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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
927.1.d.a 927.d 103.b $1$ $0.463$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-103}) \) \(\Q(\sqrt{309}) \) \(0\) \(0\) \(0\) \(2\) \(q-q^{4}+2q^{7}-2q^{13}+q^{16}+2q^{19}+\cdots\)
927.1.d.b 927.d 103.b $2$ $0.463$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-103}) \) None \(1\) \(0\) \(0\) \(-1\) \(q+(1-\beta )q^{2}+(1-\beta )q^{4}-\beta q^{7}+q^{8}+\cdots\)
927.1.d.c 927.d 103.b $4$ $0.463$ \(\Q(\zeta_{20})^+\) \(\Q(\sqrt{-103}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{7}+\cdots\)
927.1.v.a 927.v 103.f $16$ $0.463$ \(\Q(\zeta_{34})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+\zeta_{34}^{11}q^{4}+(\zeta_{34}^{2}+\zeta_{34}^{16})q^{7}+\cdots\)
927.2.a.a 927.a 1.a $1$ $7.402$ \(\Q\) None None \(1\) \(0\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
927.2.a.b 927.a 1.a $2$ $7.402$ \(\Q(\sqrt{5}) \) None None \(3\) \(0\) \(3\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3\beta q^{4}+(2-\beta )q^{5}-q^{7}+\cdots\)
927.2.a.c 927.a 1.a $3$ $7.402$ 3.3.148.1 None None \(-1\) \(0\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{5}+(-1+\cdots)q^{7}+\cdots\)
927.2.a.d 927.a 1.a $4$ $7.402$ \(\Q(\zeta_{24})^+\) None None \(0\) \(0\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{1}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
927.2.a.e 927.a 1.a $5$ $7.402$ 5.5.81509.1 None None \(2\) \(0\) \(5\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+(-\beta _{3}-\beta _{4})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
927.2.a.f 927.a 1.a $6$ $7.402$ 6.6.6999257.1 None None \(-4\) \(0\) \(-3\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
927.2.a.g 927.a 1.a $8$ $7.402$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(1\) \(0\) \(1\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}+(1+\beta _{5}+\cdots)q^{7}+\cdots\)
927.2.a.h 927.a 1.a $14$ $7.402$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(0\) \(0\) \(12\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+(1+\beta _{6}+\cdots)q^{7}+\cdots\)
927.2.c.a 927.c 309.c $16$ $7.402$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{13}q^{2}+\beta _{3}q^{4}-\beta _{8}q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
927.2.c.b 927.c 309.c $20$ $7.402$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) \(\Q(\sqrt{-103}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}-\beta _{6}q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots\)
927.2.e.a 927.e 9.c $102$ $7.402$ None None \(-11\) \(-1\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{3}]$
927.2.e.b 927.e 9.c $102$ $7.402$ None None \(9\) \(-1\) \(12\) \(0\) $\mathrm{SU}(2)[C_{3}]$
927.2.f.a 927.f 103.c $2$ $7.402$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-5\) $\mathrm{U}(1)[D_{3}]$ \(q+(2-2\zeta_{6})q^{4}+(-5+5\zeta_{6})q^{7}+5q^{13}+\cdots\)
927.2.f.b 927.f 103.c $2$ $7.402$ \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(-4\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}+(-4+4\zeta_{6})q^{5}+\cdots\)
927.2.f.c 927.f 103.c $16$ $7.402$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-1\) \(0\) \(5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{13}q^{2}+(\beta _{1}+2\beta _{6}+\beta _{12})q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots\)
927.2.f.d 927.f 103.c $16$ $7.402$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-1\) \(0\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-\beta _{3}+\beta _{13})q^{4}+(\beta _{2}-\beta _{12}+\cdots)q^{5}+\cdots\)
927.2.f.e 927.f 103.c $16$ $7.402$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(1\) \(0\) \(-3\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{4}-\beta _{5}+\beta _{7})q^{4}+\cdots\)
927.2.f.f 927.f 103.c $32$ $7.402$ None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{3}]$
927.2.g.a 927.g 927.g $204$ $7.402$ None None \(1\) \(-5\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$
927.2.h.a 927.h 927.h $204$ $7.402$ None None \(-2\) \(-5\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{3}]$
927.2.j.a 927.j 927.j $204$ $7.402$ None None \(0\) \(-3\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$
927.2.n.a 927.n 927.n $204$ $7.402$ None None \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
927.2.o.a 927.o 309.g $16$ $7.402$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(1+\beta _{10}+\beta _{11}+\beta _{12})q^{4}+\cdots\)
927.2.o.b 927.o 309.g $52$ $7.402$ None None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$
927.2.p.a 927.p 927.p $204$ $7.402$ None None \(-3\) \(3\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{6}]$
927.2.u.a 927.u 103.e $112$ $7.402$ None None \(15\) \(0\) \(11\) \(-5\) $\mathrm{SU}(2)[C_{17}]$
927.2.u.b 927.u 103.e $128$ $7.402$ None None \(-1\) \(0\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{17}]$
927.2.u.c 927.u 103.e $160$ $7.402$ None None \(1\) \(0\) \(4\) \(-12\) $\mathrm{SU}(2)[C_{17}]$
927.2.u.d 927.u 103.e $288$ $7.402$ None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{17}]$
927.2.w.a 927.w 309.k $576$ $7.402$ None None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{34}]$
927.2.y.a 927.y 927.y $3264$ $7.402$ None None \(-15\) \(-29\) \(-11\) \(-17\) $\mathrm{SU}(2)[C_{51}]$
927.2.z.a 927.z 927.z $3264$ $7.402$ None None \(-18\) \(-29\) \(-20\) \(-17\) $\mathrm{SU}(2)[C_{51}]$
927.2.ba.a 927.ba 103.g $32$ $7.402$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(5\) $\mathrm{U}(1)[D_{51}]$
927.2.ba.b 927.ba 103.g $256$ $7.402$ None None \(1\) \(0\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{51}]$
927.2.ba.c 927.ba 103.g $256$ $7.402$ None None \(33\) \(0\) \(37\) \(-29\) $\mathrm{SU}(2)[C_{51}]$
927.2.ba.d 927.ba 103.g $288$ $7.402$ None None \(-1\) \(0\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{51}]$
927.2.ba.e 927.ba 103.g $512$ $7.402$ None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{51}]$
927.2.bb.a 927.bb 927.ab $3264$ $7.402$ None None \(-15\) \(-32\) \(-17\) \(-17\) $\mathrm{SU}(2)[C_{51}]$
927.2.bg.a 927.bg 927.ag $3264$ $7.402$ None None \(-48\) \(-37\) \(-48\) \(-17\) $\mathrm{SU}(2)[C_{102}]$
927.2.bh.a 927.bh 309.o $1088$ $7.402$ None None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{102}]$
927.2.bi.a 927.bi 927.ai $3264$ $7.402$ None None \(-45\) \(-34\) \(-51\) \(-17\) $\mathrm{SU}(2)[C_{102}]$
927.2.bm.a 927.bm 927.am $3264$ $7.402$ None None \(-51\) \(-31\) \(-45\) \(-17\) $\mathrm{SU}(2)[C_{102}]$
927.3.b.a 927.b 3.b $68$ $25.259$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
927.3.d.a 927.d 103.b $5$ $25.259$ 5.5.33153125.1 \(\Q(\sqrt{-103}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{2}+(4+\beta _{1}+\beta _{4})q^{4}+(-4\beta _{1}+\cdots)q^{7}+\cdots\)
927.3.d.b 927.d 103.b $10$ $25.259$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) \(\Q(\sqrt{-103}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{2}+(4-\beta _{4})q^{4}+(-\beta _{4}+\beta _{6}+\cdots)q^{7}+\cdots\)
927.3.d.c 927.d 103.b $12$ $25.259$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{11}q^{2}+(1+\beta _{10})q^{4}-\beta _{3}q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots\)
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