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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
418.2.a.a 418.a 1.a $1$ $3.338$ \(\Q\) None \(1\) \(-1\) \(-2\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-3q^{7}+\cdots\)
418.2.a.b 418.a 1.a $1$ $3.338$ \(\Q\) None \(1\) \(0\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}+2q^{7}+q^{8}-3q^{9}+\cdots\)
418.2.a.c 418.a 1.a $1$ $3.338$ \(\Q\) None \(1\) \(3\) \(-2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}+q^{4}-2q^{5}+3q^{6}+q^{7}+\cdots\)
418.2.a.d 418.a 1.a $2$ $3.338$ \(\Q(\sqrt{13}) \) None \(-2\) \(-3\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta )q^{3}+q^{4}+(-1+\beta )q^{5}+\cdots\)
418.2.a.e 418.a 1.a $2$ $3.338$ \(\Q(\sqrt{17}) \) None \(-2\) \(1\) \(4\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta )q^{3}+q^{4}+2q^{5}+(-1+\cdots)q^{6}+\cdots\)
418.2.a.f 418.a 1.a $2$ $3.338$ \(\Q(\sqrt{21}) \) None \(2\) \(-1\) \(3\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta q^{3}+q^{4}+(2-\beta )q^{5}-\beta q^{6}+\cdots\)
418.2.a.g 418.a 1.a $3$ $3.338$ 3.3.621.1 None \(-3\) \(0\) \(-3\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{1}-\beta _{2})q^{5}+\cdots\)
418.2.a.h 418.a 1.a $3$ $3.338$ 3.3.469.1 None \(3\) \(1\) \(5\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(2-\beta _{1})q^{5}+\beta _{1}q^{6}+\cdots\)
418.2.b.a 418.b 209.d $2$ $3.338$ \(\Q(\sqrt{-10}) \) None \(-2\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}-2q^{5}+\beta q^{7}-q^{8}+3q^{9}+\cdots\)
418.2.b.b 418.b 209.d $2$ $3.338$ \(\Q(\sqrt{-10}) \) None \(2\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{4}-2q^{5}+\beta q^{7}+q^{8}+3q^{9}+\cdots\)
418.2.b.c 418.b 209.d $8$ $3.338$ 8.0.\(\cdots\).1 None \(-8\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\beta _{3}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{3}q^{6}+\cdots\)
418.2.b.d 418.b 209.d $8$ $3.338$ 8.0.\(\cdots\).1 None \(8\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta _{3}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{3}q^{6}+\cdots\)
418.2.e.a 418.e 19.c $2$ $3.338$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-2\) \(-1\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
418.2.e.b 418.e 19.c $2$ $3.338$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
418.2.e.c 418.e 19.c $2$ $3.338$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(4\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(4-4\zeta_{6})q^{5}+\cdots\)
418.2.e.d 418.e 19.c $2$ $3.338$ \(\Q(\sqrt{-3}) \) None \(-1\) \(2\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
418.2.e.e 418.e 19.c $2$ $3.338$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(3\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
418.2.e.f 418.e 19.c $2$ $3.338$ \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(3\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
418.2.e.g 418.e 19.c $4$ $3.338$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-1+\beta _{1})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
418.2.e.h 418.e 19.c $6$ $3.338$ 6.0.591408.1 None \(-3\) \(2\) \(-2\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{2}+(-\beta _{1}+\beta _{4})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
418.2.e.i 418.e 19.c $6$ $3.338$ 6.0.101617200.1 None \(3\) \(0\) \(-6\) \(12\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{2}-\beta _{1}q^{3}+(-1+\beta _{4})q^{4}-2\beta _{4}q^{5}+\cdots\)
418.2.f.a 418.f 11.c $4$ $3.338$ \(\Q(\zeta_{10})\) None \(-1\) \(-4\) \(-8\) \(-7\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
418.2.f.b 418.f 11.c $4$ $3.338$ \(\Q(\zeta_{10})\) None \(-1\) \(0\) \(8\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
418.2.f.c 418.f 11.c $4$ $3.338$ \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(-1\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
418.2.f.d 418.f 11.c $4$ $3.338$ \(\Q(\zeta_{10})\) None \(-1\) \(2\) \(2\) \(9\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
418.2.f.e 418.f 11.c $4$ $3.338$ \(\Q(\zeta_{10})\) None \(-1\) \(5\) \(3\) \(-7\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
418.2.f.f 418.f 11.c $16$ $3.338$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-4\) \(0\) \(4\) \(6\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{4}q^{2}+(-1+\beta _{1}+\beta _{2}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots\)
418.2.f.g 418.f 11.c $16$ $3.338$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(4\) \(1\) \(1\) \(-12\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1+\beta _{6}-\beta _{8}+\beta _{10})q^{2}+\beta _{1}q^{3}+\cdots\)
418.2.f.h 418.f 11.c $20$ $3.338$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(5\) \(-1\) \(-1\) \(13\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{9}q^{2}-\beta _{4}q^{3}+(-1+\beta _{8}+\beta _{9}+\cdots)q^{4}+\cdots\)
418.2.h.a 418.h 209.g $20$ $3.338$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-10\) \(3\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{10}q^{2}+\beta _{3}q^{3}+(-1+\beta _{10})q^{4}+\cdots\)
418.2.h.b 418.h 209.g $20$ $3.338$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(10\) \(3\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{10})q^{2}+\beta _{4}q^{3}-\beta _{10}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
418.2.j.a 418.j 19.e $24$ $3.338$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
418.2.j.b 418.j 19.e $24$ $3.338$ None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{9}]$
418.2.j.c 418.j 19.e $30$ $3.338$ None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{9}]$
418.2.j.d 418.j 19.e $30$ $3.338$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
418.2.m.a 418.m 209.k $40$ $3.338$ None \(-10\) \(0\) \(2\) \(-5\) $\mathrm{SU}(2)[C_{10}]$
418.2.m.b 418.m 209.k $40$ $3.338$ None \(10\) \(0\) \(2\) \(-5\) $\mathrm{SU}(2)[C_{10}]$
418.2.n.a 418.n 209.n $8$ $3.338$ \(\Q(\zeta_{15})\) None \(-1\) \(6\) \(7\) \(-2\) $\mathrm{SU}(2)[C_{15}]$ \(q+(\zeta_{15}+\zeta_{15}^{6})q^{2}+(2\zeta_{15}-2\zeta_{15}^{5}+\cdots)q^{3}+\cdots\)
418.2.n.b 418.n 209.n $8$ $3.338$ \(\Q(\zeta_{15})\) None \(1\) \(-2\) \(-5\) \(6\) $\mathrm{SU}(2)[C_{15}]$ \(q+(-\zeta_{15}-\zeta_{15}^{6})q^{2}+(2-2\zeta_{15}+2\zeta_{15}^{3}+\cdots)q^{3}+\cdots\)
418.2.n.c 418.n 209.n $8$ $3.338$ \(\Q(\zeta_{15})\) None \(1\) \(2\) \(1\) \(6\) $\mathrm{SU}(2)[C_{15}]$ \(q+(-\zeta_{15}-\zeta_{15}^{6})q^{2}+(-2+2\zeta_{15}+\cdots)q^{3}+\cdots\)
418.2.n.d 418.n 209.n $64$ $3.338$ None \(-8\) \(-6\) \(-7\) \(22\) $\mathrm{SU}(2)[C_{15}]$
418.2.n.e 418.n 209.n $72$ $3.338$ None \(9\) \(-2\) \(8\) \(-20\) $\mathrm{SU}(2)[C_{15}]$
418.2.q.a 418.q 209.p $60$ $3.338$ None \(0\) \(-3\) \(0\) \(-18\) $\mathrm{SU}(2)[C_{18}]$
418.2.q.b 418.q 209.p $60$ $3.338$ None \(0\) \(-3\) \(0\) \(18\) $\mathrm{SU}(2)[C_{18}]$
418.2.s.a 418.s 209.t $80$ $3.338$ None \(-10\) \(-3\) \(-2\) \(-10\) $\mathrm{SU}(2)[C_{30}]$
418.2.s.b 418.s 209.t $80$ $3.338$ None \(10\) \(-3\) \(-2\) \(-10\) $\mathrm{SU}(2)[C_{30}]$
418.2.u.a 418.u 209.u $216$ $3.338$ None \(0\) \(0\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{45}]$
418.2.u.b 418.u 209.u $264$ $3.338$ None \(0\) \(6\) \(0\) \(-15\) $\mathrm{SU}(2)[C_{45}]$
418.2.v.a 418.v 209.w $240$ $3.338$ None \(0\) \(3\) \(0\) \(33\) $\mathrm{SU}(2)[C_{90}]$
418.2.v.b 418.v 209.w $240$ $3.338$ None \(0\) \(3\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{90}]$
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