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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
552.1.h.a \(1\) \(0.275\) \(\Q\) \(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-138}) \) \(\Q(\sqrt{6}) \) \(-1\) \(-1\) \(0\) \(0\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
552.1.h.b \(1\) \(0.275\) \(\Q\) \(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-138}) \) \(\Q(\sqrt{6}) \) \(1\) \(-1\) \(0\) \(0\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
552.1.h.c \(2\) \(0.275\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-23}) \) None \(-1\) \(1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}+q^{8}+\cdots\)
552.1.h.d \(2\) \(0.275\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-23}) \) None \(1\) \(1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots\)
552.2.a.a \(1\) \(4.408\) \(\Q\) None None \(0\) \(-1\) \(-2\) \(2\) \(+\) \(q-q^{3}-2q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots\)
552.2.a.b \(1\) \(4.408\) \(\Q\) None None \(0\) \(-1\) \(0\) \(-2\) \(-\) \(q-q^{3}-2q^{7}+q^{9}+2q^{13}+8q^{17}+\cdots\)
552.2.a.c \(1\) \(4.408\) \(\Q\) None None \(0\) \(-1\) \(2\) \(-4\) \(+\) \(q-q^{3}+2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
552.2.a.d \(1\) \(4.408\) \(\Q\) None None \(0\) \(-1\) \(4\) \(2\) \(-\) \(q-q^{3}+4q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots\)
552.2.a.e \(1\) \(4.408\) \(\Q\) None None \(0\) \(1\) \(-2\) \(-4\) \(+\) \(q+q^{3}-2q^{5}-4q^{7}+q^{9}-2q^{13}+\cdots\)
552.2.a.f \(2\) \(4.408\) \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(2\) \(4\) \(-\) \(q+q^{3}+(1+\beta )q^{5}+2q^{7}+q^{9}+(1+\beta )q^{11}+\cdots\)
552.2.a.g \(3\) \(4.408\) 3.3.148.1 None None \(0\) \(3\) \(0\) \(2\) \(-\) \(q+q^{3}+\beta _{2}q^{5}+(1+\beta _{1})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
552.2.b.a \(6\) \(4.408\) 6.0.8869743.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(\beta _{2}+\beta _{5})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
552.2.b.b \(6\) \(4.408\) 6.0.8869743.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(\beta _{2}+\beta _{5})q^{4}+(1+\cdots)q^{6}+\cdots\)
552.2.b.c \(80\) \(4.408\) None None \(0\) \(0\) \(0\) \(0\)
552.2.f.a \(2\) \(4.408\) \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(0\) \(8\) \(q+(1+i)q^{2}+iq^{3}+2iq^{4}+2iq^{5}+\cdots\)
552.2.f.b \(4\) \(4.408\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(-8\) \(q+\zeta_{8}^{3}q^{2}+\zeta_{8}q^{3}+2q^{4}+(2\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
552.2.f.c \(18\) \(4.408\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(0\) \(0\) \(8\) \(q-\beta _{3}q^{2}-\beta _{4}q^{3}-\beta _{2}q^{4}+\beta _{9}q^{5}+\cdots\)
552.2.f.d \(20\) \(4.408\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(-2\) \(0\) \(0\) \(-8\) \(q-\beta _{1}q^{2}+\beta _{5}q^{3}+\beta _{2}q^{4}+\beta _{11}q^{5}+\cdots\)
552.2.j.a \(2\) \(4.408\) \(\Q(\sqrt{-2}) \) None None \(0\) \(-2\) \(-8\) \(0\) \(q+\beta q^{2}+(-1+\beta )q^{3}-2q^{4}-4q^{5}+\cdots\)
552.2.j.b \(2\) \(4.408\) \(\Q(\sqrt{-2}) \) None None \(0\) \(-2\) \(8\) \(0\) \(q+\beta q^{2}+(-1+\beta )q^{3}-2q^{4}+4q^{5}+\cdots\)
552.2.j.c \(42\) \(4.408\) None None \(0\) \(2\) \(-8\) \(0\)
552.2.j.d \(42\) \(4.408\) None None \(0\) \(2\) \(8\) \(0\)
552.2.m.a \(8\) \(4.408\) 8.0.40960000.1 None None \(0\) \(-4\) \(0\) \(0\) \(q+(-1-\beta _{2})q^{3}+\beta _{3}q^{5}+\beta _{5}q^{7}+(1+\cdots)q^{9}+\cdots\)
552.2.m.b \(16\) \(4.408\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(4\) \(0\) \(0\) \(q-\beta _{7}q^{3}-\beta _{5}q^{5}-\beta _{1}q^{7}+(\beta _{2}+\beta _{4}+\cdots)q^{9}+\cdots\)
552.2.n.a \(24\) \(4.408\) None None \(-4\) \(24\) \(0\) \(0\)
552.2.n.b \(24\) \(4.408\) None None \(0\) \(-24\) \(0\) \(0\)
552.2.q.a \(30\) \(4.408\) None None \(0\) \(-3\) \(0\) \(-2\)
552.2.q.b \(30\) \(4.408\) None None \(0\) \(-3\) \(0\) \(0\)
552.2.q.c \(30\) \(4.408\) None None \(0\) \(3\) \(-2\) \(-2\)
552.2.q.d \(30\) \(4.408\) None None \(0\) \(3\) \(2\) \(4\)
552.2.t.a \(240\) \(4.408\) None None \(0\) \(24\) \(0\) \(0\)
552.2.t.b \(240\) \(4.408\) None None \(4\) \(-24\) \(0\) \(0\)
552.2.u.a \(240\) \(4.408\) None None \(0\) \(0\) \(0\) \(0\)
552.2.x.a \(920\) \(4.408\) None None \(0\) \(-18\) \(0\) \(0\)
552.2.bb.a \(480\) \(4.408\) None None \(4\) \(0\) \(0\) \(8\)
552.2.bf.a \(920\) \(4.408\) None None \(0\) \(0\) \(0\) \(-44\)
552.3.c.a \(24\) \(15.041\) None None \(0\) \(0\) \(0\) \(0\)
552.3.d.a \(88\) \(15.041\) None None \(0\) \(0\) \(0\) \(0\)
552.3.g.a \(44\) \(15.041\) None None \(0\) \(-4\) \(0\) \(24\)
552.3.l.a \(96\) \(15.041\) None None \(4\) \(0\) \(0\) \(0\)
552.4.a.a \(1\) \(32.569\) \(\Q\) None None \(0\) \(3\) \(-14\) \(2\) \(-\) \(q+3q^{3}-14q^{5}+2q^{7}+9q^{9}+58q^{11}+\cdots\)
552.4.a.b \(1\) \(32.569\) \(\Q\) None None \(0\) \(3\) \(8\) \(-22\) \(-\) \(q+3q^{3}+8q^{5}-22q^{7}+9q^{9}-4q^{11}+\cdots\)
552.4.a.c \(2\) \(32.569\) \(\Q(\sqrt{2}) \) None None \(0\) \(-6\) \(-8\) \(4\) \(+\) \(q-3q^{3}+(-4+4\beta )q^{5}+(2+9\beta )q^{7}+\cdots\)
552.4.a.d \(2\) \(32.569\) \(\Q(\sqrt{93}) \) None None \(0\) \(-6\) \(2\) \(10\) \(+\) \(q-3q^{3}+(1+\beta )q^{5}+(5-\beta )q^{7}+9q^{9}+\cdots\)
552.4.a.e \(2\) \(32.569\) \(\Q(\sqrt{5}) \) None None \(0\) \(6\) \(-14\) \(10\) \(-\) \(q+3q^{3}+(-7-\beta )q^{5}+(5+\beta )q^{7}+9q^{9}+\cdots\)
552.4.a.f \(2\) \(32.569\) \(\Q(\sqrt{2}) \) None None \(0\) \(6\) \(-4\) \(-8\) \(-\) \(q+3q^{3}+(-2+\beta )q^{5}+(-4+3\beta )q^{7}+\cdots\)
552.4.a.g \(4\) \(32.569\) 4.4.1623576.1 None None \(0\) \(-12\) \(-14\) \(14\) \(-\) \(q-3q^{3}+(-3+\beta _{3})q^{5}+(4-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
552.4.a.h \(4\) \(32.569\) 4.4.2239521.1 None None \(0\) \(12\) \(2\) \(50\) \(+\) \(q+3q^{3}+(1+\beta _{3})q^{5}+(12-\beta _{2})q^{7}+\cdots\)
552.4.a.i \(5\) \(32.569\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(0\) \(-15\) \(4\) \(-14\) \(-\) \(q-3q^{3}+(1-\beta _{1})q^{5}+(-3-\beta _{2})q^{7}+\cdots\)
552.4.a.j \(5\) \(32.569\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(0\) \(-15\) \(16\) \(0\) \(+\) \(q-3q^{3}+(3-\beta _{2})q^{5}-\beta _{3}q^{7}+9q^{9}+\cdots\)
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