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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
92.2.a.a 92.a 1.a $1$ $0.735$ \(\Q\) None \(0\) \(-3\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-2q^{5}-4q^{7}+6q^{9}+2q^{11}+\cdots\)
92.2.a.b 92.a 1.a $1$ $0.735$ \(\Q\) None \(0\) \(1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}-2q^{9}-q^{13}-6q^{17}+\cdots\)
92.2.b.a 92.b 92.b $4$ $0.735$ \(\Q(i, \sqrt{14})\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{1})q^{2}+\beta _{1}q^{3}+2\beta _{1}q^{4}+\cdots\)
92.2.b.b 92.b 92.b $6$ $0.735$ 6.0.8869743.1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{2}+(-\beta _{2}-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots\)
92.2.e.a 92.e 23.c $20$ $0.735$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(2\) \(2\) \(2\) $\mathrm{SU}(2)[C_{11}]$ \(q+(1-\beta _{6}+\beta _{8}-\beta _{9}-\beta _{10}-\beta _{11}+\cdots)q^{3}+\cdots\)
92.2.h.a 92.h 92.h $100$ $0.735$ None \(-7\) \(0\) \(-22\) \(0\) $\mathrm{SU}(2)[C_{22}]$
92.3.c.a 92.c 4.b $22$ $2.507$ None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$
92.3.d.a 92.d 23.b $4$ $2.507$ 4.0.53792.1 None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}-\beta _{2}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
92.3.f.a 92.f 23.d $40$ $2.507$ None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
92.3.g.a 92.g 92.g $220$ $2.507$ None \(-11\) \(0\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{22}]$
92.4.a.a 92.a 1.a $3$ $5.428$ 3.3.1229.1 None \(0\) \(-4\) \(-10\) \(-46\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(-4-\beta _{1}+3\beta _{2})q^{5}+\cdots\)
92.4.a.b 92.a 1.a $3$ $5.428$ 3.3.28669.1 None \(0\) \(8\) \(0\) \(42\) $+$ $\mathrm{SU}(2)$ \(q+(3+\beta _{2})q^{3}+\beta _{1}q^{5}+(14-\beta _{1})q^{7}+\cdots\)
92.4.b.a 92.b 92.b $2$ $5.428$ \(\Q(\sqrt{-23}) \) \(\Q(\sqrt{-23}) \) \(-3\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-1-\beta )q^{2}+(-2+4\beta )q^{3}+(-5+\cdots)q^{4}+\cdots\)
92.4.b.b 92.b 92.b $4$ $5.428$ \(\Q(\sqrt{-3}, \sqrt{-23})\) \(\Q(\sqrt{-23}) \) \(3\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(1+\beta _{1}+\beta _{3})q^{2}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
92.4.b.c 92.b 92.b $28$ $5.428$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
92.4.e.a 92.e 23.c $60$ $5.428$ None \(0\) \(-4\) \(10\) \(4\) $\mathrm{SU}(2)[C_{11}]$
92.4.h.a 92.h 92.h $340$ $5.428$ None \(-11\) \(0\) \(-22\) \(0\) $\mathrm{SU}(2)[C_{22}]$
92.5.c.a 92.c 4.b $44$ $9.510$ None \(0\) \(0\) \(24\) \(0\) $\mathrm{SU}(2)[C_{2}]$
92.5.d.a 92.d 23.b $8$ $9.510$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{2})q^{3}+\beta _{3}q^{5}-\beta _{6}q^{7}+(40+\cdots)q^{9}+\cdots\)
92.5.f.a 92.f 23.d $80$ $9.510$ None \(0\) \(10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
92.5.g.a 92.g 92.g $460$ $9.510$ None \(-3\) \(0\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{22}]$
92.6.a.a 92.a 1.a $4$ $14.755$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(-7\) \(-36\) \(46\) $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{3}+(-9-2\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
92.6.a.b 92.a 1.a $4$ $14.755$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(29\) \(14\) \(248\) $-$ $\mathrm{SU}(2)$ \(q+(7+\beta _{1})q^{3}+(3+2\beta _{1}-\beta _{2})q^{5}+(62+\cdots)q^{7}+\cdots\)
92.6.b.a 92.b 92.b $6$ $14.755$ 6.0.8869743.1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-3\beta _{1}-2\beta _{3}+\beta _{4}+\beta _{5})q^{2}+(-5\beta _{1}+\cdots)q^{3}+\cdots\)
92.6.b.b 92.b 92.b $52$ $14.755$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
92.6.e.a 92.e 23.c $100$ $14.755$ None \(0\) \(2\) \(-86\) \(-118\) $\mathrm{SU}(2)[C_{11}]$
92.6.h.a 92.h 92.h $580$ $14.755$ None \(-11\) \(0\) \(-22\) \(0\) $\mathrm{SU}(2)[C_{22}]$
92.7.c.a 92.c 4.b $66$ $21.165$ None \(0\) \(0\) \(-44\) \(0\) $\mathrm{SU}(2)[C_{2}]$
92.7.d.a 92.d 23.b $12$ $21.165$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(32\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(3+\beta _{2})q^{3}-\beta _{1}q^{5}+\beta _{7}q^{7}+(320+\cdots)q^{9}+\cdots\)
92.7.f.a 92.f 23.d $120$ $21.165$ None \(0\) \(-32\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
92.7.g.a 92.g 92.g $700$ $21.165$ None \(-19\) \(0\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{22}]$
92.8.a.a 92.a 1.a $7$ $28.739$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-67\) \(-180\) \(-1640\) $-$ $\mathrm{SU}(2)$ \(q+(-10+\beta _{1})q^{3}+(-26-\beta _{5})q^{5}+\cdots\)
92.8.a.b 92.a 1.a $7$ $28.739$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(41\) \(70\) \(1246\) $+$ $\mathrm{SU}(2)$ \(q+(6-\beta _{1})q^{3}+(10-\beta _{1}-\beta _{2})q^{5}+(179+\cdots)q^{7}+\cdots\)
92.8.b.a 92.b 92.b $6$ $28.739$ 6.0.8869743.1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(3\beta _{1}-4\beta _{3}+\beta _{5})q^{2}+(-11\beta _{1}+18\beta _{3}+\cdots)q^{3}+\cdots\)
92.8.b.b 92.b 92.b $76$ $28.739$ None \(-16\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
92.8.e.a 92.e 23.c $140$ $28.739$ None \(0\) \(26\) \(110\) \(394\) $\mathrm{SU}(2)[C_{11}]$
92.8.h.a 92.h 92.h $820$ $28.739$ None \(5\) \(0\) \(-22\) \(0\) $\mathrm{SU}(2)[C_{22}]$
92.9.c.a 92.c 4.b $88$ $37.479$ None \(0\) \(0\) \(-336\) \(0\) $\mathrm{SU}(2)[C_{2}]$
92.9.d.a 92.d 23.b $16$ $37.479$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-70\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-4+\beta _{2})q^{3}+\beta _{1}q^{5}-\beta _{9}q^{7}+(1370+\cdots)q^{9}+\cdots\)
92.9.f.a 92.f 23.d $160$ $37.479$ None \(0\) \(70\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
92.9.g.a 92.g 92.g $940$ $37.479$ None \(-3\) \(0\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{22}]$
92.10.a.a 92.a 1.a $8$ $47.383$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-316\) \(154\) \(-9198\) $+$ $\mathrm{SU}(2)$ \(q+(-40+\beta _{1})q^{3}+(18+2\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
92.10.a.b 92.a 1.a $8$ $47.383$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(8\) \(1404\) \(18042\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{3}+(176-\beta _{3})q^{5}+(2255+\cdots)q^{7}+\cdots\)
92.10.b.a 92.b 92.b $2$ $47.383$ \(\Q(\sqrt{-23}) \) \(\Q(\sqrt{-23}) \) \(45\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(23-\beta )q^{2}+(22-44\beta )q^{3}+(523+\cdots)q^{4}+\cdots\)
92.10.b.b 92.b 92.b $4$ $47.383$ \(\Q(\sqrt{-3}, \sqrt{-23})\) \(\Q(\sqrt{-23}) \) \(-45\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-11+5\beta _{1}-6\beta _{2})q^{2}+(11+65\beta _{1}+\cdots)q^{3}+\cdots\)
92.10.b.c 92.b 92.b $100$ $47.383$ None \(32\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
92.10.e.a 92.e 23.c $180$ $47.383$ None \(0\) \(-148\) \(-226\) \(3812\) $\mathrm{SU}(2)[C_{11}]$
92.10.h.a 92.h 92.h $1060$ $47.383$ None \(-43\) \(0\) \(-22\) \(0\) $\mathrm{SU}(2)[C_{22}]$
92.11.c.a 92.c 4.b $110$ $58.453$ None \(0\) \(0\) \(3116\) \(0\) $\mathrm{SU}(2)[C_{2}]$
92.11.d.a 92.d 23.b $20$ $58.453$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(62\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(3+\beta _{2})q^{3}+\beta _{1}q^{5}+\beta _{10}q^{7}+(13723+\cdots)q^{9}+\cdots\)
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