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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
155.1.c.a \(1\) \(0.077\) \(\Q\) \(\Q(\sqrt{-31}) \), \(\Q(\sqrt{-155}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q+q^{4}-q^{5}-q^{9}+q^{16}-2q^{19}-q^{20}+\cdots\)
155.1.c.b \(2\) \(0.077\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(1\) \(0\) \(q+(\zeta_{6}+\zeta_{6}^{2})q^{2}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{4}+\cdots\)
155.2.a.a \(1\) \(1.238\) \(\Q\) None None \(-2\) \(-1\) \(1\) \(-2\) \(+\) \(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots\)
155.2.a.b \(1\) \(1.238\) \(\Q\) None None \(-1\) \(2\) \(-1\) \(4\) \(-\) \(q-q^{2}+2q^{3}-q^{4}-q^{5}-2q^{6}+4q^{7}+\cdots\)
155.2.a.c \(1\) \(1.238\) \(\Q\) None None \(0\) \(-1\) \(-1\) \(0\) \(+\) \(q-q^{3}-2q^{4}-q^{5}-2q^{9}-4q^{11}+\cdots\)
155.2.a.d \(4\) \(1.238\) 4.4.20308.1 None None \(-1\) \(-1\) \(-4\) \(0\) \(-\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\cdots\)
155.2.a.e \(4\) \(1.238\) 4.4.8468.1 None None \(1\) \(1\) \(4\) \(2\) \(-\) \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{4}+\cdots\)
155.2.b.a \(4\) \(1.238\) \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{3})q^{2}-\beta _{1}q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
155.2.b.b \(10\) \(1.238\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-1-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)
155.2.e.a \(2\) \(1.238\) \(\Q(\sqrt{-3}) \) None None \(-4\) \(-2\) \(-1\) \(-4\) \(q-2q^{2}+(-2+2\zeta_{6})q^{3}+2q^{4}-\zeta_{6}q^{5}+\cdots\)
155.2.e.b \(2\) \(1.238\) \(\Q(\sqrt{-3}) \) None None \(4\) \(-2\) \(1\) \(2\) \(q+2q^{2}+(-2+2\zeta_{6})q^{3}+2q^{4}+\zeta_{6}q^{5}+\cdots\)
155.2.e.c \(8\) \(1.238\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-2\) \(3\) \(4\) \(-1\) \(q-\beta _{6}q^{2}+(\beta _{1}-\beta _{4}-\beta _{6})q^{3}+(\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots\)
155.2.e.d \(8\) \(1.238\) 8.0.42575625.1 None None \(2\) \(-1\) \(-4\) \(1\) \(q+(1+\beta _{4}+\beta _{7})q^{2}+(-\beta _{1}-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
155.2.f.a \(12\) \(1.238\) 12.0.\(\cdots\).1 \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}+(2\beta _{1}+\beta _{2}-\beta _{3}-\beta _{7})q^{4}+\cdots\)
155.2.f.b \(16\) \(1.238\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-4\) \(0\) \(-4\) \(-12\) \(q+(-\beta _{3}+\beta _{5})q^{2}+\beta _{9}q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
155.2.h.a \(24\) \(1.238\) None None \(-2\) \(-4\) \(24\) \(-3\)
155.2.h.b \(24\) \(1.238\) None None \(2\) \(0\) \(-24\) \(-9\)
155.2.j.a \(28\) \(1.238\) None None \(0\) \(0\) \(0\) \(0\)
155.2.n.a \(56\) \(1.238\) None None \(0\) \(0\) \(-10\) \(0\)
155.2.p.a \(4\) \(1.238\) \(\Q(\zeta_{12})\) None None \(-4\) \(-6\) \(-2\) \(-2\) \(q+(-1-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
155.2.p.b \(4\) \(1.238\) \(\Q(\zeta_{12})\) None None \(-4\) \(-6\) \(4\) \(4\) \(q+(-1-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
155.2.p.c \(48\) \(1.238\) None None \(0\) \(6\) \(-4\) \(-8\)
155.2.q.a \(40\) \(1.238\) None None \(-2\) \(-1\) \(20\) \(4\)
155.2.q.b \(40\) \(1.238\) None None \(2\) \(3\) \(-20\) \(-2\)
155.2.r.a \(112\) \(1.238\) None None \(-6\) \(-10\) \(-16\) \(-18\)
155.2.u.a \(112\) \(1.238\) None None \(0\) \(0\) \(-5\) \(0\)
155.2.x.a \(224\) \(1.238\) None None \(-12\) \(-14\) \(-8\) \(6\)
155.3.c.a \(2\) \(4.223\) \(\Q(\sqrt{31}) \) \(\Q(\sqrt{-155}) \) None \(0\) \(0\) \(-10\) \(0\) \(q+\beta q^{3}+4q^{4}-5q^{5}+22q^{9}+4\beta q^{12}+\cdots\)
155.3.c.b \(2\) \(4.223\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-155}) \) None \(0\) \(0\) \(10\) \(0\) \(q-\beta q^{3}+4q^{4}+5q^{5}-4q^{9}-4\beta q^{12}+\cdots\)
155.3.c.c \(6\) \(4.223\) 6.0.21717639.1 \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{2})q^{2}+(-4+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
155.3.c.d \(20\) \(4.223\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(-8\) \(0\) \(q-\beta _{8}q^{2}+\beta _{4}q^{3}+(-2+\beta _{3})q^{4}+(-2+\cdots)q^{5}+\cdots\)
155.3.d.a \(4\) \(4.223\) 4.0.8000.2 None None \(-4\) \(0\) \(0\) \(-24\) \(q-q^{2}+\beta _{1}q^{3}-3q^{4}-\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots\)
155.3.d.b \(16\) \(4.223\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(4\) \(0\) \(0\) \(4\) \(q-\beta _{9}q^{2}+\beta _{1}q^{3}+(3-\beta _{7})q^{4}+\beta _{2}q^{5}+\cdots\)
155.3.g.a \(60\) \(4.223\) None None \(-4\) \(0\) \(-4\) \(12\)
155.3.i.a \(60\) \(4.223\) None None \(0\) \(0\) \(-4\) \(0\)
155.3.k.a \(44\) \(4.223\) None None \(0\) \(-6\) \(0\) \(22\)
155.3.l.a \(40\) \(4.223\) None None \(0\) \(0\) \(0\) \(5\)
155.3.l.b \(40\) \(4.223\) None None \(0\) \(0\) \(0\) \(15\)
155.3.m.a \(120\) \(4.223\) None None \(0\) \(0\) \(-2\) \(0\)
155.3.o.a \(120\) \(4.223\) None None \(-8\) \(-6\) \(-2\) \(6\)
155.3.s.a \(240\) \(4.223\) None None \(-6\) \(-10\) \(-16\) \(18\)
155.3.t.a \(88\) \(4.223\) None None \(0\) \(3\) \(0\) \(-16\)
155.3.t.b \(88\) \(4.223\) None None \(0\) \(3\) \(0\) \(-6\)
155.3.v.a \(240\) \(4.223\) None None \(0\) \(0\) \(-1\) \(0\)
155.3.w.a \(480\) \(4.223\) None None \(-12\) \(-14\) \(-8\) \(-66\)
155.4.a.a \(1\) \(9.145\) \(\Q\) None None \(1\) \(2\) \(-5\) \(16\) \(-\) \(q+q^{2}+2q^{3}-7q^{4}-5q^{5}+2q^{6}+\cdots\)
155.4.a.b \(4\) \(9.145\) 4.4.382240.1 None None \(2\) \(-4\) \(-20\) \(-24\) \(-\) \(q-\beta _{3}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
155.4.a.c \(6\) \(9.145\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(-3\) \(-12\) \(30\) \(-34\) \(-\) \(q-\beta _{1}q^{2}+(-3+\beta _{1}-\beta _{4})q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)
155.4.a.d \(9\) \(9.145\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(-1\) \(4\) \(-45\) \(20\) \(+\) \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(4+\beta _{1}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
155.4.a.e \(10\) \(9.145\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(9\) \(6\) \(50\) \(50\) \(+\) \(q+(1-\beta _{1})q^{2}+(1+\beta _{3})q^{3}+(5-\beta _{1}+\cdots)q^{4}+\cdots\)
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