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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
819.1.d.a \(1\) \(0.409\) \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-91}) \) \(\Q(\sqrt{273}) \) \(0\) \(0\) \(0\) \(-1\) \(q+q^{4}-q^{7}+q^{13}+q^{16}+2q^{19}+\cdots\)
819.1.d.b \(1\) \(0.409\) \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-91}) \) \(\Q(\sqrt{273}) \) \(0\) \(0\) \(0\) \(1\) \(q+q^{4}+q^{7}-q^{13}+q^{16}-2q^{19}+\cdots\)
819.1.bd.a \(2\) \(0.409\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+q^{4}-\zeta_{6}q^{7}-\zeta_{6}^{2}q^{13}+q^{16}+\zeta_{6}^{2}q^{19}+\cdots\)
819.1.bj.a \(4\) \(0.409\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(2\) \(q-\beta _{3}q^{2}-q^{4}+\beta _{2}q^{7}+(1-\beta _{2})q^{13}+\cdots\)
819.1.cg.a \(2\) \(0.409\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q-\zeta_{6}^{2}q^{4}+\zeta_{6}q^{7}-\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}+\cdots\)
819.1.cj.a \(4\) \(0.409\) \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(0\) \(4\) \(q+\zeta_{12}^{4}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}q^{5}+\zeta_{12}q^{6}+\cdots\)
819.1.cx.a \(2\) \(0.409\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}+\cdots\)
819.1.dp.a \(4\) \(0.409\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(2\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{2})q^{7}+\beta _{2}q^{13}+\cdots\)
819.1.ef.a \(2\) \(0.409\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q-q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{13}+q^{16}+(1+\cdots)q^{19}+\cdots\)
819.1.ek.a \(4\) \(0.409\) \(\Q(\zeta_{12})\) None None \(4\) \(0\) \(0\) \(-2\) \(q+q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{5}q^{5}-\zeta_{12}q^{6}+\cdots\)
819.1.eu.a \(4\) \(0.409\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{4}-\zeta_{12}q^{7}-\zeta_{12}^{5}q^{13}+\cdots\)
819.1.ff.a \(4\) \(0.409\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q-\zeta_{12}q^{4}+\zeta_{12}^{2}q^{7}+\zeta_{12}q^{13}+\zeta_{12}^{2}q^{16}+\cdots\)
819.2.a.a \(1\) \(6.540\) \(\Q\) None None \(-2\) \(0\) \(-1\) \(-1\) \(-\) \(q-2q^{2}+2q^{4}-q^{5}-q^{7}+2q^{10}+\cdots\)
819.2.a.b \(1\) \(6.540\) \(\Q\) None None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(q-q^{2}-q^{4}-q^{7}+3q^{8}-q^{13}+q^{14}+\cdots\)
819.2.a.c \(1\) \(6.540\) \(\Q\) None None \(0\) \(0\) \(3\) \(1\) \(-\) \(q-2q^{4}+3q^{5}+q^{7}+q^{13}+4q^{16}+\cdots\)
819.2.a.d \(1\) \(6.540\) \(\Q\) None None \(1\) \(0\) \(0\) \(-1\) \(+\) \(q+q^{2}-q^{4}-q^{7}-3q^{8}-q^{13}-q^{14}+\cdots\)
819.2.a.e \(1\) \(6.540\) \(\Q\) None None \(2\) \(0\) \(1\) \(1\) \(-\) \(q+2q^{2}+2q^{4}+q^{5}+q^{7}+2q^{10}+\cdots\)
819.2.a.f \(1\) \(6.540\) \(\Q\) None None \(2\) \(0\) \(3\) \(-1\) \(-\) \(q+2q^{2}+2q^{4}+3q^{5}-q^{7}+6q^{10}+\cdots\)
819.2.a.g \(2\) \(6.540\) \(\Q(\sqrt{2}) \) None None \(-2\) \(0\) \(0\) \(2\) \(+\) \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{7}+(-3+\cdots)q^{8}+\cdots\)
819.2.a.h \(2\) \(6.540\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(-6\) \(2\) \(+\) \(q+\beta q^{2}+(-3+\beta )q^{5}+q^{7}-2\beta q^{8}+\cdots\)
819.2.a.i \(3\) \(6.540\) 3.3.316.1 None None \(-1\) \(0\) \(-2\) \(-3\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1})q^{5}+\cdots\)
819.2.a.j \(3\) \(6.540\) 3.3.316.1 None None \(2\) \(0\) \(3\) \(-3\) \(-\) \(q+(1-\beta _{1})q^{2}+(2-2\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
819.2.a.k \(4\) \(6.540\) 4.4.17428.1 None None \(-1\) \(0\) \(3\) \(4\) \(-\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
819.2.a.l \(4\) \(6.540\) \(\Q(\sqrt{3}, \sqrt{11})\) None None \(0\) \(0\) \(0\) \(4\) \(-\) \(q+\beta _{1}q^{2}+(2+\beta _{3})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
819.2.a.m \(6\) \(6.540\) 6.6.199374400.1 None None \(0\) \(0\) \(0\) \(-6\) \(-\) \(q+\beta _{4}q^{2}+(2+\beta _{2})q^{4}-\beta _{3}q^{5}-q^{7}+\cdots\)
819.2.c.a \(2\) \(6.540\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-2q^{4}+3iq^{5}+iq^{7}-6q^{10}+\cdots\)
819.2.c.b \(6\) \(6.540\) 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{3}+\beta _{4})q^{2}+(-1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
819.2.c.c \(6\) \(6.540\) 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+(-\beta _{1}+\beta _{2})q^{4}+(-\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots\)
819.2.c.d \(8\) \(6.540\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(-\beta _{3}+\beta _{7})q^{5}+\cdots\)
819.2.c.e \(12\) \(6.540\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+(-1+\beta _{10})q^{4}-\beta _{1}q^{5}+\cdots\)
819.2.e.a \(32\) \(6.540\) None None \(0\) \(0\) \(0\) \(-8\)
819.2.g.a \(8\) \(6.540\) 8.0.\(\cdots\).5 \(\Q(\sqrt{-91}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2q^{4}+\beta _{5}q^{5}+\beta _{1}q^{7}+\beta _{3}q^{13}+\cdots\)
819.2.g.b \(8\) \(6.540\) 8.0.40960000.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+3q^{4}-2\beta _{1}q^{5}+(\beta _{2}+2\beta _{7})q^{7}+\cdots\)
819.2.g.c \(12\) \(6.540\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-12\) \(0\) \(0\) \(0\) \(q+(-1+\beta _{5})q^{2}+(2-\beta _{1}-\beta _{5})q^{4}+\cdots\)
819.2.g.d \(12\) \(6.540\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(12\) \(0\) \(0\) \(0\) \(q+(1-\beta _{5})q^{2}+(2-\beta _{1}-\beta _{5})q^{4}+\beta _{3}q^{5}+\cdots\)
819.2.i.a \(84\) \(6.540\) None None \(-4\) \(1\) \(-8\) \(84\)
819.2.i.b \(84\) \(6.540\) None None \(4\) \(-1\) \(8\) \(-84\)
819.2.j.a \(2\) \(6.540\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(4\) \(-5\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+4\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
819.2.j.b \(2\) \(6.540\) \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(0\) \(1\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots\)
819.2.j.c \(4\) \(6.540\) \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(-3\) \(0\) \(0\) \(-8\) \(q+(-1-\beta _{1}-\beta _{3})q^{2}+(3\beta _{1}+3\beta _{2}+\cdots)q^{4}+\cdots\)
819.2.j.d \(6\) \(6.540\) 6.0.64827.1 None None \(-2\) \(0\) \(-3\) \(0\) \(q+(-1+\beta _{4}+\beta _{5})q^{2}+(-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
819.2.j.e \(6\) \(6.540\) \(\Q(\zeta_{18})\) None None \(0\) \(0\) \(3\) \(0\) \(q+(\zeta_{18}-\zeta_{18}^{2}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)
819.2.j.f \(8\) \(6.540\) 8.0.4868829729.1 None None \(-1\) \(0\) \(3\) \(9\) \(q+(\beta _{1}-\beta _{3}-\beta _{6})q^{2}+(\beta _{3}+2\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots\)
819.2.j.g \(10\) \(6.540\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(0\) \(-3\) \(4\) \(q+(-\beta _{4}+\beta _{8})q^{2}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
819.2.j.h \(10\) \(6.540\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(4\) \(0\) \(2\) \(1\) \(q+(-\beta _{1}+\beta _{7})q^{2}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
819.2.j.i \(12\) \(6.540\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(4\) \(q+(\beta _{1}+\beta _{6})q^{2}+(-1-\beta _{5}-\beta _{9})q^{4}+\cdots\)
819.2.j.j \(20\) \(6.540\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{4}q^{2}+(-2-2\beta _{3}-\beta _{14})q^{4}-\beta _{10}q^{5}+\cdots\)
819.2.k.a \(216\) \(6.540\) None None \(-1\) \(1\) \(2\) \(-6\)
819.2.l.a \(216\) \(6.540\) None None \(-1\) \(-2\) \(2\) \(3\)
819.2.m.a \(2\) \(6.540\) \(\Q(\sqrt{-3}) \) None None \(2\) \(3\) \(-2\) \(1\) \(q+(2-2\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
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