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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
670.2.a.a \(1\) \(5.350\) \(\Q\) None \(-1\) \(-2\) \(1\) \(-1\) \(+\) \(q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-q^{7}+\cdots\)
670.2.a.b \(1\) \(5.350\) \(\Q\) None \(-1\) \(0\) \(1\) \(1\) \(+\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-3q^{9}+\cdots\)
670.2.a.c \(1\) \(5.350\) \(\Q\) None \(1\) \(-2\) \(-1\) \(1\) \(+\) \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+q^{7}+\cdots\)
670.2.a.d \(1\) \(5.350\) \(\Q\) None \(1\) \(0\) \(-1\) \(-5\) \(+\) \(q+q^{2}+q^{4}-q^{5}-5q^{7}+q^{8}-3q^{9}+\cdots\)
670.2.a.e \(2\) \(5.350\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(2\) \(+\) \(q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}+(1+\cdots)q^{7}+\cdots\)
670.2.a.f \(2\) \(5.350\) \(\Q(\sqrt{2}) \) None \(2\) \(-4\) \(2\) \(-6\) \(+\) \(q+q^{2}+(-2+\beta )q^{3}+q^{4}+q^{5}+(-2+\cdots)q^{6}+\cdots\)
670.2.a.g \(3\) \(5.350\) 3.3.148.1 None \(-3\) \(4\) \(3\) \(1\) \(-\) \(q-q^{2}+(1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
670.2.a.h \(3\) \(5.350\) 3.3.756.1 None \(3\) \(0\) \(-3\) \(3\) \(-\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
670.2.a.i \(3\) \(5.350\) 3.3.404.1 None \(3\) \(2\) \(3\) \(1\) \(-\) \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+q^{5}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
670.2.a.j \(4\) \(5.350\) 4.4.15188.1 None \(-4\) \(-2\) \(-4\) \(-5\) \(-\) \(q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\)
670.2.c.a \(10\) \(5.350\) 10.0.\(\cdots\).1 None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{3}q^{2}-\beta _{8}q^{3}-q^{4}+(\beta _{1}-\beta _{7})q^{5}+\cdots\)
670.2.c.b \(24\) \(5.350\) None \(0\) \(0\) \(-2\) \(0\)
670.2.e.a \(2\) \(5.350\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-6\) \(-2\) \(2\) \(q+(-1+\zeta_{6})q^{2}-3q^{3}-\zeta_{6}q^{4}-q^{5}+\cdots\)
670.2.e.b \(2\) \(5.350\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-6\) \(2\) \(-4\) \(q+(-1+\zeta_{6})q^{2}-3q^{3}-\zeta_{6}q^{4}+q^{5}+\cdots\)
670.2.e.c \(2\) \(5.350\) \(\Q(\sqrt{-3}) \) None \(-1\) \(2\) \(-2\) \(5\) \(q+(-1+\zeta_{6})q^{2}+q^{3}-\zeta_{6}q^{4}-q^{5}+\cdots\)
670.2.e.d \(2\) \(5.350\) \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(-2\) \(-2\) \(q+(1-\zeta_{6})q^{2}+q^{3}-\zeta_{6}q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\)
670.2.e.e \(4\) \(5.350\) \(\Q(\sqrt{-3}, \sqrt{193})\) None \(-2\) \(4\) \(-4\) \(-4\) \(q-\beta _{2}q^{2}+q^{3}+(-1+\beta _{2})q^{4}-q^{5}+\cdots\)
670.2.e.f \(4\) \(5.350\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(4\) \(-4\) \(-4\) \(q-\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(-1+\beta _{1})q^{4}+\cdots\)
670.2.e.g \(6\) \(5.350\) 6.0.954288.1 None \(3\) \(-2\) \(6\) \(-2\) \(q+(1-\beta _{3})q^{2}+\beta _{4}q^{3}-\beta _{3}q^{4}+q^{5}+\cdots\)
670.2.e.h \(6\) \(5.350\) 6.0.2696112.1 None \(3\) \(2\) \(6\) \(2\) \(q+\beta _{3}q^{2}-\beta _{2}q^{3}+(-1+\beta _{3})q^{4}+q^{5}+\cdots\)
670.2.e.i \(8\) \(5.350\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-4\) \(8\) \(8\) \(0\) \(q+(-1+\beta _{2})q^{2}+(1+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
670.2.e.j \(12\) \(5.350\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(-4\) \(-12\) \(3\) \(q-\beta _{5}q^{2}-\beta _{2}q^{3}+(-1-\beta _{5})q^{4}-q^{5}+\cdots\)
670.2.f.a \(68\) \(5.350\) None \(0\) \(0\) \(0\) \(0\)
670.2.h.a \(4\) \(5.350\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
670.2.h.b \(12\) \(5.350\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(24\) \(0\) \(q+(\beta _{3}+\beta _{4})q^{2}+(-\beta _{4}-\beta _{9})q^{3}+(1+\cdots)q^{4}+\cdots\)
670.2.h.c \(52\) \(5.350\) None \(0\) \(0\) \(-16\) \(0\)
670.2.k.a \(40\) \(5.350\) None \(-4\) \(6\) \(-4\) \(13\)
670.2.k.b \(50\) \(5.350\) None \(-5\) \(2\) \(5\) \(1\)
670.2.k.c \(50\) \(5.350\) None \(5\) \(-2\) \(-5\) \(-1\)
670.2.k.d \(60\) \(5.350\) None \(6\) \(2\) \(6\) \(3\)
670.2.m.a \(136\) \(5.350\) None \(0\) \(0\) \(0\) \(0\)
670.2.o.a \(340\) \(5.350\) None \(0\) \(0\) \(4\) \(0\)
670.2.q.a \(100\) \(5.350\) None \(5\) \(-2\) \(-10\) \(4\)
670.2.q.b \(120\) \(5.350\) None \(-6\) \(0\) \(-12\) \(0\)
670.2.q.c \(120\) \(5.350\) None \(6\) \(-4\) \(12\) \(1\)
670.2.q.d \(140\) \(5.350\) None \(-7\) \(2\) \(14\) \(-1\)
670.2.s.a \(680\) \(5.350\) None \(0\) \(0\) \(0\) \(0\)
670.2.v.a \(680\) \(5.350\) None \(0\) \(0\) \(-4\) \(0\)
670.2.w.a \(1360\) \(5.350\) None \(0\) \(0\) \(0\) \(0\)
670.3.b.a \(48\) \(18.256\) None \(0\) \(0\) \(0\) \(0\)
670.3.d.a \(68\) \(18.256\) None \(0\) \(0\) \(0\) \(0\)
670.3.i.a \(88\) \(18.256\) None \(0\) \(0\) \(0\) \(-36\)
670.4.a.a \(1\) \(39.531\) \(\Q\) None \(-2\) \(-6\) \(-5\) \(31\) \(-\) \(q-2q^{2}-6q^{3}+4q^{4}-5q^{5}+12q^{6}+\cdots\)
670.4.a.b \(1\) \(39.531\) \(\Q\) None \(-2\) \(7\) \(-5\) \(31\) \(+\) \(q-2q^{2}+7q^{3}+4q^{4}-5q^{5}-14q^{6}+\cdots\)
670.4.a.c \(6\) \(39.531\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-12\) \(7\) \(-30\) \(-10\) \(-\) \(q-2q^{2}+(1+\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots\)
670.4.a.d \(7\) \(39.531\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(14\) \(-13\) \(35\) \(-49\) \(-\) \(q+2q^{2}+(-2+\beta _{5})q^{3}+4q^{4}+5q^{5}+\cdots\)
670.4.a.e \(8\) \(39.531\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-16\) \(-12\) \(-40\) \(-59\) \(+\) \(q-2q^{2}+(-2+\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots\)
670.4.a.f \(8\) \(39.531\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-16\) \(-7\) \(40\) \(-1\) \(-\) \(q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+5q^{5}+\cdots\)
670.4.a.g \(8\) \(39.531\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(16\) \(-5\) \(-40\) \(-27\) \(-\) \(q+2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots\)
670.4.a.h \(9\) \(39.531\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-18\) \(11\) \(45\) \(6\) \(+\) \(q-2q^{2}+(1+\beta _{1})q^{3}+4q^{4}+5q^{5}+\cdots\)
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