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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
209.1.h.a $4$ $0.104$ \(\Q(\zeta_{12})\) None None \(0\) \(-2\) \(-2\) \(0\) $-$ \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{2}q^{3}-\zeta_{12}^{2}q^{5}+\cdots\)
209.1.m.a $4$ $0.104$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-2\) \(3\) $-$ \(q+\zeta_{10}^{4}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{5}+(1+\cdots)q^{7}+\cdots\)
209.2.a.a $1$ $1.669$ \(\Q\) None None \(0\) \(1\) \(-3\) \(-4\) $+$ \(q+q^{3}-2q^{4}-3q^{5}-4q^{7}-2q^{9}+\cdots\)
209.2.a.b $2$ $1.669$ \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(-2\) \(-4\) $+$ \(q+\beta q^{2}+(-1-\beta )q^{3}-q^{5}+(-2-\beta )q^{6}+\cdots\)
209.2.a.c $5$ $1.669$ 5.5.246832.1 None None \(2\) \(1\) \(-5\) \(6\) $-$ \(q+\beta _{2}q^{2}+\beta _{3}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
209.2.a.d $7$ $1.669$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(-1\) \(2\) \(2\) \(10\) $-$ \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(2+\beta _{2}+\beta _{3})q^{4}+\cdots\)
209.2.d.a $2$ $1.669$ \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(0\) $-$ \(q-2q^{4}+q^{5}+(1-2\beta )q^{7}+3q^{9}+(3+\cdots)q^{11}+\cdots\)
209.2.d.b $8$ $1.669$ 8.0.3288334336.3 None None \(0\) \(0\) \(-8\) \(0\) $-$ \(q+\beta _{7}q^{2}+\beta _{2}q^{3}-\beta _{3}q^{4}+(-1-\beta _{3}+\cdots)q^{5}+\cdots\)
209.2.d.c $8$ $1.669$ 8.0.484000000.9 None None \(0\) \(0\) \(4\) \(0\) $-$ \(q+\beta _{5}q^{2}+\beta _{2}q^{3}+(1+2\beta _{3})q^{4}+(2+\cdots)q^{5}+\cdots\)
209.2.e.a $18$ $1.669$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(-1\) \(-4\) \(0\) \(-6\) $-$ \(q-\beta _{1}q^{2}-\beta _{7}q^{3}+(-1-\beta _{4}-\beta _{9}+\cdots)q^{4}+\cdots\)
209.2.e.b $18$ $1.669$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(1\) \(0\) \(0\) \(-6\) $-$ \(q+\beta _{1}q^{2}+(\beta _{4}-\beta _{12})q^{3}+(-1+\beta _{3}+\cdots)q^{4}+\cdots\)
209.2.f.a $4$ $1.669$ \(\Q(\zeta_{10})\) None None \(-5\) \(-6\) \(-2\) \(-1\) $-$ \(q+(-1-\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
209.2.f.b $28$ $1.669$ None None \(-2\) \(1\) \(7\) \(-12\) $-$
209.2.f.c $40$ $1.669$ None None \(3\) \(3\) \(-9\) \(4\) $-$
209.2.g.a $16$ $1.669$ 16.0.\(\cdots\).1 None None \(0\) \(-12\) \(8\) \(0\) $-$ \(q+(-\beta _{1}+\beta _{5})q^{2}+(-1+\beta _{6})q^{3}+(-1+\cdots)q^{4}+\cdots\)
209.2.g.b $20$ $1.669$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(-12\) \(0\) $-$ \(q+(\beta _{1}-\beta _{6})q^{2}-\beta _{12}q^{3}+(-1+\beta _{3}+\cdots)q^{4}+\cdots\)
209.2.j.a $6$ $1.669$ \(\Q(\zeta_{18})\) None None \(3\) \(0\) \(6\) \(6\) $-$ \(q+(1-\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{2}+\cdots\)
209.2.j.b $42$ $1.669$ None None \(-3\) \(0\) \(-6\) \(-6\) $-$
209.2.j.c $48$ $1.669$ None None \(0\) \(0\) \(0\) \(0\) $-$
209.2.k.a $8$ $1.669$ 8.0.2036265625.1 \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-2\) \(-15\) $-$ \(q-2\beta _{6}q^{4}+(\beta _{1}-\beta _{3}+\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
209.2.k.b $8$ $1.669$ 8.0.484000000.9 None None \(0\) \(0\) \(4\) \(-10\) $-$ \(q+(-\beta _{1}-\beta _{4})q^{2}+(-1-\beta _{2}-3\beta _{3}+\cdots)q^{4}+\cdots\)
209.2.k.c $56$ $1.669$ None None \(0\) \(0\) \(-10\) \(20\) $-$
209.2.n.a $144$ $1.669$ None None \(-5\) \(-1\) \(-5\) \(-18\) $-$
209.2.p.a $108$ $1.669$ None None \(0\) \(-6\) \(-12\) \(0\) $-$
209.2.t.a $144$ $1.669$ None None \(-15\) \(-3\) \(-1\) \(-10\) $-$
209.2.u.a $432$ $1.669$ None None \(-18\) \(-24\) \(-18\) \(0\) $-$
209.2.w.a $432$ $1.669$ None None \(-30\) \(-24\) \(-18\) \(-30\) $-$
209.3.b.a $32$ $5.695$ None None \(0\) \(0\) \(0\) \(20\) $-$
209.3.c.a $36$ $5.695$ None None \(0\) \(-2\) \(-4\) \(0\) $-$
209.3.h.a $76$ $5.695$ None None \(0\) \(-6\) \(0\) \(0\) $-$
209.3.i.a $64$ $5.695$ None None \(0\) \(0\) \(0\) \(-20\) $-$
209.3.l.a $144$ $5.695$ None None \(0\) \(2\) \(4\) \(-15\) $-$
209.3.m.a $8$ $5.695$ 8.0.2036265625.1 \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(18\) \(-15\) $-$ \(q+4\beta _{1}q^{4}+(5+5\beta _{2}-4\beta _{3}+\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots\)
209.3.m.b $144$ $5.695$ None None \(0\) \(0\) \(-26\) \(0\) $-$
209.3.o.a $204$ $5.695$ None None \(0\) \(0\) \(0\) \(0\) $-$
209.3.q.a $228$ $5.695$ None None \(0\) \(0\) \(-12\) \(0\) $-$
209.3.r.a $304$ $5.695$ None None \(-9\) \(3\) \(-1\) \(-30\) $-$
209.3.s.a $304$ $5.695$ None None \(-5\) \(1\) \(-5\) \(10\) $-$
209.3.v.a $912$ $5.695$ None None \(-30\) \(-30\) \(-18\) \(-60\) $-$
209.3.x.a $912$ $5.695$ None None \(-18\) \(-30\) \(-18\) \(18\) $-$
209.4.a.a $8$ $12.331$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(-1\) \(-12\) \(-59\) $-$ \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(3+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
209.4.a.b $10$ $12.331$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(-6\) \(-9\) \(-10\) \(-53\) $-$ \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{4})q^{3}+(2+\cdots)q^{4}+\cdots\)
209.4.a.c $13$ $12.331$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None None \(-2\) \(11\) \(8\) \(39\) $+$ \(q-\beta _{1}q^{2}+(1+\beta _{5})q^{3}+(6+\beta _{2})q^{4}+\cdots\)
209.4.a.d $15$ $12.331$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None None \(4\) \(3\) \(10\) \(73\) $+$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(5+\beta _{2})q^{4}+(1+\beta _{6}+\cdots)q^{5}+\cdots\)
209.4.d.a $2$ $12.331$ \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-28\) \(0\) $-$ \(q-8q^{4}-14q^{5}-2\beta q^{7}+3^{3}q^{9}+(-20+\cdots)q^{11}+\cdots\)
209.4.d.b $56$ $12.331$ None None \(0\) \(0\) \(16\) \(0\) $-$
209.4.e.a $50$ $12.331$ None None \(-2\) \(-6\) \(0\) \(-20\) $-$
209.4.e.b $50$ $12.331$ None None \(2\) \(6\) \(0\) \(-20\) $-$
209.4.f.a $100$ $12.331$ None None \(2\) \(8\) \(26\) \(119\) $-$
209.4.f.b $116$ $12.331$ None None \(2\) \(-4\) \(-26\) \(-61\) $-$
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