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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
171.1.c.a \(1\) \(0.085\) \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{57}) \) \(0\) \(0\) \(0\) \(-2\) \(q+q^{4}-2q^{7}+q^{16}-q^{19}-q^{25}+\cdots\)
171.1.o.a \(4\) \(0.085\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-2\) \(-2\) \(q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{5}+\cdots\)
171.1.p.a \(2\) \(0.085\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q-\zeta_{6}q^{4}+q^{7}+(-1+\zeta_{6}^{2})q^{13}+\zeta_{6}^{2}q^{16}+\cdots\)
171.2.a.a \(1\) \(1.365\) \(\Q\) None None \(-1\) \(0\) \(2\) \(0\) \(-\) \(q-q^{2}-q^{4}+2q^{5}+3q^{8}-2q^{10}+\cdots\)
171.2.a.b \(1\) \(1.365\) \(\Q\) None None \(0\) \(0\) \(-3\) \(-1\) \(+\) \(q-2q^{4}-3q^{5}-q^{7}-3q^{11}-4q^{13}+\cdots\)
171.2.a.c \(1\) \(1.365\) \(\Q\) None None \(2\) \(0\) \(-1\) \(3\) \(-\) \(q+2q^{2}+2q^{4}-q^{5}+3q^{7}-2q^{10}+\cdots\)
171.2.a.d \(1\) \(1.365\) \(\Q\) None None \(2\) \(0\) \(3\) \(-5\) \(-\) \(q+2q^{2}+2q^{4}+3q^{5}-5q^{7}+6q^{10}+\cdots\)
171.2.a.e \(4\) \(1.365\) 4.4.13068.1 None None \(0\) \(0\) \(0\) \(2\) \(-\) \(q-\beta _{1}q^{2}+(2+\beta _{3})q^{4}+(\beta _{1}+\beta _{2})q^{5}+\cdots\)
171.2.d.a \(4\) \(1.365\) \(\Q(\sqrt{-2}, \sqrt{19})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2q^{4}+\beta _{1}q^{5}+\beta _{3}q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
171.2.d.b \(4\) \(1.365\) \(\Q(\sqrt{-2}, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{3}q^{2}+3q^{4}-\beta _{1}q^{5}-2q^{7}-\beta _{3}q^{8}+\cdots\)
171.2.e.a \(18\) \(1.365\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(-3\) \(-1\) \(-9\) \(0\) \(q+(\beta _{1}+\beta _{4})q^{2}+(\beta _{2}+\beta _{10})q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots\)
171.2.e.b \(18\) \(1.365\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(3\) \(-1\) \(7\) \(0\) \(q+(-\beta _{8}+\beta _{11})q^{2}+(-\beta _{3}+\beta _{16})q^{3}+\cdots\)
171.2.f.a \(2\) \(1.365\) \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(0\) \(2\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+q^{7}+3q^{8}+\cdots\)
171.2.f.b \(6\) \(1.365\) 6.0.954288.1 None None \(-1\) \(0\) \(2\) \(-2\) \(q+(\beta _{4}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots\)
171.2.f.c \(8\) \(1.365\) 8.0.764411904.5 None None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{5}q^{2}+(-1-\beta _{3}+\beta _{4}-\beta _{6})q^{4}+\cdots\)
171.2.g.a \(2\) \(1.365\) \(\Q(\sqrt{-3}) \) None None \(1\) \(-3\) \(6\) \(-1\) \(q+\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
171.2.g.b \(2\) \(1.365\) \(\Q(\sqrt{-3}) \) None None \(1\) \(3\) \(-2\) \(-3\) \(q+\zeta_{6}q^{2}+(2-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
171.2.g.c \(32\) \(1.365\) None None \(1\) \(-2\) \(-6\) \(1\)
171.2.h.a \(2\) \(1.365\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(-3\) \(-1\) \(q-q^{2}+(-1+2\zeta_{6})q^{3}-q^{4}-3\zeta_{6}q^{5}+\cdots\)
171.2.h.b \(2\) \(1.365\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(1\) \(-3\) \(q-q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+\zeta_{6}q^{5}+\cdots\)
171.2.h.c \(32\) \(1.365\) None None \(-2\) \(1\) \(3\) \(1\)
171.2.k.a \(36\) \(1.365\) None None \(-3\) \(-6\) \(0\) \(-1\)
171.2.l.a \(36\) \(1.365\) None None \(0\) \(0\) \(-6\) \(-4\)
171.2.m.a \(16\) \(1.365\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(8\) \(q-\beta _{1}q^{2}+(-\beta _{3}+2\beta _{4}+\beta _{10})q^{4}+\cdots\)
171.2.t.a \(36\) \(1.365\) None None \(-6\) \(-3\) \(-3\) \(-1\)
171.2.u.a \(6\) \(1.365\) \(\Q(\zeta_{18})\) None None \(-3\) \(0\) \(6\) \(3\) \(q+(-\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{5})q^{2}+(-1+\cdots)q^{4}+\cdots\)
171.2.u.b \(6\) \(1.365\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2\zeta_{18}^{2}q^{4}+(3\zeta_{18}-\zeta_{18}^{2}-2\zeta_{18}^{4}+\cdots)q^{7}+\cdots\)
171.2.u.c \(6\) \(1.365\) \(\Q(\zeta_{18})\) None None \(6\) \(0\) \(6\) \(0\) \(q+(1-\zeta_{18}+\zeta_{18}^{2})q^{2}+(1-2\zeta_{18}+\cdots)q^{4}+\cdots\)
171.2.u.d \(12\) \(1.365\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(6\) \(q-\beta _{1}q^{2}+(-1+2\beta _{6}-\beta _{7}-\beta _{9})q^{4}+\cdots\)
171.2.u.e \(12\) \(1.365\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(3\) \(0\) \(-6\) \(-9\) \(q+(-1+\beta _{1}+\beta _{2}-\beta _{5}+\beta _{9})q^{2}+(-1+\cdots)q^{4}+\cdots\)
171.2.v.a \(108\) \(1.365\) None None \(-3\) \(-12\) \(-3\) \(3\)
171.2.w.a \(108\) \(1.365\) None None \(-3\) \(-3\) \(-3\) \(-6\)
171.2.x.a \(108\) \(1.365\) None None \(-9\) \(0\) \(-9\) \(3\)
171.2.y.a \(36\) \(1.365\) None None \(0\) \(0\) \(0\) \(0\)
171.2.bd.a \(108\) \(1.365\) None None \(-9\) \(-9\) \(-9\) \(-6\)
171.3.b.a \(12\) \(4.659\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(-16\) \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\)
171.3.c.a \(1\) \(4.659\) \(\Q\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(9\) \(-5\) \(q+4q^{4}+9q^{5}-5q^{7}-3q^{11}+2^{4}q^{16}+\cdots\)
171.3.c.b \(2\) \(4.659\) \(\Q(\sqrt{-13}) \) None None \(0\) \(0\) \(-8\) \(-10\) \(q+\beta q^{2}-9q^{4}-4q^{5}-5q^{7}-5\beta q^{8}+\cdots\)
171.3.c.c \(2\) \(4.659\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-8\) \(-20\) \(q-\zeta_{6}q^{2}+q^{4}-4q^{5}-10q^{7}-5\zeta_{6}q^{8}+\cdots\)
171.3.c.d \(2\) \(4.659\) \(\Q(\sqrt{19}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(10\) \(q+4q^{4}+\beta q^{5}+5q^{7}-5\beta q^{11}+2^{4}q^{16}+\cdots\)
171.3.c.e \(4\) \(4.659\) \(\Q(\sqrt{-7}, \sqrt{10})\) None None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{1}q^{2}-3q^{4}+\beta _{2}q^{5}-2q^{7}-\beta _{1}q^{8}+\cdots\)
171.3.c.f \(4\) \(4.659\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None None \(0\) \(0\) \(10\) \(34\) \(q-\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(3-\beta _{2})q^{5}+\cdots\)
171.3.i.a \(76\) \(4.659\) None None \(0\) \(-3\) \(1\) \(-3\)
171.3.j.a \(76\) \(4.659\) None None \(0\) \(-5\) \(-3\) \(-1\)
171.3.n.a \(76\) \(4.659\) None None \(-3\) \(1\) \(0\) \(-1\)
171.3.o.a \(76\) \(4.659\) None None \(0\) \(0\) \(-2\) \(0\)
171.3.p.a \(2\) \(4.659\) \(\Q(\sqrt{-3}) \) None None \(-3\) \(0\) \(-4\) \(10\) \(q+(-1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-4+4\zeta_{6})q^{5}+\cdots\)
171.3.p.b \(2\) \(4.659\) \(\Q(\sqrt{-3}) \) None None \(3\) \(0\) \(4\) \(10\) \(q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(4-4\zeta_{6})q^{5}+\cdots\)
171.3.p.c \(6\) \(4.659\) 6.0.92607408.1 None None \(-3\) \(0\) \(-4\) \(-22\) \(q+\beta _{4}q^{2}+(1+\beta _{1}+2\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots\)
171.3.p.d \(6\) \(4.659\) 6.0.6967728.1 None None \(3\) \(0\) \(2\) \(0\) \(q+(1+\beta _{5})q^{2}+(-2\beta _{1}-2\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
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