{4}+(-2-i)q^{5}+\cdots\)
35.2.e.a \(4\) \(0.279\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(-2\) \(-2\) \(2\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots\)
35.2.f.a \(4\) \(0.279\) \(\Q(i, \sqrt{10})\) None \(-4\) \(0\) \(0\) \(4\) \(q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}-\beta _{1}q^{5}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
35.2.j.a \(4\) \(0.279\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(0\) \(q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
35.2.k.a \(4\) \(0.279\) \(\Q(\zeta_{12})\) None \(-4\) \(-2\) \(-4\) \(0\) \(q+(-1+\zeta_{12})q^{2}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
35.2.k.b \(4\) \(0.279\) \(\Q(\zeta_{12})\) None \(2\) \(-4\) \(4\) \(-10\) \(q+(1-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}+\cdots)q^{3}+\cdots\)
35.3.c.a \(1\) \(0.954\) \(\Q\) \(\Q(\sqrt{-35}) \) \(0\) \(-1\) \(5\) \(-7\) \(q-q^{3}+4q^{4}+5q^{5}-7q^{7}-8q^{9}+\cdots\)
35.3.c.b \(1\) \(0.954\) \(\Q\) \(\Q(\sqrt{-35}) \) \(0\) \(1\) \(-5\) \(7\) \(q+q^{3}+4q^{4}-5q^{5}+7q^{7}-8q^{9}+\cdots\)
35.3.c.c \(4\) \(0.954\) \(\Q(i, \sqrt{10})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}-5q^{4}+(\beta _{2}-\beta _{3})q^{5}+\cdots\)
35.3.d.a \(2\) \(0.954\) \(\Q(\sqrt{-5}) \) None \(-2\) \(0\) \(0\) \(14\) \(q-q^{2}+2\beta q^{3}-3q^{4}+\beta q^{5}-2\beta q^{6}+\cdots\)
35.3.d.b \(2\) \(0.954\) \(\Q(\sqrt{-5}) \) None \(4\) \(0\) \(0\) \(-4\) \(q+2q^{2}+\beta q^{3}-\beta q^{5}+2\beta q^{6}+(-2+\cdots)q^{7}+\cdots\)
35.3.g.a \(12\) \(0.954\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(-4\) \(-8\) \(0\) \(q-\beta _{1}q^{2}+\beta _{7}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4}+\beta _{10}+\cdots)q^{4}+\cdots\)
35.3.h.a \(12\) \(0.954\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-2\) \(-6\) \(0\) \(-2\) \(q+(\beta _{1}+\beta _{2})q^{2}+(-1+\beta _{7})q^{3}+(-2+\cdots)q^{4}+\cdots\)
35.3.i.a \(12\) \(0.954\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{11})q^{3}+(1+\beta _{3}+\cdots)q^{4}+\cdots\)
35.3.l.a \(24\) \(0.954\) None \(-2\) \(-2\) \(-4\) \(-6\)
35.4.a.a \(1\) \(2.065\) \(\Q\) None \(1\) \(-8\) \(-5\) \(7\) \(-\) \(q+q^{2}-8q^{3}-7q^{4}-5q^{5}-8q^{6}+\cdots\)
35.4.a.b \(2\) \(2.065\) \(\Q(\sqrt{2}) \) None \(8\) \(2\) \(-10\) \(-14\) \(+\) \(q+(4+\beta )q^{2}+(1-4\beta )q^{3}+(10+8\beta )q^{4}+\cdots\)
35.4.a.c \(3\) \(2.065\) 3.3.14360.1 None \(-3\) \(2\) \(15\) \(21\) \(+\) \(q+(-1+\beta _{1})q^{2}+(1+\beta _{1}-\beta _{2})q^{3}+\cdots\)
35.4.b.a \(10\) \(2.065\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(6\) \(0\) \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-4+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
35.4.e.a \(2\) \(2.065\) \(\Q(\sqrt{-3}) \) None \(-3\) \(2\) \(-5\) \(-28\) \(q-3\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
35.4.e.b \(4\) \(2.065\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(6\) \(2\) \(-10\) \(22\) \(q+(\beta _{1}-3\beta _{2}+\beta _{3})q^{2}+(1+3\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
35.4.e.c \(10\) \(2.065\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-1\) \(8\) \(25\) \(-62\) \(q+(\beta _{1}-\beta _{2})q^{2}+(-\beta _{3}-\beta _{5}+2\beta _{6}+\cdots)q^{3}+\cdots\)
35.4.f.a \(4\) \(2.065\) \(\Q(i, \sqrt{5})\) None \(-8\) \(0\) \(0\) \(-42\) \(q+(-2-2\beta _{2})q^{2}+(1+2\beta _{1}+\beta _{2})q^{3}+\cdots\)
35.4.f.b \(16\) \(2.065\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(4\) \(0\) \(0\) \(32\) \(q+\beta _{7}q^{2}-\beta _{8}q^{3}+(-4\beta _{3}+\beta _{6}-\beta _{7}+\cdots)q^{4}+\cdots\)
35.4.j.a \(20\) \(2.065\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(3\) \(0\) \(q-\beta _{1}q^{2}-\beta _{14}q^{3}+(-\beta _{2}-3\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
35.4.k.a \(40\) \(2.065\) None \(-2\) \(-6\) \(-30\) \(4\)
35.5.c.a \(1\) \(3.618\) \(\Q\) \(\Q(\sqrt{-35}) \) \(0\) \(-17\) \(25\) \(49\) \(q-17q^{3}+2^{4}q^{4}+5^{2}q^{5}+7^{2}q^{7}+\cdots\)
35.5.c.b \(1\) \(3.618\) \(\Q\) \(\Q(\sqrt{-35}) \) \(0\) \(17\) \(-25\) \(-49\) \(q+17q^{3}+2^{4}q^{4}-5^{2}q^{5}-7^{2}q^{7}+\cdots\)
35.5.c.c \(2\) \(3.618\) \(\Q(\sqrt{-6}) \) None \(0\) \(-10\) \(-10\) \(-70\) \(q+\beta q^{2}-5q^{3}+10q^{4}+(-5+10\beta )q^{5}+\cdots\)
35.5.c.d \(2\) \(3.618\) \(\Q(\sqrt{-6}) \) None \(0\) \(10\) \(10\) \(70\) \(q+\beta q^{2}+5q^{3}+10q^{4}+(5-10\beta )q^{5}+\cdots\)
35.5.c.e \(8\) \(3.618\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}+3\beta _{3}q^{3}+(-22+\beta _{2})q^{4}+\cdots\)
35.5.d.a \(12\) \(3.618\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-6\) \(0\) \(0\) \(-50\) \(q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(11-\beta _{1}+\cdots)q^{4}+\cdots\)
35.5.g.a \(24\) \(3.618\) None \(0\) \(20\) \(-48\) \(0\)
35.5.h.a \(20\) \(3.618\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(6\) \(-18\) \(0\) \(-54\) \(q+(1+\beta _{1}+\beta _{3}+\beta _{4})q^{2}+(-1-\beta _{4}+\cdots)q^{3}+\cdots\)
35.5.i.a \(28\) \(3.618\) None \(0\) \(0\) \(-30\) \(0\)
35.5.l.a \(56\) \(3.618\) None \(-2\) \(-2\) \(16\) \(46\)
35.6.a.a \(1\) \(5.613\) \(\Q\) None \(-8\) \(1\) \(25\) \(49\) \(+\) \(q-8q^{2}+q^{3}+2^{5}q^{4}+5^{2}q^{5}-8q^{6}+\cdots\)
35.6.a.b \(2\) \(5.613\) \(\Q(\sqrt{65}) \) None \(1\) \(3\) \(-50\) \(-98\) \(+\) \(q+\beta q^{2}+(3-3\beta )q^{3}+(-2^{4}+\beta )q^{4}+\cdots\)
35.6.a.c \(3\) \(5.613\) 3.3.577880.1 None \(-6\) \(26\) \(-75\) \(147\) \(-\) \(q+(-2+\beta _{1})q^{2}+(9+\beta _{2})q^{3}+(38+2\beta _{2})q^{4}+\cdots\)
35.6.a.d \(4\) \(5.613\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(7\) \(14\) \(100\) \(-196\) \(-\) \(q+(2-\beta _{1})q^{2}+(4-\beta _{1}+\beta _{3})q^{3}+(15+\cdots)q^{4}+\cdots\)
35.6.b.a \(14\) \(5.613\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(156\) \(0\) \(q-\beta _{4}q^{2}+\beta _{6}q^{3}+(-15+\beta _{1})q^{4}+\cdots\)
35.6.e.a \(12\) \(5.613\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(5\) \(-20\) \(150\) \(-20\) \(q+(1-\beta _{1}-\beta _{4})q^{2}+(\beta _{1}+\beta _{3}-3\beta _{4}+\cdots)q^{3}+\cdots\)
35.6.e.b \(16\) \(5.613\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-3\) \(2\) \(-200\) \(158\) \(q-\beta _{1}q^{2}+(-\beta _{5}+\beta _{6})q^{3}+(\beta _{1}-5^{2}\beta _{2}+\cdots)q^{4}+\cdots\)
35.6.f.a \(36\) \(5.613\) None \(-4\) \(0\) \(0\) \(-196\)
35.6.j.a \(36\) \(5.613\) None \(0\) \(0\) \(-12\) \(0\)
35.6.k.a \(72\) \(5.613\) None \(-2\) \(-6\) \(60\) \(190\)
35.7.c.a \(1\) \(8.052\) \(\Q\) \(\Q(\sqrt{-35}) \) \(0\) \(-26\) \(-125\) \(343\) \(q-26q^{3}+2^{6}q^{4}-5^{3}q^{5}+7^{3}q^{7}+\cdots\)
35.7.c.b \(1\) \(8.052\) \(\Q\) \(\Q(\sqrt{-35}) \) \(0\) \(26\) \(125\) \(-343\) \(q+26q^{3}+2^{6}q^{4}+5^{3}q^{5}-7^{3}q^{7}+\cdots\)
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