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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
78.2.a.a $1$ $0.623$ \(\Q\) None \(-1\) \(-1\) \(2\) \(4\) $-$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
78.2.b.a $2$ $0.623$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $-$ \(q+iq^{2}+q^{3}-q^{4}+2iq^{5}+iq^{6}+\cdots\)
78.2.e.a $2$ $0.623$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(6\) \(-2\) $-$ \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
78.2.e.b $2$ $0.623$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-2\) \(2\) $-$ \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
78.2.g.a $12$ $0.623$ 12.0.\(\cdots\).52 None \(0\) \(0\) \(0\) \(-12\) $-$ \(q+\beta _{2}q^{2}-\beta _{4}q^{3}+\beta _{8}q^{4}+(-\beta _{1}-\beta _{11})q^{5}+\cdots\)
78.2.i.a $4$ $0.623$ \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(6\) $-$ \(q+\zeta_{12}q^{2}+(-1+\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
78.2.i.b $4$ $0.623$ \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(-6\) $-$ \(q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
78.2.k.a $16$ $0.623$ 16.0.\(\cdots\).9 None \(0\) \(0\) \(0\) \(8\) $-$ \(q+(-\beta _{7}-\beta _{15})q^{2}+(-\beta _{1}-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
78.3.c.a $8$ $2.125$ 8.0.\(\cdots\).2 None \(0\) \(0\) \(0\) \(-8\) $-$ \(q-\beta _{2}q^{2}+\beta _{4}q^{3}-2q^{4}+(\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots\)
78.3.d.a $4$ $2.125$ \(\Q(\sqrt{2}, \sqrt{-5})\) None \(0\) \(-8\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{2}+(-2-\beta _{3})q^{3}+2q^{4}+3\beta _{1}q^{5}+\cdots\)
78.3.d.b $4$ $2.125$ \(\Q(\sqrt{2}, \sqrt{-5})\) None \(0\) \(8\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{2}+(2+\beta _{3})q^{3}+2q^{4}-\beta _{1}q^{5}+\cdots\)
78.3.f.a $4$ $2.125$ \(\Q(\zeta_{12})\) None \(4\) \(0\) \(12\) \(-4\) $-$ \(q+(1+\zeta_{12})q^{2}+\zeta_{12}^{3}q^{3}+2\zeta_{12}q^{4}+\cdots\)
78.3.f.b $8$ $2.125$ 8.0.\(\cdots\).1 None \(-8\) \(0\) \(0\) \(4\) $-$ \(q+(-1-\beta _{6})q^{2}+\beta _{1}q^{3}+2\beta _{6}q^{4}+\cdots\)
78.3.h.a $8$ $2.125$ 8.0.4857532416.2 None \(0\) \(-2\) \(0\) \(-12\) $-$ \(q+\beta _{2}q^{2}+(-1-\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
78.3.h.b $12$ $2.125$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(2\) \(0\) \(22\) $-$ \(q+\beta _{7}q^{2}+(-\beta _{4}+\beta _{9})q^{3}+2\beta _{1}q^{4}+\cdots\)
78.3.j.a $20$ $2.125$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(18\) $-$ \(q+\beta _{5}q^{2}-\beta _{1}q^{3}+(-2-2\beta _{6})q^{4}+\cdots\)
78.3.l.a $4$ $2.125$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(-12\) \(-10\) $-$ \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}+\cdots)q^{3}+\cdots\)
78.3.l.b $4$ $2.125$ \(\Q(\zeta_{12})\) None \(2\) \(0\) \(6\) \(20\) $-$ \(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
78.3.l.c $8$ $2.125$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(4\) \(0\) \(-6\) \(10\) $-$ \(q+(-\beta _{4}-\beta _{5})q^{2}+(2\beta _{2}-\beta _{5})q^{3}+(2\beta _{2}+\cdots)q^{4}+\cdots\)
78.4.a.a $1$ $4.602$ \(\Q\) None \(-2\) \(-3\) \(-16\) \(28\) $+$ \(q-2q^{2}-3q^{3}+4q^{4}-2^{4}q^{5}+6q^{6}+\cdots\)
78.4.a.b $1$ $4.602$ \(\Q\) None \(-2\) \(3\) \(-16\) \(-8\) $-$ \(q-2q^{2}+3q^{3}+4q^{4}-2^{4}q^{5}-6q^{6}+\cdots\)
78.4.a.c $1$ $4.602$ \(\Q\) None \(-2\) \(3\) \(10\) \(-8\) $+$ \(q-2q^{2}+3q^{3}+4q^{4}+10q^{5}-6q^{6}+\cdots\)
78.4.a.d $1$ $4.602$ \(\Q\) None \(2\) \(-3\) \(-20\) \(-32\) $-$ \(q+2q^{2}-3q^{3}+4q^{4}-20q^{5}-6q^{6}+\cdots\)
78.4.a.e $1$ $4.602$ \(\Q\) None \(2\) \(-3\) \(6\) \(20\) $+$ \(q+2q^{2}-3q^{3}+4q^{4}+6q^{5}-6q^{6}+\cdots\)
78.4.a.f $1$ $4.602$ \(\Q\) None \(2\) \(3\) \(4\) \(4\) $+$ \(q+2q^{2}+3q^{3}+4q^{4}+4q^{5}+6q^{6}+\cdots\)
78.4.b.a $2$ $4.602$ \(\Q(\sqrt{-1}) \) None \(0\) \(-6\) \(0\) \(0\) $-$ \(q+iq^{2}-3q^{3}-4q^{4}-4iq^{5}-3iq^{6}+\cdots\)
78.4.b.b $4$ $4.602$ \(\Q(i, \sqrt{17})\) None \(0\) \(12\) \(0\) \(0\) $-$ \(q-\beta _{1}q^{2}+3q^{3}-4q^{4}+(4\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
78.4.e.a $2$ $4.602$ \(\Q(\sqrt{-3}) \) None \(-2\) \(3\) \(14\) \(-16\) $-$ \(q+(-2+2\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
78.4.e.b $4$ $4.602$ \(\Q(\sqrt{-3}, \sqrt{673})\) None \(-4\) \(-6\) \(26\) \(-9\) $-$ \(q+(-2+2\beta _{2})q^{2}+(-3+3\beta _{2})q^{3}+\cdots\)
78.4.e.c $4$ $4.602$ \(\Q(\sqrt{-3}, \sqrt{61})\) None \(4\) \(6\) \(4\) \(-18\) $-$ \(q+(2-2\beta _{1})q^{2}+(3-3\beta _{1})q^{3}-4\beta _{1}q^{4}+\cdots\)
78.4.e.d $6$ $4.602$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(6\) \(-9\) \(-24\) \(17\) $-$ \(q+(2+2\beta _{2})q^{2}+(-3-3\beta _{2})q^{3}+4\beta _{2}q^{4}+\cdots\)
78.4.g.a $28$ $4.602$ None \(0\) \(0\) \(0\) \(20\) $-$
78.4.i.a $4$ $4.602$ \(\Q(\zeta_{12})\) None \(0\) \(-6\) \(0\) \(-42\) $-$ \(q+2\zeta_{12}q^{2}+(-3+3\zeta_{12}^{2})q^{3}+4\zeta_{12}^{2}q^{4}+\cdots\)
78.4.i.b $8$ $4.602$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(12\) \(0\) \(24\) $-$ \(q-\beta _{4}q^{2}+3\beta _{1}q^{3}+(4-4\beta _{1})q^{4}+(3+\cdots)q^{5}+\cdots\)
78.4.k.a $56$ $4.602$ None \(0\) \(0\) \(0\) \(-92\) $-$
78.5.c.a $16$ $8.063$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(12\) \(0\) \(80\) $-$ \(q+\beta _{3}q^{2}+(1+\beta _{3}-\beta _{4})q^{3}-8q^{4}+\cdots\)
78.5.d.a $20$ $8.063$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+8q^{4}+(-2\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots\)
78.5.f.a $8$ $8.063$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-16\) \(0\) \(-36\) \(-8\) $-$ \(q+(-2+2\beta _{2})q^{2}-3\beta _{1}q^{3}-8\beta _{2}q^{4}+\cdots\)
78.5.f.b $8$ $8.063$ 8.0.\(\cdots\).2 None \(16\) \(0\) \(60\) \(88\) $-$ \(q+(2+2\beta _{2})q^{2}+\beta _{3}q^{3}+8\beta _{2}q^{4}+(7+\cdots)q^{5}+\cdots\)
78.5.h.a $36$ $8.063$ None \(0\) \(0\) \(0\) \(-90\) $-$
78.5.j.a $36$ $8.063$ None \(0\) \(0\) \(0\) \(126\) $-$
78.5.l.a $8$ $8.063$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(0\) \(-72\) \(118\) $-$ \(q+(-2-2\beta _{1}+2\beta _{4})q^{2}+(-3\beta _{4}-6\beta _{5}+\cdots)q^{3}+\cdots\)
78.5.l.b $8$ $8.063$ 8.0.\(\cdots\).10 None \(8\) \(0\) \(-24\) \(22\) $-$ \(q+(2-2\beta _{1}+2\beta _{2})q^{2}+(3\beta _{2}+6\beta _{3}+\cdots)q^{3}+\cdots\)
78.5.l.c $12$ $8.063$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-12\) \(0\) \(12\) \(48\) $-$ \(q+(-2+2\beta _{1}-2\beta _{3})q^{2}+(6\beta _{2}+3\beta _{3}+\cdots)q^{3}+\cdots\)
78.5.l.d $12$ $8.063$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(0\) \(60\) \(-48\) $-$ \(q+(2+2\beta _{1}-2\beta _{2}-2\beta _{4})q^{2}+(-3\beta _{1}+\cdots)q^{3}+\cdots\)
78.6.a.a $1$ $12.510$ \(\Q\) None \(-4\) \(-9\) \(4\) \(-8\) $+$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}+4q^{5}+6^{2}q^{6}+\cdots\)
78.6.a.b $1$ $12.510$ \(\Q\) None \(-4\) \(9\) \(24\) \(-238\) $+$ \(q-4q^{2}+9q^{3}+2^{4}q^{4}+24q^{5}-6^{2}q^{6}+\cdots\)
78.6.a.c $1$ $12.510$ \(\Q\) None \(-4\) \(9\) \(76\) \(100\) $-$ \(q-4q^{2}+9q^{3}+2^{4}q^{4}+76q^{5}-6^{2}q^{6}+\cdots\)
78.6.a.d $1$ $12.510$ \(\Q\) None \(4\) \(-9\) \(4\) \(-146\) $+$ \(q+4q^{2}-9q^{3}+2^{4}q^{4}+4q^{5}-6^{2}q^{6}+\cdots\)
78.6.a.e $1$ $12.510$ \(\Q\) None \(4\) \(-9\) \(56\) \(-68\) $-$ \(q+4q^{2}-9q^{3}+2^{4}q^{4}+56q^{5}-6^{2}q^{6}+\cdots\)
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