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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
273.1.o.a \(2\) \(0.136\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+iq^{4}-iq^{7}-q^{9}-q^{12}+\cdots\)
273.1.o.b \(2\) \(0.136\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q-iq^{3}+iq^{4}+q^{7}-q^{9}+q^{12}-iq^{13}+\cdots\)
273.1.s.a \(2\) \(0.136\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{3}+q^{4}+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots\)
273.1.s.b \(4\) \(0.136\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(-2\) \(q-\zeta_{12}^{3}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{5}q^{5}+\cdots\)
273.1.x.a \(2\) \(0.136\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(-1\) \(q-q^{3}-\zeta_{6}^{2}q^{4}-\zeta_{6}q^{7}+q^{9}+\zeta_{6}^{2}q^{12}+\cdots\)
273.1.bm.a \(2\) \(0.136\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(-1\) \(q+q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{7}+q^{9}+\zeta_{6}^{2}q^{12}+\cdots\)
273.1.bm.b \(4\) \(0.136\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{4}q^{6}+\cdots\)
273.1.bp.a \(2\) \(0.136\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(1\) \(q-\zeta_{6}^{2}q^{3}-q^{4}-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots\)
273.1.bs.a \(4\) \(0.136\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}-\zeta_{12}^{3}q^{4}-\zeta_{12}q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
273.1.ch.a \(4\) \(0.136\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{4}+\zeta_{12}^{4}q^{7}+\cdots\)
273.2.a.a \(1\) \(2.180\) \(\Q\) None None \(-2\) \(-1\) \(-1\) \(1\) \(+\) \(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}+q^{7}+\cdots\)
273.2.a.b \(1\) \(2.180\) \(\Q\) None None \(2\) \(1\) \(1\) \(-1\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-q^{7}+\cdots\)
273.2.a.c \(2\) \(2.180\) \(\Q(\sqrt{2}) \) None None \(2\) \(-2\) \(0\) \(2\) \(-\) \(q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
273.2.a.d \(3\) \(2.180\) 3.3.316.1 None None \(-2\) \(-3\) \(-3\) \(-3\) \(+\) \(q+(-1+\beta _{1})q^{2}-q^{3}+(2-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
273.2.a.e \(4\) \(2.180\) 4.4.17428.1 None None \(1\) \(4\) \(-3\) \(4\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
273.2.c.a \(2\) \(2.180\) \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(0\) \(0\) \(q+2iq^{2}+q^{3}-2q^{4}+3iq^{5}+2iq^{6}+\cdots\)
273.2.c.b \(6\) \(2.180\) 6.0.350464.1 None None \(0\) \(6\) \(0\) \(0\) \(q-\beta _{4}q^{2}+q^{3}+(-\beta _{1}+\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
273.2.c.c \(8\) \(2.180\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(-8\) \(0\) \(0\) \(q+\beta _{1}q^{2}-q^{3}+(-2+\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
273.2.e.a \(32\) \(2.180\) None None \(0\) \(0\) \(0\) \(4\)
273.2.g.a \(32\) \(2.180\) None None \(0\) \(0\) \(0\) \(0\)
273.2.i.a \(2\) \(2.180\) \(\Q(\sqrt{-3}) \) None None \(1\) \(-1\) \(-4\) \(-5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
273.2.i.b \(6\) \(2.180\) \(\Q(\zeta_{18})\) None None \(0\) \(3\) \(-3\) \(0\) \(q+(-\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+\cdots\)
273.2.i.c \(6\) \(2.180\) 6.0.64827.1 None None \(2\) \(-3\) \(3\) \(0\) \(q+(\beta _{1}+\beta _{4})q^{2}-\beta _{5}q^{3}+(2\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots\)
273.2.i.d \(8\) \(2.180\) 8.0.4868829729.1 None None \(1\) \(-4\) \(-3\) \(9\) \(q+(-\beta _{1}+\beta _{3}+\beta _{6})q^{2}+\beta _{4}q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots\)
273.2.i.e \(10\) \(2.180\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(5\) \(3\) \(4\) \(q+(\beta _{4}-\beta _{8})q^{2}+(1-\beta _{2})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
273.2.j.a \(2\) \(2.180\) \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(0\) \(5\) \(q+q^{3}+(2-2\zeta_{6})q^{4}+(3-\zeta_{6})q^{7}+q^{9}+\cdots\)
273.2.j.b \(16\) \(2.180\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(-16\) \(0\) \(1\) \(q+\beta _{1}q^{2}-q^{3}+(-\beta _{3}+\beta _{5}-\beta _{9}+\beta _{14}+\cdots)q^{4}+\cdots\)
273.2.j.c \(20\) \(2.180\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(20\) \(0\) \(-9\) \(q+(\beta _{1}+\beta _{4})q^{2}+q^{3}+(-\beta _{2}-2\beta _{7}+\cdots)q^{4}+\cdots\)
273.2.k.a \(6\) \(2.180\) \(\Q(\zeta_{18})\) None None \(0\) \(-3\) \(12\) \(3\) \(q+(\zeta_{18}-\zeta_{18}^{2}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)
273.2.k.b \(6\) \(2.180\) 6.0.6040683.1 None None \(0\) \(3\) \(4\) \(-3\) \(q+(\beta _{1}+\beta _{2})q^{2}+(1-\beta _{4})q^{3}+(\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
273.2.k.c \(6\) \(2.180\) 6.0.64827.1 None None \(2\) \(-3\) \(0\) \(-3\) \(q+(\beta _{1}+\beta _{4})q^{2}+(-1+\beta _{5})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots\)
273.2.k.d \(6\) \(2.180\) 6.0.771147.1 None None \(2\) \(3\) \(0\) \(3\) \(q+(1+\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}-\beta _{4}q^{3}+\cdots\)
273.2.l.a \(2\) \(2.180\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(0\) \(-4\) \(q-\zeta_{6}q^{3}-2q^{4}+(-3+2\zeta_{6})q^{7}+(-1+\cdots)q^{9}+\cdots\)
273.2.l.b \(16\) \(2.180\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(8\) \(0\) \(1\) \(q+(-\beta _{1}-\beta _{2})q^{2}+\beta _{9}q^{3}+(1+\beta _{3}+\cdots)q^{4}+\cdots\)
273.2.l.c \(20\) \(2.180\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(-10\) \(0\) \(3\) \(q-\beta _{4}q^{2}+(-1+\beta _{7})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
273.2.n.a \(4\) \(2.180\) \(\Q(\zeta_{8})\) None None \(-4\) \(-4\) \(-8\) \(0\) \(q+(-1-\zeta_{8}^{2})q^{2}+(-1+\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
273.2.n.b \(4\) \(2.180\) \(\Q(\zeta_{8})\) None None \(4\) \(-4\) \(8\) \(0\) \(q+(1-\zeta_{8}^{2})q^{2}+(-1+\zeta_{8}+\zeta_{8}^{2})q^{3}+\cdots\)
273.2.n.c \(48\) \(2.180\) None None \(0\) \(8\) \(0\) \(0\)
273.2.p.a \(4\) \(2.180\) \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(-8\) \(4\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(-2+2\beta _{2}+\cdots)q^{5}+\cdots\)
273.2.p.b \(4\) \(2.180\) \(\Q(i, \sqrt{10})\) None None \(0\) \(0\) \(-4\) \(-4\) \(q-\beta _{2}q^{3}+2\beta _{2}q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
273.2.p.c \(4\) \(2.180\) \(\Q(i, \sqrt{10})\) None None \(0\) \(0\) \(4\) \(-4\) \(q-\beta _{2}q^{3}-2\beta _{2}q^{4}+(1-\beta _{2}+\beta _{3})q^{5}+\cdots\)
273.2.p.d \(4\) \(2.180\) \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(8\) \(0\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(2-2\beta _{2}+\cdots)q^{5}+\cdots\)
273.2.p.e \(12\) \(2.180\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(-12\) \(12\) \(q+\beta _{8}q^{2}-\beta _{4}q^{3}+(3\beta _{4}-\beta _{6}-\beta _{11})q^{4}+\cdots\)
273.2.p.f \(12\) \(2.180\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(12\) \(-4\) \(q+\beta _{8}q^{2}+\beta _{4}q^{3}+(3\beta _{4}-\beta _{6}-\beta _{11})q^{4}+\cdots\)
273.2.r.a \(2\) \(2.180\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(4\) \(q+(-1-\zeta_{6})q^{3}+2q^{4}+(1+2\zeta_{6})q^{7}+\cdots\)
273.2.r.b \(64\) \(2.180\) None None \(0\) \(0\) \(0\) \(-10\)
273.2.t.a \(2\) \(2.180\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-6\) \(5\) \(q+(-1+2\zeta_{6})q^{2}+\zeta_{6}q^{3}-q^{4}+(-4+\cdots)q^{5}+\cdots\)
273.2.t.b \(4\) \(2.180\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None None \(0\) \(-2\) \(6\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
273.2.t.c \(12\) \(2.180\) 12.0.\(\cdots\).1 None None \(0\) \(-6\) \(-6\) \(-3\) \(q+(\beta _{1}+\beta _{3}+\beta _{6})q^{2}+(-1-\beta _{4})q^{3}+\cdots\)
273.2.t.d \(20\) \(2.180\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(10\) \(6\) \(2\) \(q+(\beta _{2}+\beta _{3})q^{2}+\beta _{11}q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
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