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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
297.1.h.a 297.h 99.h $2$ $0.148$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None 99.1.h.a \(0\) \(0\) \(-1\) \(0\) \(q+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{11}-\zeta_{6}q^{16}+\cdots\)
297.1.q.a 297.q 297.q $6$ $0.148$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-11}) \) None 297.1.q.a \(0\) \(0\) \(-3\) \(0\) \(q+\zeta_{18}^{8}q^{3}+\zeta_{18}^{2}q^{4}+(-\zeta_{18}^{3}-\zeta_{18}^{7}+\cdots)q^{5}+\cdots\)
297.2.a.a 297.a 1.a $1$ $2.372$ \(\Q\) None None 297.2.a.a \(-2\) \(0\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-2q^{5}+q^{7}+4q^{10}+\cdots\)
297.2.a.b 297.a 1.a $1$ $2.372$ \(\Q\) None None 297.2.a.b \(-1\) \(0\) \(2\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+2q^{5}-5q^{7}+3q^{8}-2q^{10}+\cdots\)
297.2.a.c 297.a 1.a $1$ $2.372$ \(\Q\) None None 297.2.a.b \(1\) \(0\) \(-2\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-2q^{5}-5q^{7}-3q^{8}-2q^{10}+\cdots\)
297.2.a.d 297.a 1.a $1$ $2.372$ \(\Q\) None None 297.2.a.a \(2\) \(0\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+2q^{5}+q^{7}+4q^{10}+\cdots\)
297.2.a.e 297.a 1.a $2$ $2.372$ \(\Q(\sqrt{3}) \) None None 297.2.a.e \(-2\) \(0\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
297.2.a.f 297.a 1.a $2$ $2.372$ \(\Q(\sqrt{3}) \) None None 297.2.a.e \(2\) \(0\) \(2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(2+2\beta )q^{4}+(1-\beta )q^{5}+\cdots\)
297.2.a.g 297.a 1.a $3$ $2.372$ 3.3.564.1 None None 297.2.a.g \(-1\) \(0\) \(2\) \(7\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
297.2.a.h 297.a 1.a $3$ $2.372$ 3.3.564.1 None None 297.2.a.g \(1\) \(0\) \(-2\) \(7\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
297.2.d.a 297.d 33.d $8$ $2.372$ 8.0.\(\cdots\).14 None None 297.2.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{7}q^{2}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}-\beta _{3}q^{7}+\cdots\)
297.2.d.b 297.d 33.d $8$ $2.372$ 8.0.764411904.5 None None 297.2.d.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{2}+(1+\beta _{5})q^{4}+\beta _{2}q^{5}+(\beta _{4}+\cdots)q^{7}+\cdots\)
297.2.e.a 297.e 9.c $2$ $2.372$ \(\Q(\sqrt{-3}) \) None None 99.2.e.c \(-2\) \(0\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots\)
297.2.e.b 297.e 9.c $2$ $2.372$ \(\Q(\sqrt{-3}) \) None None 99.2.e.b \(0\) \(0\) \(-3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{4}-3\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+\cdots\)
297.2.e.c 297.e 9.c $2$ $2.372$ \(\Q(\sqrt{-3}) \) None None 99.2.e.a \(1\) \(0\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-4+\cdots)q^{7}+\cdots\)
297.2.e.d 297.e 9.c $6$ $2.372$ \(\Q(\zeta_{18})\) None None 99.2.e.d \(0\) \(0\) \(3\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta_{5}+\beta_{4}+\cdots-\beta_{2})q^{2}+\cdots+\beta_{5} q^{4}+\cdots\)
297.2.e.e 297.e 9.c $8$ $2.372$ 8.0.508277025.1 None None 99.2.e.e \(1\) \(0\) \(4\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{2}+\beta _{6})q^{2}+(\beta _{3}+3\beta _{5})q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots\)
297.2.f.a 297.f 11.c $16$ $2.372$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None 297.2.f.a \(-2\) \(0\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{6}+\beta _{12})q^{2}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
297.2.f.b 297.f 11.c $16$ $2.372$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None 297.2.f.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{12}q^{2}+(-\beta _{2}-\beta _{5}+\beta _{6}-\beta _{7}+\cdots)q^{4}+\cdots\)
297.2.f.c 297.f 11.c $16$ $2.372$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None 297.2.f.c \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{4}q^{2}+(1+\beta _{2}-2\beta _{3}-\beta _{5}-\beta _{6}+\cdots)q^{4}+\cdots\)
297.2.f.d 297.f 11.c $16$ $2.372$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None 297.2.f.a \(2\) \(0\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{6}-\beta _{12})q^{2}+(-1-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
297.2.g.a 297.g 99.g $4$ $2.372$ \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) None 99.2.g.a \(0\) \(0\) \(9\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(2-2\beta _{2})q^{4}+(2-\beta _{1}+\beta _{2})q^{5}+(\beta _{2}+\cdots)q^{11}+\cdots\)
297.2.g.b 297.g 99.g $16$ $2.372$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None 99.2.g.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{2}+\beta _{7}+\beta _{9}-\beta _{12}+\cdots)q^{4}+\cdots\)
297.2.j.a 297.j 27.e $6$ $2.372$ \(\Q(\zeta_{18})\) None None 297.2.j.a \(-3\) \(-9\) \(-9\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}^{2}-\zeta_{18}^{3})q^{2}+(-2+\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
297.2.j.b 297.j 27.e $72$ $2.372$ None None 297.2.j.b \(3\) \(9\) \(12\) \(3\) $\mathrm{SU}(2)[C_{9}]$
297.2.j.c 297.j 27.e $102$ $2.372$ None None 297.2.j.c \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{9}]$
297.2.k.a 297.k 33.f $32$ $2.372$ None None 297.2.k.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
297.2.k.b 297.k 33.f $32$ $2.372$ None None 297.2.k.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
297.2.n.a 297.n 99.m $8$ $2.372$ \(\Q(\zeta_{15})\) None None 99.2.m.a \(4\) \(0\) \(-6\) \(-1\) $\mathrm{SU}(2)[C_{15}]$ \(q+(-\zeta_{15}-\zeta_{15}^{2}-\zeta_{15}^{5}-\zeta_{15}^{6}+\cdots)q^{2}+\cdots\)
297.2.n.b 297.n 99.m $72$ $2.372$ None None 99.2.m.b \(1\) \(0\) \(8\) \(-2\) $\mathrm{SU}(2)[C_{15}]$
297.2.o.a 297.o 297.o $12$ $2.372$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-11}) \) None 297.2.o.a \(0\) \(0\) \(9\) \(0\) $\mathrm{U}(1)[D_{18}]$ \(q+(\beta _{3}-\beta _{7}-\beta _{9}-\beta _{10})q^{3}+(2\beta _{3}-2\beta _{7}+\cdots)q^{4}+\cdots\)
297.2.o.b 297.o 297.o $192$ $2.372$ None None 297.2.o.b \(0\) \(-12\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{18}]$
297.2.t.a 297.t 99.p $80$ $2.372$ None None 99.2.p.a \(15\) \(0\) \(6\) \(-5\) $\mathrm{SU}(2)[C_{30}]$
297.2.u.a 297.u 297.u $816$ $2.372$ None None 297.2.u.a \(-18\) \(-18\) \(-21\) \(-18\) $\mathrm{SU}(2)[C_{45}]$
297.2.x.a 297.x 297.x $816$ $2.372$ None None 297.2.x.a \(-30\) \(-18\) \(-21\) \(-30\) $\mathrm{SU}(2)[C_{90}]$
297.3.b.a 297.b 3.b $2$ $8.093$ \(\Q(\sqrt{-11}) \) None None 297.3.b.a \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{2}-7q^{4}-\beta q^{5}-2q^{7}+3\beta q^{8}+\cdots\)
297.3.b.b 297.b 3.b $4$ $8.093$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None 297.3.b.b \(0\) \(0\) \(0\) \(22\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{3}q^{4}+(\beta _{1}-4\beta _{2})q^{5}+(5+\cdots)q^{7}+\cdots\)
297.3.b.c 297.b 3.b $8$ $8.093$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None 297.3.b.c \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-4+\beta _{2})q^{4}+(-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\)
297.3.b.d 297.b 3.b $12$ $8.093$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None 297.3.b.d \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+(-1-\beta _{1})q^{4}+(\beta _{5}-\beta _{9}+\cdots)q^{5}+\cdots\)
297.3.c.a 297.c 11.b $16$ $8.093$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None 297.3.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{11}q^{2}+(-2-\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)
297.3.c.b 297.c 11.b $16$ $8.093$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None 297.3.c.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{8}q^{2}+(-2+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots\)
297.3.h.a 297.h 99.h $4$ $8.093$ \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) None 99.3.h.a \(0\) \(0\) \(1\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(-4-4\beta _{1})q^{4}+(1+\beta _{1}-\beta _{3})q^{5}+\cdots\)
297.3.h.b 297.h 99.h $40$ $8.093$ None None 99.3.h.b \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
297.3.i.a 297.i 9.d $40$ $8.093$ None None 99.3.i.a \(0\) \(0\) \(9\) \(2\) $\mathrm{SU}(2)[C_{6}]$
297.3.l.a 297.l 11.d $64$ $8.093$ None None 297.3.l.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
297.3.l.b 297.l 11.d $64$ $8.093$ None None 297.3.l.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
297.3.m.a 297.m 33.h $8$ $8.093$ 8.0.484000000.6 None None 297.3.m.a \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\beta _{1}-\beta _{4})q^{2}+(-1-\beta _{2}-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)
297.3.m.b 297.m 33.h $24$ $8.093$ None None 297.3.m.b \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{10}]$
297.3.m.c 297.m 33.h $32$ $8.093$ None None 297.3.m.c \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{10}]$
297.3.m.d 297.m 33.h $64$ $8.093$ None None 297.3.m.d \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{10}]$
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