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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
456.1.l.a \(1\) \(0.228\) \(\Q\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-114}) \) \(\Q(\sqrt{57}) \) \(-1\) \(1\) \(0\) \(0\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
456.1.l.b \(1\) \(0.228\) \(\Q\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-114}) \) \(\Q(\sqrt{57}) \) \(1\) \(-1\) \(0\) \(0\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
456.1.s.a \(2\) \(0.228\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(-1\) \(-2\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{6}+\cdots\)
456.1.s.b \(2\) \(0.228\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(1\) \(-1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}-q^{8}+\cdots\)
456.1.bt.a \(6\) \(0.228\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{5}q^{2}-\zeta_{18}^{7}q^{3}-\zeta_{18}q^{4}+\zeta_{18}^{3}q^{6}+\cdots\)
456.1.bt.b \(6\) \(0.228\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-2}) \) None \(0\) \(3\) \(0\) \(0\) \(q-\zeta_{18}^{5}q^{2}-\zeta_{18}^{6}q^{3}-\zeta_{18}q^{4}-\zeta_{18}^{2}q^{6}+\cdots\)
456.2.a.a \(1\) \(3.641\) \(\Q\) None None \(0\) \(-1\) \(1\) \(-3\) \(+\) \(q-q^{3}+q^{5}-3q^{7}+q^{9}-5q^{11}-2q^{13}+\cdots\)
456.2.a.b \(1\) \(3.641\) \(\Q\) None None \(0\) \(-1\) \(4\) \(4\) \(-\) \(q-q^{3}+4q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
456.2.a.c \(1\) \(3.641\) \(\Q\) None None \(0\) \(1\) \(-3\) \(-3\) \(+\) \(q+q^{3}-3q^{5}-3q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
456.2.a.d \(1\) \(3.641\) \(\Q\) None None \(0\) \(1\) \(2\) \(0\) \(-\) \(q+q^{3}+2q^{5}+q^{9}+2q^{13}+2q^{15}+\cdots\)
456.2.a.e \(2\) \(3.641\) \(\Q(\sqrt{41}) \) None None \(0\) \(-2\) \(-1\) \(-3\) \(-\) \(q-q^{3}-\beta q^{5}+(-2+\beta )q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
456.2.a.f \(2\) \(3.641\) \(\Q(\sqrt{17}) \) None None \(0\) \(2\) \(1\) \(1\) \(-\) \(q+q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+(4-\beta )q^{11}+\cdots\)
456.2.e.a \(40\) \(3.641\) None None \(0\) \(0\) \(0\) \(0\)
456.2.f.a \(10\) \(3.641\) 10.0.\(\cdots\).1 None None \(0\) \(-1\) \(0\) \(-2\) \(q+\beta _{5}q^{3}+\beta _{6}q^{5}-\beta _{4}q^{7}-\beta _{3}q^{9}+\cdots\)
456.2.f.b \(10\) \(3.641\) 10.0.\(\cdots\).1 None None \(0\) \(1\) \(0\) \(-2\) \(q-\beta _{5}q^{3}+\beta _{6}q^{5}-\beta _{4}q^{7}-\beta _{3}q^{9}+\cdots\)
456.2.g.a \(18\) \(3.641\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(2\) \(0\) \(0\) \(-12\) \(q+\beta _{14}q^{2}-\beta _{3}q^{3}-\beta _{2}q^{4}+\beta _{13}q^{5}+\cdots\)
456.2.g.b \(18\) \(3.641\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(2\) \(0\) \(0\) \(20\) \(q+\beta _{9}q^{2}+\beta _{4}q^{3}+\beta _{2}q^{4}-\beta _{5}q^{5}+\cdots\)
456.2.j.a \(4\) \(3.641\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(1+\beta _{3})q^{4}+\cdots\)
456.2.j.b \(8\) \(3.641\) 8.0.170772624.1 None None \(0\) \(-2\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(-\beta _{1}-\beta _{5}-\beta _{6}-\beta _{7})q^{3}+\cdots\)
456.2.j.c \(12\) \(3.641\) 12.0.\(\cdots\).1 None None \(0\) \(-2\) \(0\) \(0\) \(q-\beta _{1}q^{2}-\beta _{8}q^{3}+(-\beta _{4}+\beta _{5})q^{4}+\cdots\)
456.2.j.d \(24\) \(3.641\) None None \(0\) \(2\) \(0\) \(0\)
456.2.j.e \(24\) \(3.641\) None None \(0\) \(6\) \(0\) \(0\)
456.2.p.a \(12\) \(3.641\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) \(\Q(\sqrt{-38}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+\beta _{8}q^{3}-2q^{4}-\beta _{2}q^{6}+(\beta _{10}+\cdots)q^{7}+\cdots\)
456.2.p.b \(64\) \(3.641\) None None \(0\) \(0\) \(0\) \(-8\)
456.2.q.a \(2\) \(3.641\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-2\) \(-6\) \(q+(-1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{5}-3q^{7}+\cdots\)
456.2.q.b \(2\) \(3.641\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(0\) \(6\) \(q+(-1+\zeta_{6})q^{3}+3q^{7}-\zeta_{6}q^{9}+2q^{11}+\cdots\)
456.2.q.c \(2\) \(3.641\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(2\) \(-10\) \(q+(1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{5}-5q^{7}+\cdots\)
456.2.q.d \(4\) \(3.641\) \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(0\) \(-2\) \(2\) \(8\) \(q+(-1-\beta _{1})q^{3}+(1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
456.2.q.e \(4\) \(3.641\) \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(0\) \(2\) \(-2\) \(0\) \(q+(1+\beta _{1})q^{3}+(-1-\beta _{1}-\beta _{2})q^{5}+\cdots\)
456.2.q.f \(6\) \(3.641\) \(\Q(\zeta_{18})\) None None \(0\) \(3\) \(0\) \(6\) \(q+\zeta_{18}q^{3}+\zeta_{18}^{2}q^{5}+(1+\zeta_{18}^{5})q^{7}+\cdots\)
456.2.u.a \(4\) \(3.641\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots\)
456.2.u.b \(4\) \(3.641\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots\)
456.2.u.c \(8\) \(3.641\) 8.0.4857532416.1 None None \(0\) \(2\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{7})q^{2}-\beta _{3}q^{3}+(-2+2\beta _{6}+\cdots)q^{4}+\cdots\)
456.2.u.d \(136\) \(3.641\) None None \(0\) \(-2\) \(0\) \(0\)
456.2.v.a \(152\) \(3.641\) None None \(0\) \(0\) \(0\) \(-16\)
456.2.y.a \(80\) \(3.641\) None None \(0\) \(0\) \(0\) \(0\)
456.2.be.a \(80\) \(3.641\) None None \(0\) \(0\) \(0\) \(0\)
456.2.bf.a \(4\) \(3.641\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(1\) \(-3\) \(2\) \(q+\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
456.2.bf.b \(4\) \(3.641\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(2\) \(3\) \(2\) \(q+(1-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{1})q^{5}+(1+\cdots)q^{7}+\cdots\)
456.2.bf.c \(16\) \(3.641\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(-1\) \(-3\) \(0\) \(q-\beta _{1}q^{3}-\beta _{14}q^{5}+(\beta _{5}-\beta _{13})q^{7}+\cdots\)
456.2.bf.d \(16\) \(3.641\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(1\) \(3\) \(0\) \(q+\beta _{4}q^{3}+(-\beta _{11}+\beta _{14})q^{5}+(\beta _{5}-\beta _{13}+\cdots)q^{7}+\cdots\)
456.2.bg.a \(12\) \(3.641\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(-3\) \(0\) \(q+(\beta _{2}-\beta _{11})q^{3}-\beta _{1}q^{5}+(-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
456.2.bg.b \(12\) \(3.641\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(3\) \(-6\) \(q-\beta _{4}q^{3}+(1+\beta _{6}+\beta _{9}+\beta _{11})q^{5}+\cdots\)
456.2.bg.c \(18\) \(3.641\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(0\) \(-3\) \(0\) \(q-\beta _{7}q^{3}+(\beta _{2}-\beta _{4})q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
456.2.bg.d \(18\) \(3.641\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(0\) \(0\) \(3\) \(6\) \(q+\beta _{9}q^{3}+(1+\beta _{5}-\beta _{6}+\beta _{12}+\beta _{16}+\cdots)q^{5}+\cdots\)
456.2.bj.a \(456\) \(3.641\) None None \(0\) \(0\) \(0\) \(-12\)
456.2.bk.a \(240\) \(3.641\) None None \(0\) \(0\) \(0\) \(0\)
456.2.bm.a \(60\) \(3.641\) None None \(0\) \(-3\) \(0\) \(0\)
456.2.bm.b \(60\) \(3.641\) None None \(0\) \(0\) \(0\) \(0\)
456.2.bp.a \(240\) \(3.641\) None None \(0\) \(0\) \(0\) \(0\)
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