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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
555.1.b.a \(8\) \(0.277\) \(\Q(\zeta_{16})\) \(\Q(\sqrt{-111}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{16}-\zeta_{16}^{7})q^{2}+\zeta_{16}^{4}q^{3}+(-1+\cdots)q^{4}+\cdots\)
555.2.a.a \(1\) \(4.432\) \(\Q\) None None \(0\) \(1\) \(-1\) \(-2\) \(-\) \(q+q^{3}-2q^{4}-q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots\)
555.2.a.b \(1\) \(4.432\) \(\Q\) None None \(0\) \(1\) \(1\) \(2\) \(-\) \(q+q^{3}-2q^{4}+q^{5}+2q^{7}+q^{9}-2q^{12}+\cdots\)
555.2.a.c \(2\) \(4.432\) \(\Q(\sqrt{5}) \) None None \(-3\) \(2\) \(2\) \(-4\) \(+\) \(q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+q^{5}+\cdots\)
555.2.a.d \(2\) \(4.432\) \(\Q(\sqrt{13}) \) None None \(-1\) \(-2\) \(2\) \(-6\) \(+\) \(q-\beta q^{2}-q^{3}+(1+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
555.2.a.e \(2\) \(4.432\) \(\Q(\sqrt{5}) \) None None \(-1\) \(2\) \(-2\) \(-2\) \(+\) \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
555.2.a.f \(2\) \(4.432\) \(\Q(\sqrt{5}) \) None None \(1\) \(-2\) \(-2\) \(0\) \(+\) \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
555.2.a.g \(2\) \(4.432\) \(\Q(\sqrt{13}) \) None None \(1\) \(2\) \(-2\) \(2\) \(-\) \(q+\beta q^{2}+q^{3}+(1+\beta )q^{4}-q^{5}+\beta q^{6}+\cdots\)
555.2.a.h \(3\) \(4.432\) 3.3.469.1 None None \(1\) \(-3\) \(3\) \(4\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
555.2.a.i \(3\) \(4.432\) 3.3.229.1 None None \(2\) \(3\) \(3\) \(-4\) \(-\) \(q+(1+\beta _{2})q^{2}+q^{3}+(2+\beta _{1})q^{4}+q^{5}+\cdots\)
555.2.a.j \(5\) \(4.432\) 5.5.600268.1 None None \(-3\) \(-5\) \(-5\) \(2\) \(-\) \(q+(-1+\beta _{3})q^{2}-q^{3}+(2-\beta _{3}+\beta _{4})q^{4}+\cdots\)
555.2.c.a \(2\) \(4.432\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) \(q+2iq^{2}+iq^{3}-2q^{4}+(-1+2i)q^{5}+\cdots\)
555.2.c.b \(8\) \(4.432\) 8.0.309760000.3 None None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{4}+\beta _{5})q^{2}-\beta _{5}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
555.2.c.c \(26\) \(4.432\) None None \(0\) \(0\) \(-2\) \(0\)
555.2.e.a \(2\) \(4.432\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(-8\) \(q-q^{3}+2q^{4}+iq^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
555.2.e.b \(10\) \(4.432\) 10.0.\(\cdots\).1 None None \(0\) \(10\) \(0\) \(16\) \(q+\beta _{3}q^{2}+q^{3}+(-1+\beta _{1})q^{4}+\beta _{6}q^{5}+\cdots\)
555.2.e.c \(12\) \(4.432\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(-12\) \(0\) \(8\) \(q-\beta _{8}q^{2}-q^{3}+(-2-\beta _{7})q^{4}+\beta _{2}q^{5}+\cdots\)
555.2.g.a \(40\) \(4.432\) None None \(0\) \(0\) \(0\) \(0\)
555.2.i.a \(2\) \(4.432\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(-1\) \(1\) \(-1\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{3}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
555.2.i.b \(4\) \(4.432\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(-2\) \(-2\) \(2\) \(2\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
555.2.i.c \(4\) \(4.432\) \(\Q(\zeta_{12})\) None None \(0\) \(-2\) \(2\) \(-2\) \(q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{3}+(-1+\cdots)q^{4}+\cdots\)
555.2.i.d \(10\) \(4.432\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(1\) \(-5\) \(-5\) \(-1\) \(q+(-\beta _{1}+\beta _{2})q^{2}-\beta _{6}q^{3}+(\beta _{3}-\beta _{6}+\cdots)q^{4}+\cdots\)
555.2.i.e \(14\) \(4.432\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(-1\) \(7\) \(-7\) \(5\) \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(\beta _{4}+\beta _{5}+\beta _{7})q^{4}+\cdots\)
555.2.i.f \(14\) \(4.432\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(-1\) \(7\) \(7\) \(1\) \(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(\beta _{3}-\beta _{5}+\beta _{10}+\cdots)q^{4}+\cdots\)
555.2.j.a \(76\) \(4.432\) None None \(0\) \(0\) \(4\) \(0\)
555.2.m.a \(16\) \(4.432\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}-\beta _{10})q^{3}-2\beta _{9}q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
555.2.m.b \(128\) \(4.432\) None None \(0\) \(0\) \(0\) \(0\)
555.2.n.a \(32\) \(4.432\) \(\Q(\sqrt{-111}) \) None \(0\) \(0\) \(0\) \(0\)
555.2.n.b \(112\) \(4.432\) None None \(0\) \(-8\) \(0\) \(-8\)
555.2.o.a \(144\) \(4.432\) None None \(0\) \(0\) \(0\) \(-8\)
555.2.s.a \(104\) \(4.432\) None None \(0\) \(0\) \(0\) \(0\)
555.2.t.a \(76\) \(4.432\) None None \(-4\) \(0\) \(-8\) \(0\)
555.2.x.a \(80\) \(4.432\) None None \(0\) \(0\) \(-12\) \(0\)
555.2.z.a \(20\) \(4.432\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(6\) \(-10\) \(0\) \(2\) \(q-\beta _{4}q^{2}+(-1-\beta _{2})q^{3}+(\beta _{1}-\beta _{4}+\cdots)q^{4}+\cdots\)
555.2.z.b \(28\) \(4.432\) None None \(6\) \(14\) \(0\) \(-6\)
555.2.bb.a \(72\) \(4.432\) None None \(0\) \(0\) \(-2\) \(0\)
555.2.bc.a \(6\) \(4.432\) \(\Q(\zeta_{18})\) None None \(0\) \(0\) \(0\) \(3\) \(q-\zeta_{18}^{2}q^{3}+2\zeta_{18}^{5}q^{4}+(-\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
555.2.bc.b \(36\) \(4.432\) None None \(3\) \(0\) \(0\) \(12\)
555.2.bc.c \(36\) \(4.432\) None None \(3\) \(0\) \(0\) \(-6\)
555.2.bc.d \(36\) \(4.432\) None None \(3\) \(0\) \(0\) \(0\)
555.2.bc.e \(42\) \(4.432\) None None \(3\) \(0\) \(0\) \(-3\)
555.2.bd.a \(152\) \(4.432\) None None \(4\) \(0\) \(8\) \(0\)
555.2.bg.a \(208\) \(4.432\) None None \(0\) \(0\) \(0\) \(0\)
555.2.bh.a \(288\) \(4.432\) None None \(0\) \(-4\) \(0\) \(-4\)
555.2.bi.a \(288\) \(4.432\) None None \(0\) \(0\) \(0\) \(-4\)
555.2.bm.a \(288\) \(4.432\) None None \(0\) \(0\) \(0\) \(0\)
555.2.bn.a \(152\) \(4.432\) None None \(0\) \(0\) \(-4\) \(0\)
555.2.bp.a \(240\) \(4.432\) None None \(0\) \(0\) \(12\) \(0\)
555.2.bs.a \(216\) \(4.432\) None None \(0\) \(0\) \(6\) \(0\)
555.2.bt.a \(72\) \(4.432\) None None \(-6\) \(0\) \(0\) \(-12\)
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