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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2169.1.bp.a \(8\) \(1.082\) \(\Q(\zeta_{16})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{6}q^{4}+(-\zeta_{16}^{2}-\zeta_{16}^{7})q^{7}+\cdots\)
2169.1.de.a \(32\) \(1.082\) \(\Q(\zeta_{80})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{80}^{30}q^{4}+(\zeta_{80}^{18}-\zeta_{80}^{19})q^{7}+\cdots\)
2169.2.a.a \(1\) \(17.320\) \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) \(+\) \(q-2q^{4}-2q^{7}+q^{11}+4q^{16}+2q^{17}+\cdots\)
2169.2.a.b \(1\) \(17.320\) \(\Q\) None None \(1\) \(0\) \(2\) \(0\) \(-\) \(q+q^{2}-q^{4}+2q^{5}-3q^{8}+2q^{10}+\cdots\)
2169.2.a.c \(2\) \(17.320\) \(\Q(\sqrt{5}) \) None None \(-2\) \(0\) \(-4\) \(2\) \(-\) \(q-q^{2}-q^{4}-2q^{5}+(1+\beta )q^{7}+3q^{8}+\cdots\)
2169.2.a.d \(5\) \(17.320\) 5.5.24217.1 None None \(2\) \(0\) \(8\) \(-7\) \(+\) \(q+(\beta _{1}+\beta _{2}-\beta _{4})q^{2}-\beta _{4}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
2169.2.a.e \(7\) \(17.320\) 7.7.31056073.1 None None \(4\) \(0\) \(8\) \(-7\) \(-\) \(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\)
2169.2.a.f \(9\) \(17.320\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(-3\) \(0\) \(-12\) \(-5\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{8})q^{5}+\cdots\)
2169.2.a.g \(10\) \(17.320\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(4\) \(0\) \(10\) \(3\) \(-\) \(q-\beta _{9}q^{2}+(1+\beta _{7}-\beta _{9})q^{4}+(\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
2169.2.a.h \(12\) \(17.320\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-3\) \(0\) \(-6\) \(3\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{9})q^{5}+\cdots\)
2169.2.a.i \(13\) \(17.320\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None None \(-1\) \(0\) \(-6\) \(9\) \(-\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{7}q^{5}+(1+\beta _{11}+\cdots)q^{7}+\cdots\)
2169.2.a.j \(14\) \(17.320\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(0\) \(0\) \(-14\) \(+\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{12}q^{5}+(-1-\beta _{8}+\cdots)q^{7}+\cdots\)
2169.2.a.k \(26\) \(17.320\) None None \(0\) \(0\) \(0\) \(22\) \(-\)
2169.2.d.a \(4\) \(17.320\) 4.0.696972.1 \(\Q(\sqrt{-723}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2q^{4}+\beta _{2}q^{11}+4q^{16}+\beta _{1}q^{17}+\cdots\)
2169.2.d.b \(4\) \(17.320\) \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(8\) \(0\) \(q+\beta _{2}q^{2}+q^{4}+(2-\beta _{2})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
2169.2.d.c \(16\) \(17.320\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(2\) \(0\) \(-4\) \(0\) \(q-\beta _{11}q^{2}+(1-\beta _{5}+\beta _{6}-\beta _{8})q^{4}+\cdots\)
2169.2.d.d \(18\) \(17.320\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(0\) \(0\) \(-4\) \(0\) \(q-\beta _{3}q^{2}-\beta _{2}q^{4}+\beta _{13}q^{5}+\beta _{1}q^{7}+\cdots\)
2169.2.d.e \(22\) \(17.320\) None None \(0\) \(0\) \(4\) \(0\)
2169.2.d.f \(36\) \(17.320\) None None \(0\) \(0\) \(0\) \(0\)
2169.4.a.a \(25\) \(127.975\) None None \(7\) \(0\) \(54\) \(-86\) \(-\)
2169.4.a.b \(27\) \(127.975\) None None \(11\) \(0\) \(50\) \(-68\) \(+\)
2169.4.a.c \(29\) \(127.975\) None None \(-9\) \(0\) \(-62\) \(-30\) \(-\)
2169.4.a.d \(31\) \(127.975\) None None \(7\) \(0\) \(58\) \(26\) \(+\)
2169.4.a.e \(33\) \(127.975\) None None \(-9\) \(0\) \(-50\) \(58\) \(-\)
2169.4.a.f \(35\) \(127.975\) None None \(-9\) \(0\) \(-66\) \(110\) \(+\)
2169.4.a.g \(54\) \(127.975\) None None \(0\) \(0\) \(0\) \(-136\) \(-\)
2169.4.a.h \(66\) \(127.975\) None None \(0\) \(0\) \(0\) \(116\) \(+\)
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