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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
207.1.d.a $1$ $0.103$ \(\Q\) \(\Q(\sqrt{-23}) \) None \(1\) \(0\) \(0\) \(0\) $-$ \(q+q^{2}-q^{8}-q^{13}-q^{16}-q^{23}+q^{25}+\cdots\)
207.1.f.a $6$ $0.103$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{2}+\zeta_{18}^{2}q^{3}+(-\zeta_{18}^{3}+\cdots)q^{4}+\cdots\)
207.2.a.a $1$ $1.653$ \(\Q\) None None \(-1\) \(0\) \(0\) \(-2\) $+$ \(q-q^{2}-q^{4}-2q^{7}+3q^{8}-4q^{11}+\cdots\)
207.2.a.b $2$ $1.653$ \(\Q(\sqrt{2}) \) None None \(-2\) \(0\) \(-4\) \(-4\) $+$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(-2-\beta )q^{5}+\cdots\)
207.2.a.c $2$ $1.653$ \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(2\) \(2\) $-$ \(q-\beta q^{2}+3q^{4}+(1+\beta )q^{5}+(1-\beta )q^{7}+\cdots\)
207.2.a.d $2$ $1.653$ \(\Q(\sqrt{5}) \) None None \(1\) \(0\) \(2\) \(2\) $-$ \(q+\beta q^{2}+(-1+\beta )q^{4}+2\beta q^{5}+(2-2\beta )q^{7}+\cdots\)
207.2.a.e $2$ $1.653$ \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(4\) \(-4\) $-$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(2-\beta )q^{5}+\cdots\)
207.2.c.a $8$ $1.653$ 8.0.3057647616.5 None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{2}-\beta _{5}q^{4}-\beta _{7}q^{5}+\beta _{6}q^{7}+\cdots\)
207.2.e.a $16$ $1.653$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-1\) \(-1\) \(0\) \(7\) $-$ \(q-\beta _{1}q^{2}+(-\beta _{8}+\beta _{14})q^{3}+(-1+\beta _{7}+\cdots)q^{4}+\cdots\)
207.2.e.b $28$ $1.653$ None None \(-1\) \(-1\) \(0\) \(-9\) $-$
207.2.g.a $12$ $1.653$ 12.0.\(\cdots\).2 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{10}q^{2}+\beta _{7}q^{3}+(2-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
207.2.g.b $32$ $1.653$ None None \(-6\) \(-6\) \(0\) \(0\) $-$
207.2.i.a $10$ $1.653$ \(\Q(\zeta_{22})\) None None \(-4\) \(0\) \(3\) \(6\) $-$ \(q+(-1+\zeta_{22}-\zeta_{22}^{2}-\zeta_{22}^{4}-\zeta_{22}^{6}+\cdots)q^{2}+\cdots\)
207.2.i.b $10$ $1.653$ \(\Q(\zeta_{22})\) None None \(4\) \(0\) \(-5\) \(-8\) $-$ \(q+(1+\zeta_{22}^{2}-\zeta_{22}^{3}+\zeta_{22}^{4}-\zeta_{22}^{5}+\cdots)q^{2}+\cdots\)
207.2.i.c $10$ $1.653$ \(\Q(\zeta_{22})\) None None \(7\) \(0\) \(3\) \(-5\) $-$ \(q+(1-\zeta_{22}-\zeta_{22}^{7}+\zeta_{22}^{8})q^{2}+(1+\cdots)q^{4}+\cdots\)
207.2.i.d $20$ $1.653$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(4\) \(0\) \(6\) \(-6\) $-$ \(q+(-\beta _{1}-\beta _{3}+\beta _{4}-\beta _{5}-2\beta _{6}-2\beta _{7}+\cdots)q^{2}+\cdots\)
207.2.i.e $40$ $1.653$ None None \(0\) \(0\) \(0\) \(8\) $-$
207.2.k.a $80$ $1.653$ None None \(0\) \(0\) \(0\) \(0\) $-$
207.2.m.a $440$ $1.653$ None None \(-9\) \(-20\) \(-11\) \(-9\) $-$
207.2.o.a $440$ $1.653$ None None \(-27\) \(-16\) \(-33\) \(-11\) $-$
207.3.b.a $16$ $5.640$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{2}+(-3+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)
207.3.d.a $3$ $5.640$ 3.3.621.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\beta _{1}q^{2}+(4-\beta _{1}+\beta _{2})q^{4}+(7-4\beta _{1}+\cdots)q^{8}+\cdots\)
207.3.d.b $4$ $5.640$ 4.0.27648.1 None None \(-4\) \(0\) \(0\) \(0\) $-$ \(q+(-1-\beta _{3})q^{2}+(3+2\beta _{3})q^{4}+\beta _{2}q^{5}+\cdots\)
207.3.d.c $4$ $5.640$ 4.0.27648.1 None None \(4\) \(0\) \(0\) \(0\) $-$ \(q+(1+\beta _{3})q^{2}+(3+2\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots\)
207.3.d.d $8$ $5.640$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(4\) \(0\) \(0\) \(0\) $-$ \(q+(1+\beta _{3})q^{2}+\beta _{5}q^{4}+\beta _{1}q^{5}-\beta _{6}q^{7}+\cdots\)
207.3.f.a $12$ $5.640$ 12.0.\(\cdots\).2 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+(\beta _{1}+\beta _{5}-\beta _{9}-\beta _{10}-\beta _{11})q^{2}+\cdots\)
207.3.f.b $80$ $5.640$ None None \(-2\) \(-6\) \(0\) \(0\) $-$
207.3.h.a $88$ $5.640$ None None \(0\) \(4\) \(0\) \(2\) $-$
207.3.j.a $30$ $5.640$ None None \(11\) \(0\) \(11\) \(-11\) $-$
207.3.j.b $80$ $5.640$ None None \(-4\) \(0\) \(0\) \(0\) $-$
207.3.j.c $80$ $5.640$ None None \(0\) \(0\) \(0\) \(0\) $-$
207.3.l.a $160$ $5.640$ None None \(0\) \(0\) \(0\) \(0\) $-$
207.3.n.a $920$ $5.640$ None None \(-27\) \(-20\) \(-45\) \(-9\) $-$
207.3.p.a $920$ $5.640$ None None \(-9\) \(-16\) \(-11\) \(-11\) $-$
207.4.a.a $1$ $12.213$ \(\Q\) None None \(2\) \(0\) \(6\) \(-8\) $-$ \(q+2q^{2}-4q^{4}+6q^{5}-8q^{7}-24q^{8}+\cdots\)
207.4.a.b $2$ $12.213$ \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(-8\) \(-28\) $-$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(-4-4\beta )q^{5}+\cdots\)
207.4.a.c $2$ $12.213$ \(\Q(\sqrt{5}) \) None None \(4\) \(0\) \(26\) \(-10\) $+$ \(q+(2+\beta )q^{2}+(1+4\beta )q^{4}+(13-\beta )q^{5}+\cdots\)
207.4.a.d $4$ $12.213$ 4.4.2009704.1 None None \(-4\) \(0\) \(-4\) \(-14\) $-$ \(q+(-1+\beta _{1})q^{2}+(7-2\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
207.4.a.e $4$ $12.213$ 4.4.334189.1 None None \(-2\) \(0\) \(-14\) \(16\) $+$ \(q+(-1-\beta _{3})q^{2}+(6-3\beta _{1}-2\beta _{2}-2\beta _{3})q^{4}+\cdots\)
207.4.a.f $4$ $12.213$ 4.4.1140200.1 None None \(2\) \(0\) \(2\) \(32\) $+$ \(q-\beta _{1}q^{2}+(6-\beta _{1}-2\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
207.4.a.g $5$ $12.213$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(-4\) \(0\) \(-20\) \(-10\) $-$ \(q+(-1+\beta _{1})q^{2}+(3-\beta _{1}+\beta _{2})q^{4}+\cdots\)
207.4.a.h $5$ $12.213$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(4\) \(0\) \(20\) \(-10\) $+$ \(q+(1-\beta _{1})q^{2}+(3-\beta _{1}+\beta _{2})q^{4}+(4+\cdots)q^{5}+\cdots\)
207.4.c.a $24$ $12.213$ None None \(0\) \(0\) \(0\) \(0\) $-$
207.4.e.a $60$ $12.213$ None None \(2\) \(-1\) \(0\) \(62\) $-$
207.4.e.b $72$ $12.213$ None None \(2\) \(-1\) \(0\) \(-50\) $-$
207.4.g.a $12$ $12.213$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+(-\beta _{4}+\beta _{6}+\beta _{8}+\beta _{9}+2\beta _{10}-\beta _{11})q^{2}+\cdots\)
207.4.g.b $128$ $12.213$ None None \(-6\) \(0\) \(0\) \(0\) $-$
207.4.i.a $50$ $12.213$ None None \(11\) \(0\) \(19\) \(-19\) $-$
207.4.i.b $60$ $12.213$ None None \(-4\) \(0\) \(6\) \(-4\) $-$
207.4.i.c $60$ $12.213$ None None \(0\) \(0\) \(-22\) \(24\) $-$
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