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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.2.a.a 126.a 1.a $1$ $1.006$ \(\Q\) None \(-1\) \(0\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots\)
126.2.a.b 126.a 1.a $1$ $1.006$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}-4q^{13}+q^{14}+\cdots\)
126.2.e.a 126.e 63.h $2$ $1.006$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(1-2\zeta_{6})q^{3}+q^{4}-3\zeta_{6}q^{5}+\cdots\)
126.2.e.b 126.e 63.h $2$ $1.006$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(1-2\zeta_{6})q^{3}+q^{4}+3\zeta_{6}q^{5}+\cdots\)
126.2.e.c 126.e 63.h $6$ $1.006$ 6.0.309123.1 None \(-6\) \(2\) \(1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-\beta _{2}-\beta _{4})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
126.2.e.d 126.e 63.h $6$ $1.006$ 6.0.309123.1 None \(6\) \(-2\) \(-5\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(\beta _{3}-\beta _{4}-\beta _{5})q^{3}+q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
126.2.f.a 126.f 9.c $2$ $1.006$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
126.2.f.b 126.f 9.c $2$ $1.006$ \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(2-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
126.2.f.c 126.f 9.c $4$ $1.006$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(4\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2})q^{2}+(1-\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
126.2.f.d 126.f 9.c $4$ $1.006$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(2\) \(-1\) \(-3\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-1+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
126.2.g.a 126.g 7.c $2$ $1.006$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
126.2.g.b 126.g 7.c $2$ $1.006$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(3\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
126.2.g.c 126.g 7.c $2$ $1.006$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
126.2.g.d 126.g 7.c $2$ $1.006$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
126.2.h.a 126.h 63.g $2$ $1.006$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(-6\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
126.2.h.b 126.h 63.g $2$ $1.006$ \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(6\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
126.2.h.c 126.h 63.g $6$ $1.006$ 6.0.309123.1 None \(-3\) \(4\) \(10\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{2}+(1-\beta _{5})q^{3}+(-1-\beta _{4})q^{4}+\cdots\)
126.2.h.d 126.h 63.g $6$ $1.006$ 6.0.309123.1 None \(3\) \(2\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{2}+(\beta _{1}+\beta _{2}-\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)
126.2.k.a 126.k 21.g $8$ $1.006$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{24}-\zeta_{24}^{3})q^{2}+(1-\zeta_{24}^{2})q^{4}+\cdots\)
126.2.l.a 126.l 63.i $16$ $1.006$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{6}q^{2}-\beta _{11}q^{3}-q^{4}+(1+\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
126.2.m.a 126.m 63.o $16$ $1.006$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{10}q^{2}-\beta _{1}q^{3}+\beta _{5}q^{4}+(\beta _{1}-\beta _{6}+\cdots)q^{5}+\cdots\)
126.2.t.a 126.t 63.s $16$ $1.006$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}+\beta _{6})q^{2}+(-\beta _{11}-\beta _{14})q^{3}+\cdots\)
126.3.b.a 126.b 3.b $4$ $3.433$ \(\Q(\sqrt{-2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-2q^{4}+(-\beta _{1}+2\beta _{2})q^{5}+\cdots\)
126.3.c.a 126.c 7.b $4$ $3.433$ \(\Q(\sqrt{2}, \sqrt{-33})\) None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+2q^{4}-\beta _{2}q^{5}+(-4+\beta _{3})q^{7}+\cdots\)
126.3.c.b 126.c 7.b $4$ $3.433$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+2q^{4}+(2\beta _{2}-\beta _{3})q^{5}+(2+\cdots)q^{7}+\cdots\)
126.3.i.a 126.i 63.n $32$ $3.433$ None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$
126.3.j.a 126.j 63.k $32$ $3.433$ None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$
126.3.n.a 126.n 7.d $4$ $3.433$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(-12\) \(-10\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(-2+2\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
126.3.n.b 126.n 7.d $4$ $3.433$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(14\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(2\beta _{1}+4\beta _{3})q^{5}+\cdots\)
126.3.n.c 126.n 7.d $4$ $3.433$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(6\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(1-2\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
126.3.o.a 126.o 63.l $32$ $3.433$ None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$
126.3.p.a 126.p 63.t $32$ $3.433$ None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$
126.3.q.a 126.q 9.d $24$ $3.433$ None \(0\) \(0\) \(36\) \(0\) $\mathrm{SU}(2)[C_{6}]$
126.3.r.a 126.r 63.j $32$ $3.433$ None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$
126.3.s.a 126.s 21.h $4$ $3.433$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(-14\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+3\beta _{1}q^{5}+(-7+\cdots)q^{7}+\cdots\)
126.3.s.b 126.s 21.h $4$ $3.433$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(26\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+\beta _{1}q^{5}+(5+3\beta _{2}+\cdots)q^{7}+\cdots\)
126.4.a.a 126.a 1.a $1$ $7.434$ \(\Q\) None \(-2\) \(0\) \(-18\) \(7\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}-18q^{5}+7q^{7}-8q^{8}+\cdots\)
126.4.a.b 126.a 1.a $1$ $7.434$ \(\Q\) None \(-2\) \(0\) \(-6\) \(7\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}-6q^{5}+7q^{7}-8q^{8}+\cdots\)
126.4.a.c 126.a 1.a $1$ $7.434$ \(\Q\) None \(-2\) \(0\) \(-2\) \(-7\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}-2q^{5}-7q^{7}-8q^{8}+\cdots\)
126.4.a.d 126.a 1.a $1$ $7.434$ \(\Q\) None \(-2\) \(0\) \(12\) \(7\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+12q^{5}+7q^{7}-8q^{8}+\cdots\)
126.4.a.e 126.a 1.a $1$ $7.434$ \(\Q\) None \(-2\) \(0\) \(22\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+22q^{5}-7q^{7}-8q^{8}+\cdots\)
126.4.a.f 126.a 1.a $1$ $7.434$ \(\Q\) None \(2\) \(0\) \(-22\) \(-7\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}-22q^{5}-7q^{7}+8q^{8}+\cdots\)
126.4.a.g 126.a 1.a $1$ $7.434$ \(\Q\) None \(2\) \(0\) \(6\) \(7\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+6q^{5}+7q^{7}+8q^{8}+\cdots\)
126.4.a.h 126.a 1.a $1$ $7.434$ \(\Q\) None \(2\) \(0\) \(14\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+14q^{5}-7q^{7}+8q^{8}+\cdots\)
126.4.d.a 126.d 21.c $8$ $7.434$ 8.0.\(\cdots\).6 None \(0\) \(0\) \(0\) \(40\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-4q^{4}-\beta _{5}q^{5}+(5+\beta _{7})q^{7}+\cdots\)
126.4.e.a 126.e 63.h $24$ $7.434$ None \(-48\) \(-2\) \(10\) \(-5\) $\mathrm{SU}(2)[C_{3}]$
126.4.e.b 126.e 63.h $24$ $7.434$ None \(48\) \(2\) \(10\) \(17\) $\mathrm{SU}(2)[C_{3}]$
126.4.f.a 126.f 9.c $6$ $7.434$ 6.0.309123.1 None \(6\) \(-12\) \(-9\) \(-21\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\beta _{3}q^{2}+(-2-\beta _{1}+\beta _{5})q^{3}+(-4+\cdots)q^{4}+\cdots\)
126.4.f.b 126.f 9.c $8$ $7.434$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(9\) \(1\) \(28\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2-2\beta _{1})q^{2}+(2+\beta _{1}-\beta _{2})q^{3}+\cdots\)
126.4.f.c 126.f 9.c $10$ $7.434$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(4\) \(1\) \(35\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\beta _{3})q^{2}-\beta _{2}q^{3}-4\beta _{3}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
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