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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
804.1.h.a \(1\) \(0.401\) \(\Q\) \(\Q(\sqrt{-201}) \) None \(-1\) \(-1\) \(1\) \(1\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
804.1.h.b \(1\) \(0.401\) \(\Q\) \(\Q(\sqrt{-201}) \) None \(-1\) \(1\) \(1\) \(-1\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
804.1.h.c \(1\) \(0.401\) \(\Q\) \(\Q(\sqrt{-201}) \) None \(1\) \(-1\) \(-1\) \(1\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
804.1.h.d \(1\) \(0.401\) \(\Q\) \(\Q(\sqrt{-201}) \) None \(1\) \(1\) \(-1\) \(-1\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
804.1.k.a \(2\) \(0.401\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(-2\) \(q+q^{3}-\zeta_{6}q^{7}+q^{9}-\zeta_{6}^{2}q^{13}+\zeta_{6}^{2}q^{19}+\cdots\)
804.1.be.a \(20\) \(0.401\) \(\Q(\zeta_{33})\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(2\) \(q+\zeta_{66}^{30}q^{3}+(-\zeta_{66}^{17}+\zeta_{66}^{26}+\cdots)q^{7}+\cdots\)
804.2.a.a \(1\) \(6.420\) \(\Q\) None None \(0\) \(-1\) \(-3\) \(3\) \(+\) \(q-q^{3}-3q^{5}+3q^{7}+q^{9}-2q^{11}+\cdots\)
804.2.a.b \(1\) \(6.420\) \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) \(+\) \(q-q^{3}+q^{9}-2q^{11}-4q^{13}-3q^{17}+\cdots\)
804.2.a.c \(1\) \(6.420\) \(\Q\) None None \(0\) \(-1\) \(4\) \(0\) \(-\) \(q-q^{3}+4q^{5}+q^{9}+2q^{13}-4q^{15}+\cdots\)
804.2.a.d \(1\) \(6.420\) \(\Q\) None None \(0\) \(1\) \(-1\) \(-3\) \(+\) \(q+q^{3}-q^{5}-3q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
804.2.a.e \(3\) \(6.420\) 3.3.1076.1 None None \(0\) \(-3\) \(-3\) \(-5\) \(-\) \(q-q^{3}+(-1-\beta _{1})q^{5}+(-2-\beta _{1}+\beta _{2})q^{7}+\cdots\)
804.2.a.f \(5\) \(6.420\) 5.5.24571284.1 None None \(0\) \(5\) \(3\) \(5\) \(-\) \(q+q^{3}+(1-\beta _{1})q^{5}+(1-\beta _{2})q^{7}+q^{9}+\cdots\)
804.2.c.a \(4\) \(6.420\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{3})q^{3}-2q^{4}-\zeta_{8}^{2}q^{5}+\cdots\)
804.2.c.b \(128\) \(6.420\) None None \(0\) \(0\) \(0\) \(0\)
804.2.e.a \(34\) \(6.420\) None None \(0\) \(-34\) \(0\) \(-4\)
804.2.e.b \(34\) \(6.420\) None None \(0\) \(34\) \(0\) \(4\)
804.2.g.a \(2\) \(6.420\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{3}-2\zeta_{6}q^{7}-3q^{9}-4\zeta_{6}q^{13}+\cdots\)
804.2.g.b \(4\) \(6.420\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+(2\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+(2+\cdots)q^{9}+\cdots\)
804.2.g.c \(16\) \(6.420\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{12}q^{5}+\beta _{10}q^{7}+\beta _{2}q^{9}+\cdots\)
804.2.i.a \(2\) \(6.420\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(-4\) \(3\) \(q-q^{3}-2q^{5}+3\zeta_{6}q^{7}+q^{9}-3\zeta_{6}q^{11}+\cdots\)
804.2.i.b \(2\) \(6.420\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(4\) \(-5\) \(q-q^{3}+2q^{5}-5\zeta_{6}q^{7}+q^{9}-5\zeta_{6}q^{11}+\cdots\)
804.2.i.c \(2\) \(6.420\) \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(4\) \(3\) \(q+q^{3}+2q^{5}+3\zeta_{6}q^{7}+q^{9}-\zeta_{6}q^{11}+\cdots\)
804.2.i.d \(8\) \(6.420\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(-8\) \(2\) \(1\) \(q-q^{3}+\beta _{6}q^{5}+(-\beta _{1}+\beta _{6})q^{7}+q^{9}+\cdots\)
804.2.i.e \(8\) \(6.420\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(8\) \(-6\) \(0\) \(q+q^{3}+(-1-\beta _{2}+\beta _{5}-\beta _{6})q^{5}-\beta _{3}q^{7}+\cdots\)
804.2.j.a \(68\) \(6.420\) None None \(0\) \(-68\) \(0\) \(4\)
804.2.j.b \(68\) \(6.420\) None None \(0\) \(68\) \(0\) \(-4\)
804.2.l.a \(264\) \(6.420\) None None \(0\) \(0\) \(0\) \(0\)
804.2.o.a \(2\) \(6.420\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-6\) \(q+(-1+2\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{7}+\cdots\)
804.2.o.b \(4\) \(6.420\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(-4\) \(8\) \(6\) \(q+(-1-\beta _{3})q^{3}+2q^{5}+(2+2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
804.2.o.c \(4\) \(6.420\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(4\) \(-8\) \(6\) \(q+(1+\beta _{3})q^{3}-2q^{5}+(2-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
804.2.o.d \(36\) \(6.420\) None None \(0\) \(0\) \(0\) \(0\)
804.2.q.a \(60\) \(6.420\) None None \(0\) \(-6\) \(-2\) \(-2\)
804.2.q.b \(60\) \(6.420\) None None \(0\) \(6\) \(2\) \(2\)
804.2.s.a \(20\) \(6.420\) \(\Q(\zeta_{33})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{33}^{13}q^{3}+(-2\zeta_{33}^{7}-2\zeta_{33}^{8}+\cdots)q^{7}+\cdots\)
804.2.s.b \(200\) \(6.420\) None None \(0\) \(0\) \(0\) \(0\)
804.2.u.a \(340\) \(6.420\) None None \(0\) \(-34\) \(0\) \(-4\)
804.2.u.b \(340\) \(6.420\) None None \(0\) \(34\) \(0\) \(4\)
804.2.w.a \(1320\) \(6.420\) None None \(0\) \(0\) \(0\) \(0\)
804.2.y.a \(100\) \(6.420\) None None \(0\) \(-10\) \(2\) \(-3\)
804.2.y.b \(120\) \(6.420\) None None \(0\) \(12\) \(-2\) \(1\)
804.2.ba.a \(20\) \(6.420\) \(\Q(\zeta_{33})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(6\) \(q+(-2\zeta_{33}-\zeta_{33}^{12})q^{3}+(1-\zeta_{33}+\cdots)q^{7}+\cdots\)
804.2.ba.b \(440\) \(6.420\) None None \(0\) \(0\) \(0\) \(-12\)
804.2.bd.a \(2640\) \(6.420\) None None \(0\) \(0\) \(0\) \(0\)
804.2.bf.a \(680\) \(6.420\) None None \(0\) \(-68\) \(0\) \(4\)
804.2.bf.b \(680\) \(6.420\) None None \(0\) \(68\) \(0\) \(-4\)
804.3.b.a \(22\) \(21.907\) None None \(0\) \(0\) \(0\) \(0\)
804.3.d.a \(44\) \(21.907\) None None \(0\) \(0\) \(0\) \(-8\)
804.3.k.a \(2\) \(21.907\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-6\) \(0\) \(-2\) \(q-3q^{3}+(-2+2\zeta_{6})q^{7}+9q^{9}+\zeta_{6}q^{13}+\cdots\)
804.3.k.b \(88\) \(21.907\) None None \(0\) \(6\) \(0\) \(8\)
804.3.m.a \(22\) \(21.907\) None None \(0\) \(0\) \(0\) \(9\)
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