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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
93.1.l.a 93.l 93.l $4$ $0.046$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-3}) \) None 93.1.l.a \(0\) \(-1\) \(0\) \(-2\) \(q-\zeta_{10}q^{3}-\zeta_{10}^{3}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots\)
93.2.a.a 93.a 1.a $2$ $0.743$ \(\Q(\sqrt{5}) \) None None 93.2.a.a \(-3\) \(-2\) \(-4\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(-3+\cdots)q^{5}+\cdots\)
93.2.a.b 93.a 1.a $3$ $0.743$ 3.3.229.1 None None 93.2.a.b \(0\) \(3\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
93.2.c.a 93.c 93.c $8$ $0.743$ 8.0.\(\cdots\).2 None None 93.2.c.a \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+\beta _{6}q^{3}+\beta _{3}q^{4}+\beta _{1}q^{5}+\cdots\)
93.2.e.a 93.e 31.c $4$ $0.743$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None 93.2.e.a \(0\) \(2\) \(4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{2}+(1+\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
93.2.e.b 93.e 31.c $6$ $0.743$ 6.0.591408.1 None None 93.2.e.b \(0\) \(-3\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{2}-\beta _{4}q^{3}+(1-\beta _{2}+\beta _{3})q^{4}+\cdots\)
93.2.f.a 93.f 31.d $8$ $0.743$ \(\Q(\zeta_{15})\) None None 93.2.f.a \(3\) \(2\) \(-6\) \(9\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{15}+\zeta_{15}^{3})q^{2}+(1+\zeta_{15}^{2}+\cdots)q^{3}+\cdots\)
93.2.f.b 93.f 31.d $16$ $0.743$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None 93.2.f.b \(-3\) \(-4\) \(6\) \(-7\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{1}q^{2}+\beta _{8}q^{3}+(-1-\beta _{8}-\beta _{9}+\cdots)q^{4}+\cdots\)
93.2.g.a 93.g 93.g $2$ $0.743$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None 93.2.g.a \(0\) \(-3\) \(0\) \(4\) $\mathrm{U}(1)[D_{6}]$ \(q+(-1-\zeta_{6})q^{3}+2q^{4}+(4-4\zeta_{6})q^{7}+\cdots\)
93.2.g.b 93.g 93.g $2$ $0.743$ \(\Q(\sqrt{-3}) \) None None 93.2.g.b \(0\) \(0\) \(3\) \(1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-2\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-q^{4}+\cdots\)
93.2.g.c 93.g 93.g $2$ $0.743$ \(\Q(\sqrt{-3}) \) None None 93.2.g.b \(0\) \(3\) \(-3\) \(1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+2\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-q^{4}+\cdots\)
93.2.g.d 93.g 93.g $4$ $0.743$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None 93.2.g.d \(0\) \(-6\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{2}+(-1+\beta _{1})q^{3}-4q^{4}+\beta _{3}q^{5}+\cdots\)
93.2.g.e 93.g 93.g $4$ $0.743$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None 93.2.g.e \(0\) \(1\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(1-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
93.2.g.f 93.g 93.g $4$ $0.743$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None 93.2.g.e \(0\) \(2\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(1-\beta _{1}+\beta _{3})q^{3}+\cdots\)
93.2.k.a 93.k 93.k $32$ $0.743$ None None 93.2.k.a \(0\) \(-5\) \(0\) \(8\) $\mathrm{SU}(2)[C_{10}]$
93.2.m.a 93.m 31.g $16$ $0.743$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None 93.2.m.a \(0\) \(-2\) \(6\) \(-9\) $\mathrm{SU}(2)[C_{15}]$ \(q+(-\beta _{7}+\beta _{12}+\beta _{13})q^{2}+(-1+\beta _{2}+\cdots)q^{3}+\cdots\)
93.2.m.b 93.m 31.g $24$ $0.743$ None None 93.2.m.b \(0\) \(3\) \(-6\) \(-1\) $\mathrm{SU}(2)[C_{15}]$
93.2.p.a 93.p 93.p $8$ $0.743$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-3}) \) None 93.2.p.a \(0\) \(3\) \(0\) \(-4\) $\mathrm{U}(1)[D_{30}]$ \(q+(\zeta_{15}^{2}+2\zeta_{15}^{7})q^{3}+2\zeta_{15}^{6}q^{4}+\cdots\)
93.2.p.b 93.p 93.p $64$ $0.743$ None None 93.2.p.b \(0\) \(-10\) \(0\) \(-26\) $\mathrm{SU}(2)[C_{30}]$
93.3.b.a 93.b 3.b $20$ $2.534$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None 93.3.b.a \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(-2+\beta _{2})q^{4}+\beta _{11}q^{5}+\cdots\)
93.3.d.a 93.d 31.b $2$ $2.534$ \(\Q(\sqrt{-3}) \) None None 93.3.d.a \(-6\) \(0\) \(-12\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-3q^{2}-\zeta_{6}q^{3}+5q^{4}-6q^{5}+3\zeta_{6}q^{6}+\cdots\)
93.3.d.b 93.d 31.b $8$ $2.534$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None 93.3.d.b \(6\) \(0\) \(12\) \(-20\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{5})q^{2}+\beta _{1}q^{3}+(2-\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots\)
93.3.h.a 93.h 93.h $2$ $2.534$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None 93.3.h.a \(0\) \(3\) \(0\) \(-2\) $\mathrm{U}(1)[D_{6}]$ \(q+3\zeta_{6}q^{3}+4q^{4}-2\zeta_{6}q^{7}+(-9+9\zeta_{6})q^{9}+\cdots\)
93.3.h.b 93.h 93.h $36$ $2.534$ None None 93.3.h.b \(0\) \(-2\) \(0\) \(-14\) $\mathrm{SU}(2)[C_{6}]$
93.3.i.a 93.i 31.e $10$ $2.534$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None 93.3.i.a \(-6\) \(15\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{8}-\beta _{9})q^{2}+(1+\beta _{2})q^{3}+\cdots\)
93.3.i.b 93.i 31.e $12$ $2.534$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None 93.3.i.b \(6\) \(-18\) \(0\) \(9\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{3})q^{2}+(-2+\beta _{5})q^{3}+(3-\beta _{2}+\cdots)q^{4}+\cdots\)
93.3.j.a 93.j 31.f $40$ $2.534$ None None 93.3.j.a \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{10}]$
93.3.l.a 93.l 93.l $8$ $2.534$ 8.0.3844000000.4 None None 93.3.l.a \(0\) \(-6\) \(0\) \(24\) $\mathrm{SU}(2)[C_{10}]$ \(q+\beta _{1}q^{2}-3\beta _{3}q^{3}+(-2-3\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots\)
93.3.l.b 93.l 93.l $72$ $2.534$ None None 93.3.l.b \(0\) \(5\) \(0\) \(-54\) $\mathrm{SU}(2)[C_{10}]$
93.3.n.a 93.n 31.h $40$ $2.534$ None None 93.3.n.a \(6\) \(-15\) \(0\) \(11\) $\mathrm{SU}(2)[C_{30}]$
93.3.n.b 93.n 31.h $48$ $2.534$ None None 93.3.n.b \(-6\) \(18\) \(0\) \(1\) $\mathrm{SU}(2)[C_{30}]$
93.3.o.a 93.o 93.o $8$ $2.534$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-3}) \) None 93.3.o.a \(0\) \(-3\) \(0\) \(2\) $\mathrm{U}(1)[D_{30}]$ \(q-3\zeta_{15}^{4}q^{3}+(-4\zeta_{15}^{2}-4\zeta_{15}^{7})q^{4}+\cdots\)
93.3.o.b 93.o 93.o $144$ $2.534$ None None 93.3.o.b \(0\) \(-8\) \(0\) \(14\) $\mathrm{SU}(2)[C_{30}]$
93.4.a.a 93.a 1.a $1$ $5.487$ \(\Q\) None None 93.4.a.a \(3\) \(-3\) \(-9\) \(-34\) $-$ $\mathrm{SU}(2)$ \(q+3q^{2}-3q^{3}+q^{4}-9q^{5}-9q^{6}+\cdots\)
93.4.a.b 93.a 1.a $2$ $5.487$ \(\Q(\sqrt{29}) \) None None 93.4.a.b \(-5\) \(-6\) \(8\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+(-2-\beta )q^{2}-3q^{3}+(3+5\beta )q^{4}+\cdots\)
93.4.a.c 93.a 1.a $2$ $5.487$ \(\Q(\sqrt{17}) \) None None 93.4.a.c \(-3\) \(6\) \(-8\) \(-37\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+3q^{3}+(-3+3\beta )q^{4}+\cdots\)
93.4.a.d 93.a 1.a $2$ $5.487$ \(\Q(\sqrt{41}) \) None None 93.4.a.d \(-1\) \(-6\) \(-11\) \(29\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-3q^{3}+(2+\beta )q^{4}+(-7+3\beta )q^{5}+\cdots\)
93.4.a.e 93.a 1.a $3$ $5.487$ 3.3.2089.1 None None 93.4.a.e \(3\) \(-9\) \(8\) \(19\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}-3q^{3}+(1+3\beta _{1}+2\beta _{2})q^{4}+\cdots\)
93.4.a.f 93.a 1.a $6$ $5.487$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None 93.4.a.f \(3\) \(18\) \(12\) \(47\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+3q^{3}+(6+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)
93.4.c.a 93.c 93.c $2$ $5.487$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None 93.4.c.a \(0\) \(0\) \(0\) \(40\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{6}q^{3}+8q^{4}+20q^{7}-3^{3}q^{9}-8\zeta_{6}q^{12}+\cdots\)
93.4.c.b 93.c 93.c $28$ $5.487$ None None 93.4.c.b \(0\) \(0\) \(0\) \(-64\) $\mathrm{SU}(2)[C_{2}]$
93.4.e.a 93.e 31.c $14$ $5.487$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None 93.4.e.a \(-6\) \(-21\) \(-4\) \(-17\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+3\beta _{3}q^{3}+(3-\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots\)
93.4.e.b 93.e 31.c $18$ $5.487$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None 93.4.e.b \(6\) \(27\) \(4\) \(-9\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{2}+3\beta _{4}q^{3}+(5-\beta _{2})q^{4}+(\beta _{5}+\cdots)q^{5}+\cdots\)
93.4.f.a 93.f 31.d $32$ $5.487$ None None 93.4.f.a \(0\) \(-24\) \(-54\) \(-25\) $\mathrm{SU}(2)[C_{5}]$
93.4.f.b 93.f 31.d $32$ $5.487$ None None 93.4.f.b \(0\) \(24\) \(54\) \(-25\) $\mathrm{SU}(2)[C_{5}]$
93.4.g.a 93.g 93.g $60$ $5.487$ None None 93.4.g.a \(0\) \(-3\) \(0\) \(24\) $\mathrm{SU}(2)[C_{6}]$
93.4.k.a 93.k 93.k $8$ $5.487$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-3}) \) None 93.4.k.a \(0\) \(0\) \(0\) \(-40\) $\mathrm{U}(1)[D_{10}]$ \(q+\zeta_{15}^{6}q^{3}+8\zeta_{15}^{2}q^{4}+(-10-10\zeta_{15}^{2}+\cdots)q^{7}+\cdots\)
93.4.k.b 93.k 93.k $112$ $5.487$ None None 93.4.k.b \(0\) \(-5\) \(0\) \(24\) $\mathrm{SU}(2)[C_{10}]$
93.4.m.a 93.m 31.g $56$ $5.487$ None None 93.4.m.a \(6\) \(21\) \(54\) \(32\) $\mathrm{SU}(2)[C_{15}]$
93.4.m.b 93.m 31.g $72$ $5.487$ None None 93.4.m.b \(-6\) \(-27\) \(-54\) \(24\) $\mathrm{SU}(2)[C_{15}]$
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