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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
27.2.a.a $1$ $0.216$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-1\) $-$ \(q-2q^{4}-q^{7}+5q^{13}+4q^{16}-7q^{19}+\cdots\)
27.2.e.a $12$ $0.216$ 12.0.\(\cdots\).1 None \(-6\) \(-6\) \(-3\) \(-6\) $-$ \(q+(-1-\beta _{3}+\beta _{8})q^{2}+(-1-\beta _{2}+\beta _{6}+\cdots)q^{3}+\cdots\)
27.3.b.a $1$ $0.736$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-13\) $-$ \(q+4q^{4}-13q^{7}-q^{13}+2^{4}q^{16}+11q^{19}+\cdots\)
27.3.b.b $2$ $0.736$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(10\) $-$ \(q+iq^{2}-5q^{4}-iq^{5}+5q^{7}-iq^{8}+\cdots\)
27.3.d.a $2$ $0.736$ \(\Q(\sqrt{-3}) \) None \(3\) \(0\) \(-6\) \(-2\) $-$ \(q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-4+2\zeta_{6})q^{5}+\cdots\)
27.3.f.a $30$ $0.736$ None \(-6\) \(-6\) \(-15\) \(-6\) $-$
27.4.a.a $1$ $1.593$ \(\Q\) None \(-3\) \(0\) \(-15\) \(-25\) $-$ \(q-3q^{2}+q^{4}-15q^{5}-5^{2}q^{7}+21q^{8}+\cdots\)
27.4.a.b $1$ $1.593$ \(\Q\) None \(3\) \(0\) \(15\) \(-25\) $+$ \(q+3q^{2}+q^{4}+15q^{5}-5^{2}q^{7}-21q^{8}+\cdots\)
27.4.a.c $2$ $1.593$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(22\) $+$ \(q+\beta q^{2}+10q^{4}-4\beta q^{5}+11q^{7}+2\beta q^{8}+\cdots\)
27.4.c.a $4$ $1.593$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(3\) \(0\) \(15\) \(-7\) $-$ \(q+(\beta _{1}+\beta _{3})q^{2}+(-4+\beta _{1}-3\beta _{2}+3\beta _{3})q^{4}+\cdots\)
27.4.e.a $48$ $1.593$ None \(-6\) \(-6\) \(6\) \(-6\) $-$
27.5.b.a $1$ $2.791$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(71\) $-$ \(q+2^{4}q^{4}+71q^{7}-337q^{13}+2^{8}q^{16}+\cdots\)
27.5.b.b $2$ $2.791$ \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(34\) $-$ \(q+\beta q^{2}-38q^{4}+2\beta q^{5}+17q^{7}-22\beta q^{8}+\cdots\)
27.5.b.c $2$ $2.791$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-38\) $-$ \(q+iq^{2}+7q^{4}+11iq^{5}-19q^{7}+23iq^{8}+\cdots\)
27.5.d.a $6$ $2.791$ 6.0.39400128.1 None \(3\) \(0\) \(12\) \(12\) $-$ \(q+\beta _{1}q^{2}+(4\beta _{1}+2\beta _{2}-\beta _{3}-3\beta _{4}+\cdots)q^{4}+\cdots\)
27.5.f.a $66$ $2.791$ None \(-6\) \(-6\) \(3\) \(-6\) $-$
27.6.a.a $1$ $4.330$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-211\) $+$ \(q-2^{5}q^{4}-211q^{7}-775q^{13}+2^{10}q^{16}+\cdots\)
27.6.a.b $2$ $4.330$ \(\Q(\sqrt{17}) \) None \(-9\) \(0\) \(-72\) \(-8\) $+$ \(q+(-4-\beta )q^{2}+(22+9\beta )q^{4}+(-41+\cdots)q^{5}+\cdots\)
27.6.a.c $2$ $4.330$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(0\) \(334\) $-$ \(q+\beta q^{2}+22q^{4}+8\beta q^{5}+167q^{7}+\cdots\)
27.6.a.d $2$ $4.330$ \(\Q(\sqrt{17}) \) None \(9\) \(0\) \(72\) \(-8\) $-$ \(q+(4+\beta )q^{2}+(22+9\beta )q^{4}+(41-10\beta )q^{5}+\cdots\)
27.6.c.a $8$ $4.330$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(-3\) \(0\) \(-78\) \(28\) $-$ \(q+(-1+\beta _{1}-\beta _{2}-\beta _{3})q^{2}+(-13\beta _{1}+\cdots)q^{4}+\cdots\)
27.6.e.a $84$ $4.330$ None \(-6\) \(-6\) \(-93\) \(-6\) $-$
27.7.b.a $2$ $6.211$ \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(-806\) $-$ \(q+\beta q^{2}-26q^{4}+14\beta q^{5}-403q^{7}+\cdots\)
27.7.b.b $2$ $6.211$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(598\) $-$ \(q+iq^{2}+28q^{4}-40iq^{5}+299q^{7}+\cdots\)
27.7.b.c $4$ $6.211$ \(\Q(i, \sqrt{41})\) None \(0\) \(0\) \(0\) \(-676\) $-$ \(q-\beta _{1}q^{2}+(-7^{2}+\beta _{3})q^{4}+(7\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
27.7.d.a $10$ $6.211$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(3\) \(0\) \(219\) \(-121\) $-$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-5^{2}\beta _{4}+\beta _{5})q^{4}+\cdots\)
27.7.f.a $102$ $6.211$ None \(-6\) \(-6\) \(210\) \(-6\) $-$
27.8.a.a $1$ $8.434$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1763\) $+$ \(q-2^{7}q^{4}+1763q^{7}+12605q^{13}+\cdots\)
27.8.a.b $2$ $8.434$ \(\Q(\sqrt{65}) \) None \(-9\) \(0\) \(-180\) \(700\) $-$ \(q+(-5-\beta )q^{2}+(43+9\beta )q^{4}+(-91+\cdots)q^{5}+\cdots\)
27.8.a.c $2$ $8.434$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-1118\) $-$ \(q+\beta q^{2}-20q^{4}-34\beta q^{5}-559q^{7}+\cdots\)
27.8.a.d $2$ $8.434$ \(\Q(\sqrt{42}) \) None \(0\) \(0\) \(0\) \(-2522\) $+$ \(q+\beta q^{2}+250q^{4}+20\beta q^{5}-1261q^{7}+\cdots\)
27.8.a.e $2$ $8.434$ \(\Q(\sqrt{65}) \) None \(9\) \(0\) \(180\) \(700\) $+$ \(q+(5+\beta )q^{2}+(43+9\beta )q^{4}+(91+2\beta )q^{5}+\cdots\)
27.8.c.a $12$ $8.434$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(9\) \(0\) \(180\) \(-84\) $-$ \(q+(-\beta _{1}+\beta _{6}+\beta _{7})q^{2}+(-52+3\beta _{6}+\cdots)q^{4}+\cdots\)
27.8.e.a $120$ $8.434$ None \(-6\) \(-6\) \(-219\) \(-6\) $-$
27.9.b.a $1$ $10.999$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(239\) $-$ \(q+2^{8}q^{4}+239q^{7}+56447q^{13}+2^{16}q^{16}+\cdots\)
27.9.b.b $2$ $10.999$ \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(3934\) $-$ \(q+\beta q^{2}-608q^{4}-28\beta q^{5}+1967q^{7}+\cdots\)
27.9.b.c $2$ $10.999$ \(\Q(\sqrt{-30}) \) None \(0\) \(0\) \(0\) \(-1358\) $-$ \(q+\beta q^{2}-14q^{4}+26\beta q^{5}-679q^{7}+\cdots\)
27.9.b.d $6$ $10.999$ 6.0.6171673600.1 None \(0\) \(0\) \(0\) \(-1698\) $-$ \(q+\beta _{1}q^{2}+(-131+\beta _{2})q^{4}+(20\beta _{1}+\cdots)q^{5}+\cdots\)
27.9.d.a $14$ $10.999$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(3\) \(0\) \(-438\) \(922\) $-$ \(q+\beta _{2}q^{2}+(-2\beta _{1}-2\beta _{2}+110\beta _{3}+\cdots)q^{4}+\cdots\)
27.9.f.a $138$ $10.999$ None \(-6\) \(-6\) \(-447\) \(-6\) $-$
27.10.a.a $2$ $13.906$ \(\Q(\sqrt{14}) \) None \(0\) \(0\) \(0\) \(-1526\) $+$ \(q+\beta q^{2}-8q^{4}-22\beta q^{5}-763q^{7}+\cdots\)
27.10.a.b $3$ $13.906$ 3.3.177113.1 None \(-3\) \(0\) \(1983\) \(-3693\) $-$ \(q+(-1-\beta _{1})q^{2}+(199-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
27.10.a.c $3$ $13.906$ 3.3.177113.1 None \(3\) \(0\) \(-1983\) \(-3693\) $+$ \(q+(1+\beta _{1})q^{2}+(199-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
27.10.a.d $4$ $13.906$ 4.4.203942560.1 None \(0\) \(0\) \(0\) \(11852\) $-$ \(q+\beta _{1}q^{2}+(559+\beta _{3})q^{4}+(-10\beta _{1}+\cdots)q^{5}+\cdots\)
27.10.c.a $16$ $13.906$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-15\) \(0\) \(-453\) \(-343\) $-$ \(q+(-2+\beta _{8}+2\beta _{9})q^{2}+(2\beta _{1}-2\beta _{8}+\cdots)q^{4}+\cdots\)
27.10.e.a $156$ $13.906$ None \(-6\) \(-6\) \(2382\) \(-6\) $-$
27.11.b.a $1$ $17.155$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(10907\) $-$ \(q+2^{10}q^{4}+10907q^{7}-141961q^{13}+\cdots\)
27.11.b.b $2$ $17.155$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-32186\) $-$ \(q-\zeta_{6}q^{2}-1676q^{4}+2^{4}\zeta_{6}q^{5}-16093q^{7}+\cdots\)
27.11.b.c $4$ $17.155$ \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None \(0\) \(0\) \(0\) \(20516\) $-$ \(q-\beta _{1}q^{2}+(-137-\beta _{3})q^{4}+(-43\beta _{1}+\cdots)q^{5}+\cdots\)
27.11.b.d $6$ $17.155$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(0\) \(4638\) $-$ \(q+\beta _{1}q^{2}+(-443+\beta _{2})q^{4}+(-26\beta _{1}+\cdots)q^{5}+\cdots\)
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