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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
176.1.h.a 176.h 11.b $1$ $0.088$ \(\Q\) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(-1\) \(0\) \(q+q^{3}-q^{5}-q^{11}-q^{15}+q^{23}-q^{27}+\cdots\)
176.2.a.a 176.a 1.a $1$ $1.405$ \(\Q\) None None \(0\) \(-1\) \(-3\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}-2q^{7}-2q^{9}+q^{11}+\cdots\)
176.2.a.b 176.a 1.a $1$ $1.405$ \(\Q\) None None \(0\) \(1\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+2q^{7}-2q^{9}-q^{11}+4q^{13}+\cdots\)
176.2.a.c 176.a 1.a $1$ $1.405$ \(\Q\) None None \(0\) \(3\) \(-3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-3q^{5}+2q^{7}+6q^{9}+q^{11}+\cdots\)
176.2.a.d 176.a 1.a $2$ $1.405$ \(\Q(\sqrt{17}) \) None None \(0\) \(-1\) \(3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(2-\beta )q^{5}+2\beta q^{7}+(1+\beta )q^{9}+\cdots\)
176.2.e.a 176.e 44.c $2$ $1.405$ \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(6\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta q^{3}+3q^{5}-8q^{9}+\beta q^{11}-3\beta q^{15}+\cdots\)
176.2.e.b 176.e 44.c $4$ $1.405$ \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(-6\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{3}+(-2+\beta _{3})q^{5}+(-1+\beta _{3})q^{9}+\cdots\)
176.2.i.a 176.i 176.i $44$ $1.405$ None None \(0\) \(-4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$
176.2.j.a 176.j 16.e $40$ $1.405$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
176.2.m.a 176.m 11.c $4$ $1.405$ \(\Q(\zeta_{10})\) None None \(0\) \(-3\) \(3\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+(1+\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
176.2.m.b 176.m 11.c $4$ $1.405$ \(\Q(\zeta_{10})\) None None \(0\) \(1\) \(3\) \(7\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(1+\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
176.2.m.c 176.m 11.c $4$ $1.405$ \(\Q(\zeta_{10})\) None None \(0\) \(4\) \(-6\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(-2+\cdots)q^{5}+\cdots\)
176.2.m.d 176.m 11.c $8$ $1.405$ 8.0.682515625.5 None None \(0\) \(1\) \(-3\) \(-7\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{1}-\beta _{4}+\beta _{6})q^{3}+(\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
176.2.q.a 176.q 44.g $8$ $1.405$ 8.0.484000000.6 None None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+\beta _{1}q^{3}+(\beta _{2}-\beta _{3}+\beta _{5})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
176.2.q.b 176.q 44.g $16$ $1.405$ 16.0.\(\cdots\).1 None None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\beta _{2}+\beta _{4}-\beta _{6}-\beta _{9}+\beta _{11})q^{3}+(1+\cdots)q^{5}+\cdots\)
176.2.w.a 176.w 176.w $176$ $1.405$ None None \(-6\) \(-6\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{20}]$
176.2.x.a 176.x 176.x $176$ $1.405$ None None \(-10\) \(-6\) \(-6\) \(-20\) $\mathrm{SU}(2)[C_{20}]$
176.3.d.a 176.d 4.b $2$ $4.796$ \(\Q(\sqrt{-11}) \) None None \(0\) \(0\) \(10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{3}+5q^{5}-2\beta q^{7}-2q^{9}+\beta q^{11}+\cdots\)
176.3.d.b 176.d 4.b $8$ $4.796$ 8.0.\(\cdots\).2 None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{4}-\beta _{5}+\beta _{7})q^{7}+\cdots\)
176.3.h.a 176.h 11.b $1$ $4.796$ \(\Q\) \(\Q(\sqrt{-11}) \) None \(0\) \(5\) \(-1\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+5q^{3}-q^{5}+2^{4}q^{9}+11q^{11}-5q^{15}+\cdots\)
176.3.h.b 176.h 11.b $2$ $4.796$ \(\Q(\sqrt{33}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(-5\) \(1\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-2-\beta )q^{3}+(2-3\beta )q^{5}+(3+5\beta )q^{9}+\cdots\)
176.3.h.c 176.h 11.b $2$ $4.796$ \(\Q(\sqrt{-2}) \) None None \(0\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-q^{5}+\beta q^{7}-8q^{9}+(-7-\beta )q^{11}+\cdots\)
176.3.h.d 176.h 11.b $6$ $4.796$ 6.0.1750426112.2 None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{1})q^{3}+\beta _{3}q^{5}-\beta _{2}q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots\)
176.3.k.a 176.k 16.f $80$ $4.796$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
176.3.l.a 176.l 176.l $92$ $4.796$ None None \(0\) \(-4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$
176.3.n.a 176.n 11.d $4$ $4.796$ \(\Q(\zeta_{10})\) None None \(0\) \(0\) \(-4\) \(-10\) $\mathrm{SU}(2)[C_{10}]$ \(q+(2-3\zeta_{10}+3\zeta_{10}^{2}-2\zeta_{10}^{3})q^{3}+\cdots\)
176.3.n.b 176.n 11.d $8$ $4.796$ 8.0.64000000.1 None None \(0\) \(2\) \(2\) \(30\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-1-\beta _{1}+2\beta _{2}+\beta _{3}-2\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
176.3.n.c 176.n 11.d $8$ $4.796$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(5\) \(-1\) \(-15\) $\mathrm{SU}(2)[C_{10}]$ \(q+(1-\beta _{2}+\beta _{4})q^{3}+(-1+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
176.3.n.d 176.n 11.d $24$ $4.796$ None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
176.3.r.a 176.r 44.h $16$ $4.796$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q-\beta _{11}q^{3}+(-2\beta _{4}+\beta _{6}-\beta _{7}+\beta _{10}+\cdots)q^{5}+\cdots\)
176.3.r.b 176.r 44.h $32$ $4.796$ None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{10}]$
176.3.u.a 176.u 176.u $368$ $4.796$ None None \(-10\) \(-6\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{20}]$
176.3.v.a 176.v 176.v $368$ $4.796$ None None \(-6\) \(-6\) \(-6\) \(-12\) $\mathrm{SU}(2)[C_{20}]$
176.4.a.a 176.a 1.a $1$ $10.384$ \(\Q\) None None \(0\) \(-7\) \(9\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-7q^{3}+9q^{5}-2q^{7}+22q^{9}+11q^{11}+\cdots\)
176.4.a.b 176.a 1.a $1$ $10.384$ \(\Q\) None None \(0\) \(-4\) \(14\) \(8\) $+$ $\mathrm{SU}(2)$ \(q-4q^{3}+14q^{5}+8q^{7}-11q^{9}+11q^{11}+\cdots\)
176.4.a.c 176.a 1.a $1$ $10.384$ \(\Q\) None None \(0\) \(-1\) \(-3\) \(10\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}+10q^{7}-26q^{9}-11q^{11}+\cdots\)
176.4.a.d 176.a 1.a $1$ $10.384$ \(\Q\) None None \(0\) \(1\) \(-7\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-7q^{5}+6q^{7}-26q^{9}+11q^{11}+\cdots\)
176.4.a.e 176.a 1.a $1$ $10.384$ \(\Q\) None None \(0\) \(5\) \(-7\) \(26\) $+$ $\mathrm{SU}(2)$ \(q+5q^{3}-7q^{5}+26q^{7}-2q^{9}+11q^{11}+\cdots\)
176.4.a.f 176.a 1.a $1$ $10.384$ \(\Q\) None None \(0\) \(7\) \(-19\) \(-14\) $-$ $\mathrm{SU}(2)$ \(q+7q^{3}-19q^{5}-14q^{7}+22q^{9}-11q^{11}+\cdots\)
176.4.a.g 176.a 1.a $2$ $10.384$ \(\Q(\sqrt{97}) \) None None \(0\) \(-9\) \(11\) \(-10\) $-$ $\mathrm{SU}(2)$ \(q+(-4-\beta )q^{3}+(6-\beta )q^{5}+(-8+6\beta )q^{7}+\cdots\)
176.4.a.h 176.a 1.a $2$ $10.384$ \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(-6\) \(56\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-3+4\beta )q^{5}+(28+\beta )q^{7}+\cdots\)
176.4.a.i 176.a 1.a $2$ $10.384$ \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(2\) \(-20\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(1+2\beta )q^{5}+(-10+\beta )q^{7}+\cdots\)
176.4.a.j 176.a 1.a $3$ $10.384$ 3.3.11109.1 None None \(0\) \(-2\) \(8\) \(-24\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(3+\beta _{2})q^{5}+(-8+\cdots)q^{7}+\cdots\)
176.4.e.a 176.e 44.c $2$ $10.384$ \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(-36\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2\beta q^{3}-18q^{5}-17q^{9}+11\beta q^{11}+\cdots\)
176.4.e.b 176.e 44.c $2$ $10.384$ \(\Q(\sqrt{-19}) \) None None \(0\) \(0\) \(14\) \(-40\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{3}+7q^{5}-20q^{7}+8q^{9}+(20+\cdots)q^{11}+\cdots\)
176.4.e.c 176.e 44.c $2$ $10.384$ \(\Q(\sqrt{-19}) \) None None \(0\) \(0\) \(14\) \(40\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{3}+7q^{5}+20q^{7}+8q^{9}+(-20+\cdots)q^{11}+\cdots\)
176.4.e.d 176.e 44.c $4$ $10.384$ \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(36\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-2\beta _{1}-\beta _{2})q^{3}+(9+\beta _{3})q^{5}+(-2^{5}+\cdots)q^{9}+\cdots\)
176.4.e.e 176.e 44.c $8$ $10.384$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(-28\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{2}+\beta _{3})q^{3}+(-4+\beta _{1})q^{5}-\beta _{4}q^{7}+\cdots\)
176.4.i.a 176.i 176.i $140$ $10.384$ None None \(0\) \(-4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$
176.4.j.a 176.j 16.e $120$ $10.384$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
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