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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
805.1.t.a \(2\) \(0.402\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(-1\) \(-1\) \(q+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
805.1.t.b \(2\) \(0.402\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(1\) \(1\) \(q+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
805.2.a.a \(1\) \(6.428\) \(\Q\) None None \(-1\) \(0\) \(-1\) \(-1\) \(-\) \(q-q^{2}-q^{4}-q^{5}-q^{7}+3q^{8}-3q^{9}+\cdots\)
805.2.a.b \(1\) \(6.428\) \(\Q\) None None \(-1\) \(0\) \(-1\) \(-1\) \(-\) \(q-q^{2}-q^{4}-q^{5}-q^{7}+3q^{8}-3q^{9}+\cdots\)
805.2.a.c \(1\) \(6.428\) \(\Q\) None None \(2\) \(-1\) \(-1\) \(-1\) \(+\) \(q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}-q^{7}+\cdots\)
805.2.a.d \(1\) \(6.428\) \(\Q\) None None \(2\) \(3\) \(-1\) \(-1\) \(-\) \(q+2q^{2}+3q^{3}+2q^{4}-q^{5}+6q^{6}+\cdots\)
805.2.a.e \(2\) \(6.428\) \(\Q(\sqrt{5}) \) None None \(3\) \(0\) \(-2\) \(-2\) \(-\) \(q+(1+\beta )q^{2}+(1-2\beta )q^{3}+3\beta q^{4}-q^{5}+\cdots\)
805.2.a.f \(3\) \(6.428\) \(\Q(\zeta_{14})^+\) None None \(-2\) \(0\) \(-3\) \(-3\) \(+\) \(q+(-1-\beta _{2})q^{2}+(-1+2\beta _{1}-\beta _{2})q^{3}+\cdots\)
805.2.a.g \(4\) \(6.428\) 4.4.2777.1 None None \(-2\) \(-5\) \(4\) \(4\) \(+\) \(q+(-1+\beta _{3})q^{2}+(-1-\beta _{1})q^{3}+(1+\cdots)q^{4}+\cdots\)
805.2.a.h \(4\) \(6.428\) 4.4.22545.1 None None \(-1\) \(0\) \(-4\) \(-4\) \(-\) \(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(3+\beta _{3})q^{4}+\cdots\)
805.2.a.i \(4\) \(6.428\) 4.4.7537.1 None None \(1\) \(4\) \(-4\) \(4\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
805.2.a.j \(4\) \(6.428\) 4.4.2777.1 None None \(3\) \(6\) \(4\) \(-4\) \(-\) \(q+(1-\beta _{1})q^{2}+(1+\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
805.2.a.k \(5\) \(6.428\) 5.5.122821.1 None None \(-3\) \(-6\) \(5\) \(-5\) \(+\) \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{3})q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots\)
805.2.a.l \(5\) \(6.428\) 5.5.255877.1 None None \(-1\) \(-4\) \(-5\) \(5\) \(+\) \(q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
805.2.a.m \(8\) \(6.428\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(1\) \(7\) \(8\) \(8\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
805.2.c.a \(2\) \(6.428\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) \(q+iq^{3}+2q^{4}+(2-i)q^{5}+iq^{7}+2q^{9}+\cdots\)
805.2.c.b \(24\) \(6.428\) None None \(0\) \(0\) \(-2\) \(0\)
805.2.c.c \(42\) \(6.428\) None None \(0\) \(0\) \(2\) \(0\)
805.2.d.a \(4\) \(6.428\) \(\Q(\sqrt{-5}, \sqrt{23})\) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2q^{4}-\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}-3q^{9}+\cdots\)
805.2.d.b \(8\) \(6.428\) 8.0.40960000.1 None None \(0\) \(-8\) \(0\) \(0\) \(q+(\beta _{4}-\beta _{5})q^{2}-q^{3}-\beta _{2}q^{4}+(\beta _{3}+2\beta _{7})q^{5}+\cdots\)
805.2.d.c \(8\) \(6.428\) 8.0.40960000.1 None None \(0\) \(8\) \(0\) \(0\) \(q+(-\beta _{4}+\beta _{5})q^{2}+q^{3}-\beta _{2}q^{4}+(-2\beta _{3}+\cdots)q^{5}+\cdots\)
805.2.d.d \(12\) \(6.428\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(-12\) \(0\) \(0\) \(q-\beta _{3}q^{2}-q^{3}+(-2-\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots\)
805.2.d.e \(12\) \(6.428\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(12\) \(0\) \(0\) \(q+\beta _{3}q^{2}+q^{3}+(-2-\beta _{2})q^{4}-\beta _{11}q^{5}+\cdots\)
805.2.d.f \(48\) \(6.428\) None None \(0\) \(0\) \(0\) \(0\)
805.2.f.a \(32\) \(6.428\) None None \(-2\) \(0\) \(-32\) \(-3\)
805.2.f.b \(32\) \(6.428\) None None \(-2\) \(0\) \(32\) \(3\)
805.2.i.a \(2\) \(6.428\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(-2\) \(1\) \(-5\) \(q-2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
805.2.i.b \(4\) \(6.428\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(2\) \(2\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
805.2.i.c \(24\) \(6.428\) None None \(7\) \(2\) \(12\) \(3\)
805.2.i.d \(26\) \(6.428\) None None \(5\) \(2\) \(-13\) \(0\)
805.2.i.e \(30\) \(6.428\) None None \(-5\) \(0\) \(15\) \(-3\)
805.2.i.f \(34\) \(6.428\) None None \(-5\) \(2\) \(-17\) \(-1\)
805.2.k.a \(176\) \(6.428\) None None \(0\) \(0\) \(0\) \(-8\)
805.2.l.a \(144\) \(6.428\) None None \(0\) \(8\) \(0\) \(0\)
805.2.p.a \(64\) \(6.428\) None None \(2\) \(0\) \(-32\) \(3\)
805.2.p.b \(64\) \(6.428\) None None \(2\) \(0\) \(32\) \(-3\)
805.2.r.a \(8\) \(6.428\) 8.0.\(\cdots\).4 \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{3}q^{4}+(\beta _{4}+\beta _{5})q^{5}+\beta _{1}q^{7}+(3+\cdots)q^{9}+\cdots\)
805.2.r.b \(176\) \(6.428\) None None \(0\) \(0\) \(0\) \(0\)
805.2.s.a \(4\) \(6.428\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-4\) \(0\) \(q-2\zeta_{12}q^{3}+(-2+2\zeta_{12}^{2})q^{4}+(\zeta_{12}+\cdots)q^{5}+\cdots\)
805.2.s.b \(4\) \(6.428\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(4\) \(0\) \(q+\zeta_{12}q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
805.2.s.c \(4\) \(6.428\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(4\) \(0\) \(q+2\zeta_{12}q^{2}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots\)
805.2.s.d \(164\) \(6.428\) None None \(0\) \(0\) \(-4\) \(0\)
805.2.u.a \(110\) \(6.428\) None None \(0\) \(-2\) \(11\) \(-11\)
805.2.u.b \(110\) \(6.428\) None None \(4\) \(2\) \(-11\) \(-11\)
805.2.u.c \(130\) \(6.428\) None None \(-2\) \(-2\) \(13\) \(13\)
805.2.u.d \(130\) \(6.428\) None None \(2\) \(2\) \(-13\) \(13\)
805.2.v.a \(352\) \(6.428\) None None \(0\) \(0\) \(0\) \(8\)
805.2.y.a \(368\) \(6.428\) None None \(-4\) \(-4\) \(0\) \(0\)
805.2.bb.a \(320\) \(6.428\) None None \(2\) \(0\) \(-32\) \(-3\)
805.2.bb.b \(320\) \(6.428\) None None \(2\) \(0\) \(32\) \(3\)
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