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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
575.1.c.a 575.c 115.c $2$ $0.287$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}+q^{6}-iq^{8}+iq^{13}+\cdots\)
575.1.c.b 575.c 115.c $6$ $0.287$ 6.0.419904.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(-\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
575.1.d.a 575.d 23.b $1$ $0.287$ \(\Q\) \(\Q(\sqrt{-23}) \) None \(1\) \(1\) \(0\) \(0\) \(q+q^{2}+q^{3}+q^{6}-q^{8}+q^{13}-q^{16}+\cdots\)
575.1.d.b 575.d 23.b $3$ $0.287$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
575.1.d.c 575.d 23.b $3$ $0.287$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
575.2.a.a 575.a 1.a $1$ $4.591$ \(\Q\) None None \(-2\) \(-2\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-2q^{3}+2q^{4}+4q^{6}-q^{7}+\cdots\)
575.2.a.b 575.a 1.a $1$ $4.591$ \(\Q\) None None \(-2\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-q^{7}-3q^{9}+2q^{11}+\cdots\)
575.2.a.c 575.a 1.a $1$ $4.591$ \(\Q\) None None \(-1\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{7}+3q^{8}-3q^{9}-q^{11}+\cdots\)
575.2.a.d 575.a 1.a $1$ $4.591$ \(\Q\) None None \(1\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{7}-3q^{8}-3q^{9}-q^{11}+\cdots\)
575.2.a.e 575.a 1.a $1$ $4.591$ \(\Q\) None None \(2\) \(2\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{3}+2q^{4}+4q^{6}+q^{7}+\cdots\)
575.2.a.f 575.a 1.a $2$ $4.591$ \(\Q(\sqrt{5}) \) None None \(1\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
575.2.a.g 575.a 1.a $2$ $4.591$ \(\Q(\sqrt{5}) \) None None \(3\) \(2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+q^{3}+3\beta q^{4}+(1+\beta )q^{6}+\cdots\)
575.2.a.h 575.a 1.a $4$ $4.591$ 4.4.15317.1 None None \(-2\) \(2\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
575.2.a.i 575.a 1.a $4$ $4.591$ 4.4.5744.1 None None \(0\) \(-2\) \(0\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
575.2.a.j 575.a 1.a $4$ $4.591$ 4.4.5744.1 None None \(0\) \(2\) \(0\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
575.2.a.k 575.a 1.a $7$ $4.591$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(-1\) \(0\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
575.2.a.l 575.a 1.a $7$ $4.591$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(1\) \(0\) \(0\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
575.2.b.a 575.b 5.b $2$ $4.591$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-2q^{4}+iq^{7}+3q^{9}+2q^{11}+\cdots\)
575.2.b.b 575.b 5.b $2$ $4.591$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}-iq^{7}+3iq^{8}+3q^{9}+\cdots\)
575.2.b.c 575.b 5.b $4$ $4.591$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{3})q^{2}+\beta _{3}q^{3}+3\beta _{2}q^{4}+(1+\cdots)q^{6}+\cdots\)
575.2.b.d 575.b 5.b $4$ $4.591$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(2\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
575.2.b.e 575.b 5.b $8$ $4.591$ 8.0.\(\cdots\).11 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
575.2.b.f 575.b 5.b $14$ $4.591$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{10}q^{3}+(-2+\beta _{2})q^{4}+\cdots\)
575.2.e.a 575.e 115.e $4$ $4.591$ \(\Q(i, \sqrt{46})\) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+2\beta _{2}q^{4}+\beta _{1}q^{7}-3\beta _{2}q^{9}-4q^{16}+\cdots\)
575.2.e.b 575.e 115.e $8$ $4.591$ 8.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{2}+\beta _{1}q^{4}-\beta _{7}q^{7}+\beta _{5}q^{8}+\cdots\)
575.2.e.c 575.e 115.e $12$ $4.591$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta _{1}q^{2}-\beta _{10}q^{3}+(\beta _{6}-2\beta _{7}+\beta _{9}+\cdots)q^{4}+\cdots\)
575.2.e.d 575.e 115.e $20$ $4.591$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(4\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{2}-\beta _{2}q^{3}+\beta _{4}q^{4}+(-1+\beta _{3}+\cdots)q^{6}+\cdots\)
575.2.e.e 575.e 115.e $24$ $4.591$ \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$
575.2.g.a 575.g 25.d $4$ $4.591$ \(\Q(\zeta_{10})\) None None \(1\) \(-5\) \(-5\) \(4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
575.2.g.b 575.g 25.d $108$ $4.591$ None None \(-4\) \(1\) \(3\) \(24\) $\mathrm{SU}(2)[C_{5}]$
575.2.g.c 575.g 25.d $112$ $4.591$ None None \(1\) \(4\) \(-2\) \(-36\) $\mathrm{SU}(2)[C_{5}]$
575.2.i.a 575.i 25.e $216$ $4.591$ None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{10}]$
575.2.k.a 575.k 23.c $10$ $4.591$ \(\Q(\zeta_{22})\) None None \(-5\) \(-1\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{11}]$ \(q+(-\zeta_{22}-\zeta_{22}^{3}+\zeta_{22}^{4}-\zeta_{22}^{5}+\cdots)q^{2}+\cdots\)
575.2.k.b 575.k 23.c $10$ $4.591$ \(\Q(\zeta_{22})\) None None \(7\) \(7\) \(0\) \(5\) $\mathrm{SU}(2)[C_{11}]$ \(q+(1-\zeta_{22}-\zeta_{22}^{7}+\zeta_{22}^{8})q^{2}+(1+\cdots)q^{3}+\cdots\)
575.2.k.c 575.k 23.c $20$ $4.591$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(4\) \(-1\) \(0\) \(4\) $\mathrm{SU}(2)[C_{11}]$ \(q+(1-\beta _{2}-\beta _{3}-\beta _{4}-\beta _{6}-\beta _{8}+\beta _{13}+\cdots)q^{2}+\cdots\)
575.2.k.d 575.k 23.c $50$ $4.591$ None None \(5\) \(2\) \(0\) \(5\) $\mathrm{SU}(2)[C_{11}]$
575.2.k.e 575.k 23.c $80$ $4.591$ None None \(-2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{11}]$
575.2.k.f 575.k 23.c $80$ $4.591$ None None \(2\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{11}]$
575.2.k.g 575.k 23.c $100$ $4.591$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{11}]$
575.2.m.a 575.m 575.m $464$ $4.591$ None None \(-16\) \(-12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$
575.2.p.a 575.p 115.j $20$ $4.591$ \(\Q(\zeta_{44})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$ \(q+(-\zeta_{44}^{3}+\zeta_{44}^{5}+\zeta_{44}^{9}+\zeta_{44}^{13}+\cdots)q^{2}+\cdots\)
575.2.p.b 575.p 115.j $20$ $4.591$ \(\Q(\zeta_{44})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$ \(q+(-\zeta_{44}-\zeta_{44}^{5}+\zeta_{44}^{7}+\zeta_{44}^{11}+\cdots)q^{2}+\cdots\)
575.2.p.c 575.p 115.j $40$ $4.591$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
575.2.p.d 575.p 115.j $100$ $4.591$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
575.2.p.e 575.p 115.j $160$ $4.591$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
575.2.r.a 575.r 115.l $160$ $4.591$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{44}]$
575.2.r.b 575.r 115.l $200$ $4.591$ None None \(18\) \(14\) \(0\) \(22\) $\mathrm{SU}(2)[C_{44}]$
575.2.r.c 575.r 115.l $320$ $4.591$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{44}]$
575.2.s.a 575.s 575.s $2320$ $4.591$ None None \(-27\) \(-31\) \(-30\) \(-76\) $\mathrm{SU}(2)[C_{55}]$
575.2.u.a 575.u 575.u $2320$ $4.591$ None None \(-45\) \(-45\) \(-46\) \(0\) $\mathrm{SU}(2)[C_{110}]$
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