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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
84.1.p.a $2$ $0.042$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) $-$ \(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}-q^{13}+\cdots\)
84.2.a.a $1$ $0.671$ \(\Q\) None None \(0\) \(-1\) \(4\) \(-1\) $-$ \(q-q^{3}+4q^{5}-q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots\)
84.2.a.b $1$ $0.671$ \(\Q\) None None \(0\) \(1\) \(0\) \(1\) $-$ \(q+q^{3}+q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots\)
84.2.b.a $4$ $0.671$ 4.0.2312.1 None None \(-1\) \(-4\) \(0\) \(2\) $-$ \(q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
84.2.b.b $4$ $0.671$ 4.0.2312.1 None None \(-1\) \(4\) \(0\) \(-2\) $-$ \(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
84.2.e.a $12$ $0.671$ 12.0.\(\cdots\).2 None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{4}q^{2}-\beta _{9}q^{3}+(-\beta _{2}-\beta _{3})q^{4}+\cdots\)
84.2.f.a $2$ $0.671$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(4\) $-$ \(q-\zeta_{6}q^{3}+(2-\zeta_{6})q^{7}-3q^{9}+4\zeta_{6}q^{13}+\cdots\)
84.2.i.a $2$ $0.671$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(2\) \(1\) $-$ \(q+\zeta_{6}q^{3}+(2-2\zeta_{6})q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
84.2.k.a $2$ $0.671$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(3\) \(4\) $-$ \(q+(-2+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
84.2.k.b $2$ $0.671$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-3\) \(4\) $-$ \(q+(1-2\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
84.2.k.c $2$ $0.671$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(-5\) $-$ \(q+(1+\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
84.2.n.a $24$ $0.671$ None None \(0\) \(0\) \(0\) \(0\) $-$
84.2.o.a $8$ $0.671$ 8.0.562828176.1 None None \(1\) \(-4\) \(0\) \(2\) $-$ \(q-\beta _{4}q^{2}+(-1+\beta _{3})q^{3}+(\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots\)
84.2.o.b $8$ $0.671$ 8.0.562828176.1 None None \(1\) \(4\) \(0\) \(-2\) $-$ \(q+\beta _{6}q^{2}+\beta _{3}q^{3}+(\beta _{1}-\beta _{2})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
84.3.c.a $4$ $2.289$ 4.0.116032.1 None None \(0\) \(6\) \(0\) \(0\) $-$ \(q+(2-\beta _{1})q^{3}+(-2+\beta _{1}-\beta _{2}-2\beta _{3})q^{5}+\cdots\)
84.3.d.a $2$ $2.289$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(-14\) $-$ \(q-\zeta_{6}q^{3}-4\zeta_{6}q^{5}-7q^{7}-3q^{9}+18q^{11}+\cdots\)
84.3.g.a $12$ $2.289$ 12.0.\(\cdots\).1 None None \(2\) \(0\) \(8\) \(0\) $-$ \(q-\beta _{9}q^{2}+\beta _{6}q^{3}+(\beta _{5}-\beta _{6})q^{4}+(1+\cdots)q^{5}+\cdots\)
84.3.h.a $1$ $2.289$ \(\Q\) \(\Q(\sqrt{-21}) \) None \(-2\) \(-3\) \(-4\) \(7\) $-$ \(q-2q^{2}-3q^{3}+4q^{4}-4q^{5}+6q^{6}+\cdots\)
84.3.h.b $1$ $2.289$ \(\Q\) \(\Q(\sqrt{-21}) \) None \(-2\) \(3\) \(4\) \(-7\) $-$ \(q-2q^{2}+3q^{3}+4q^{4}+4q^{5}-6q^{6}+\cdots\)
84.3.h.c $1$ $2.289$ \(\Q\) \(\Q(\sqrt{-21}) \) None \(2\) \(-3\) \(4\) \(7\) $-$ \(q+2q^{2}-3q^{3}+4q^{4}+4q^{5}-6q^{6}+\cdots\)
84.3.h.d $1$ $2.289$ \(\Q\) \(\Q(\sqrt{-21}) \) None \(2\) \(3\) \(-4\) \(-7\) $-$ \(q+2q^{2}+3q^{3}+4q^{4}-4q^{5}+6q^{6}+\cdots\)
84.3.h.e $24$ $2.289$ None None \(0\) \(0\) \(0\) \(0\) $-$
84.3.j.a $56$ $2.289$ None None \(0\) \(0\) \(0\) \(0\) $-$
84.3.l.a $2$ $2.289$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(3\) \(5\) \(-7\) $-$ \(q-2\zeta_{6}q^{2}+(2-\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
84.3.l.b $2$ $2.289$ \(\Q(\sqrt{-3}) \) None None \(4\) \(-3\) \(5\) \(7\) $-$ \(q+2q^{2}+(-2+\zeta_{6})q^{3}+4q^{4}+(5-5\zeta_{6})q^{5}+\cdots\)
84.3.l.c $14$ $2.289$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(-3\) \(-21\) \(-5\) \(-19\) $-$ \(q+(-\beta _{1}-\beta _{4})q^{2}+(-1+\beta _{3})q^{3}+(1+\cdots)q^{4}+\cdots\)
84.3.l.d $14$ $2.289$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(3\) \(21\) \(-5\) \(19\) $-$ \(q+(\beta _{4}+\beta _{9})q^{2}+(2-\beta _{2})q^{3}-\beta _{10}q^{4}+\cdots\)
84.3.m.a $2$ $2.289$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(3\) \(13\) $-$ \(q+(1+\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(5+3\zeta_{6})q^{7}+\cdots\)
84.3.m.b $4$ $2.289$ \(\Q(\sqrt{-3}, \sqrt{65})\) None None \(0\) \(-6\) \(-9\) \(2\) $-$ \(q+(-2+\beta _{1})q^{3}+(-2-\beta _{1}+\beta _{3})q^{5}+\cdots\)
84.3.p.a $2$ $2.289$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(11\) $-$ \(q+3\zeta_{6}q^{3}+(3+5\zeta_{6})q^{7}+(-9+9\zeta_{6})q^{9}+\cdots\)
84.3.p.b $4$ $2.289$ \(\Q(\sqrt{-3}, \sqrt{-5})\) None None \(0\) \(-4\) \(0\) \(22\) $-$ \(q+(\beta _{1}-2\beta _{2}-\beta _{3})q^{3}-3\beta _{1}q^{5}+(8+\cdots)q^{7}+\cdots\)
84.3.p.c $4$ $2.289$ \(\Q(\sqrt{-3}, \sqrt{-35})\) None None \(0\) \(1\) \(0\) \(-28\) $-$ \(q+\beta _{1}q^{3}+(\beta _{2}+2\beta _{3})q^{5}-7q^{7}+(9\beta _{2}+\cdots)q^{9}+\cdots\)
84.4.a.a $1$ $4.956$ \(\Q\) None None \(0\) \(-3\) \(6\) \(7\) $+$ \(q-3q^{3}+6q^{5}+7q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
84.4.a.b $1$ $4.956$ \(\Q\) None None \(0\) \(3\) \(14\) \(-7\) $+$ \(q+3q^{3}+14q^{5}-7q^{7}+9q^{9}+4q^{11}+\cdots\)
84.4.b.a $12$ $4.956$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(1\) \(-36\) \(0\) \(10\) $-$ \(q+\beta _{1}q^{2}-3q^{3}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{8}+\cdots)q^{5}+\cdots\)
84.4.b.b $12$ $4.956$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(1\) \(36\) \(0\) \(-10\) $-$ \(q+\beta _{1}q^{2}+3q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{8}+\cdots)q^{5}+\cdots\)
84.4.e.a $36$ $4.956$ None None \(0\) \(0\) \(0\) \(0\) $-$
84.4.f.a $8$ $4.956$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(0\) \(0\) \(-20\) $-$ \(q-\beta _{2}q^{3}-\beta _{5}q^{5}+(-3-\beta _{7})q^{7}+(-2+\cdots)q^{9}+\cdots\)
84.4.i.a $4$ $4.956$ \(\Q(\sqrt{-3}, \sqrt{193})\) None None \(0\) \(-6\) \(-11\) \(6\) $-$ \(q+(-3+3\beta _{2})q^{3}+(\beta _{1}-6\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
84.4.i.b $4$ $4.956$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None None \(0\) \(6\) \(3\) \(-20\) $-$ \(q-3\beta _{2}q^{3}+(1+2\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots\)
84.4.k.a $2$ $4.956$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-9\) \(0\) \(-17\) $-$ \(q+(-3-3\zeta_{6})q^{3}+(-18+19\zeta_{6})q^{7}+\cdots\)
84.4.k.b $2$ $4.956$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(9\) \(0\) \(37\) $-$ \(q+(3+3\zeta_{6})q^{3}+(18+\zeta_{6})q^{7}+3^{3}\zeta_{6}q^{9}+\cdots\)
84.4.k.c $12$ $4.956$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(-42\) $-$ \(q-\beta _{5}q^{3}-\beta _{9}q^{5}+(-1+2\beta _{1}-2\beta _{4}+\cdots)q^{7}+\cdots\)
84.4.n.a $88$ $4.956$ None None \(0\) \(0\) \(0\) \(0\) $-$
84.4.o.a $24$ $4.956$ None None \(-1\) \(-36\) \(0\) \(10\) $-$
84.4.o.b $24$ $4.956$ None None \(-1\) \(36\) \(0\) \(-10\) $-$
84.5.c.a $8$ $8.683$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(-18\) \(0\) \(0\) $-$ \(q+(-2-\beta _{3})q^{3}+(\beta _{1}+\beta _{3})q^{5}+\beta _{2}q^{7}+\cdots\)
84.5.d.a $6$ $8.683$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(0\) \(0\) \(0\) \(42\) $-$ \(q+\beta _{2}q^{3}+(\beta _{2}-\beta _{5})q^{5}+(7-\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
84.5.g.a $24$ $8.683$ None None \(-6\) \(0\) \(-48\) \(0\) $-$
84.5.h.a $1$ $8.683$ \(\Q\) \(\Q(\sqrt{-21}) \) None \(-4\) \(-9\) \(-34\) \(-49\) $-$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}-34q^{5}+6^{2}q^{6}+\cdots\)
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