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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
36.2.a.a $1$ $0.287$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-4\) $-$ \(q-4q^{7}+2q^{13}+8q^{19}-5q^{25}-4q^{31}+\cdots\)
36.2.b.a $2$ $0.287$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta q^{2}-2q^{4}-\beta q^{5}-2\beta q^{8}+2q^{10}+\cdots\)
36.2.e.a $2$ $0.287$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(1\) $-$ \(q+(1-2\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+\zeta_{6}q^{7}+\cdots\)
36.2.h.a $8$ $0.287$ 8.0.170772624.1 None \(-3\) \(0\) \(-6\) \(0\) $-$ \(q+(1-\beta _{1}+\beta _{4}+\beta _{7})q^{2}+(-\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots\)
36.3.d.a $1$ $0.981$ \(\Q\) \(\Q(\sqrt{-1}) \) \(-2\) \(0\) \(8\) \(0\) $-$ \(q-2q^{2}+4q^{4}+8q^{5}-8q^{8}-2^{4}q^{10}+\cdots\)
36.3.d.b $1$ $0.981$ \(\Q\) \(\Q(\sqrt{-1}) \) \(2\) \(0\) \(-8\) \(0\) $-$ \(q+2q^{2}+4q^{4}-8q^{5}+8q^{8}-2^{4}q^{10}+\cdots\)
36.3.d.c $2$ $0.981$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(4\) \(0\) $-$ \(q+(1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{4}+2q^{5}+\cdots\)
36.3.f.a $2$ $0.981$ \(\Q(\sqrt{-3}) \) None \(-2\) \(3\) \(-4\) \(6\) $-$ \(q+(-2+2\zeta_{6})q^{2}+3\zeta_{6}q^{3}-4\zeta_{6}q^{4}+\cdots\)
36.3.f.b $2$ $0.981$ \(\Q(\sqrt{-3}) \) None \(4\) \(-3\) \(-4\) \(-6\) $-$ \(q+2q^{2}-3\zeta_{6}q^{3}+4q^{4}+(-4+4\zeta_{6})q^{5}+\cdots\)
36.3.f.c $16$ $0.981$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-3\) \(0\) \(6\) \(0\) $-$ \(q-\beta _{1}q^{2}+\beta _{14}q^{3}+(-\beta _{2}+\beta _{3})q^{4}+\cdots\)
36.3.g.a $4$ $0.981$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(3\) \(9\) \(-1\) $-$ \(q+(1-\beta _{1}+\beta _{3})q^{3}+(2-2\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
36.4.a.a $1$ $2.124$ \(\Q\) None \(0\) \(0\) \(18\) \(8\) $+$ \(q+18q^{5}+8q^{7}-6^{2}q^{11}-10q^{13}+\cdots\)
36.4.b.a $2$ $2.124$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) $-$ \(q+2\beta q^{2}-8q^{4}+13\beta q^{5}-2^{4}\beta q^{8}+\cdots\)
36.4.b.b $4$ $2.124$ \(\Q(\sqrt{-2}, \sqrt{-15})\) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+(-\beta _{1}-\beta _{2})q^{2}+(7-\beta _{3})q^{4}-7\beta _{2}q^{5}+\cdots\)
36.4.e.a $6$ $2.124$ 6.0.6831243.2 None \(0\) \(-3\) \(6\) \(-6\) $-$ \(q+(-1-\beta _{2})q^{3}+(1-3\beta _{1}-2\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
36.4.h.a $8$ $2.124$ 8.0.\(\cdots\).1 None \(-3\) \(0\) \(66\) \(0\) $-$ \(q-\beta _{7}q^{2}+(-\beta _{2}+\beta _{5})q^{3}+(2\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots\)
36.4.h.b $24$ $2.124$ None \(0\) \(0\) \(-72\) \(0\) $-$
36.5.c.a $2$ $3.721$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(136\) $-$ \(q+\beta q^{5}+68q^{7}+4\beta q^{11}-2^{4}q^{13}+\cdots\)
36.5.d.a $1$ $3.721$ \(\Q\) \(\Q(\sqrt{-1}) \) \(4\) \(0\) \(14\) \(0\) $-$ \(q+4q^{2}+2^{4}q^{4}+14q^{5}+2^{6}q^{8}+56q^{10}+\cdots\)
36.5.d.b $4$ $3.721$ \(\Q(\sqrt{-3}, \sqrt{13})\) None \(-6\) \(0\) \(-24\) \(0\) $-$ \(q+(-2+\beta _{1})q^{2}+(-4-2\beta _{1}+\beta _{3})q^{4}+\cdots\)
36.5.d.c $4$ $3.721$ \(\Q(i, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(4\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
36.5.f.a $44$ $3.721$ None \(-1\) \(0\) \(-2\) \(0\) $-$
36.5.g.a $8$ $3.721$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-9\) \(-9\) \(13\) $-$ \(q+(-1+\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots\)
36.6.a.a $1$ $5.774$ \(\Q\) None \(0\) \(0\) \(-54\) \(-88\) $+$ \(q-54q^{5}-88q^{7}-540q^{11}-418q^{13}+\cdots\)
36.6.a.b $1$ $5.774$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(236\) $-$ \(q+236q^{7}+1202q^{13}-1432q^{19}+\cdots\)
36.6.b.a $2$ $5.774$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) $-$ \(q+4\beta q^{2}-2^{5}q^{4}-79\beta q^{5}-2^{7}\beta q^{8}+\cdots\)
36.6.b.b $8$ $5.774$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{2}q^{2}+(6+\beta _{7})q^{4}+(6\beta _{1}+3\beta _{2}+\cdots)q^{5}+\cdots\)
36.6.e.a $10$ $5.774$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(12\) \(-21\) \(29\) $-$ \(q+(2+2\beta _{1}-\beta _{3}-\beta _{4})q^{3}+(4\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
36.6.h.a $56$ $5.774$ None \(-3\) \(0\) \(-6\) \(0\) $-$
36.7.c.a $2$ $8.282$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-488\) $-$ \(q+5\beta q^{5}-244q^{7}+188\beta q^{11}-2728q^{13}+\cdots\)
36.7.d.a $1$ $8.282$ \(\Q\) \(\Q(\sqrt{-1}) \) \(-8\) \(0\) \(-88\) \(0\) $-$ \(q-8q^{2}+2^{6}q^{4}-88q^{5}-2^{9}q^{8}+704q^{10}+\cdots\)
36.7.d.b $1$ $8.282$ \(\Q\) \(\Q(\sqrt{-1}) \) \(8\) \(0\) \(88\) \(0\) $-$ \(q+8q^{2}+2^{6}q^{4}+88q^{5}+2^{9}q^{8}+704q^{10}+\cdots\)
36.7.d.c $2$ $8.282$ \(\Q(\sqrt{-15}) \) None \(-4\) \(0\) \(-20\) \(0\) $-$ \(q+(-2-\beta )q^{2}+(-56+4\beta )q^{4}-10q^{5}+\cdots\)
36.7.d.d $4$ $8.282$ \(\Q(\sqrt{13}, \sqrt{-51})\) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{2}+(-38+\beta _{3})q^{4}+(-10\beta _{1}+\cdots)q^{5}+\cdots\)
36.7.d.e $6$ $8.282$ 6.0.50898483.1 None \(10\) \(0\) \(44\) \(0\) $-$ \(q+(2-\beta _{1})q^{2}+(26-\beta _{1}-\beta _{2})q^{4}+(7+\cdots)q^{5}+\cdots\)
36.7.f.a $68$ $8.282$ None \(-1\) \(0\) \(-2\) \(0\) $-$
36.7.g.a $12$ $8.282$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(6\) \(-216\) \(-120\) $-$ \(q+(-2+4\beta _{1}+\beta _{3})q^{3}+(-24+12\beta _{1}+\cdots)q^{5}+\cdots\)
36.8.a.a $1$ $11.246$ \(\Q\) None \(0\) \(0\) \(-270\) \(1112\) $+$ \(q-270q^{5}+1112q^{7}+5724q^{11}+\cdots\)
36.8.a.b $1$ $11.246$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-508\) $-$ \(q-508q^{7}-14614q^{13}-57448q^{19}+\cdots\)
36.8.a.c $1$ $11.246$ \(\Q\) None \(0\) \(0\) \(378\) \(-832\) $+$ \(q+378q^{5}-832q^{7}+2484q^{11}+14870q^{13}+\cdots\)
36.8.b.a $2$ $11.246$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) $-$ \(q+8\beta q^{2}-2^{7}q^{4}+307\beta q^{5}-2^{10}\beta q^{8}+\cdots\)
36.8.b.b $12$ $11.246$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{2}+(17+\beta _{3})q^{4}+(-9\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
36.8.e.a $14$ $11.246$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(321\) \(-83\) $-$ \(q+(-2-4\beta _{2}-\beta _{4})q^{3}+(\beta _{1}-46\beta _{2}+\cdots)q^{5}+\cdots\)
36.8.h.a $80$ $11.246$ None \(-3\) \(0\) \(-6\) \(0\) $-$
36.9.c.a $2$ $14.666$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(616\) $-$ \(q+\beta q^{5}+308q^{7}+244\beta q^{11}+18464q^{13}+\cdots\)
36.9.d.a $1$ $14.666$ \(\Q\) \(\Q(\sqrt{-1}) \) \(-16\) \(0\) \(1054\) \(0\) $-$ \(q-2^{4}q^{2}+2^{8}q^{4}+1054q^{5}-2^{12}q^{8}+\cdots\)
36.9.d.b $2$ $14.666$ \(\Q(\sqrt{-39}) \) None \(20\) \(0\) \(-1220\) \(0\) $-$ \(q+(10-\beta )q^{2}+(-56-20\beta )q^{4}-610q^{5}+\cdots\)
36.9.d.c $8$ $14.666$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-6\) \(0\) \(336\) \(0\) $-$ \(q+(-1-\beta _{1})q^{2}+(-6+\beta _{1}+\beta _{3})q^{4}+\cdots\)
36.9.d.d $8$ $14.666$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{2}+(-53-\beta _{5})q^{4}+(3\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
36.9.f.a $92$ $14.666$ None \(-1\) \(0\) \(-2\) \(0\) $-$
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