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Label Char Prim Dim $A$ Field CM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
234.2.a.a 234.a 1.a $1$ $1.868$ \(\Q\) None 234.2.a.a \(-1\) \(0\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-2q^{7}-q^{8}+2q^{10}+\cdots\)
234.2.a.b 234.a 1.a $1$ $1.868$ \(\Q\) None 26.2.a.b \(-1\) \(0\) \(1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
234.2.a.c 234.a 1.a $1$ $1.868$ \(\Q\) None 78.2.a.a \(1\) \(0\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}+4q^{7}+q^{8}-2q^{10}+\cdots\)
234.2.a.d 234.a 1.a $1$ $1.868$ \(\Q\) None 234.2.a.a \(1\) \(0\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}-2q^{7}+q^{8}+2q^{10}+\cdots\)
234.2.a.e 234.a 1.a $1$ $1.868$ \(\Q\) None 26.2.a.a \(1\) \(0\) \(3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{5}-q^{7}+q^{8}+3q^{10}+\cdots\)
234.2.b.a 234.b 13.b $2$ $1.868$ \(\Q(\sqrt{-1}) \) None 78.2.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{5}+2iq^{7}-iq^{8}+\cdots\)
234.2.b.b 234.b 13.b $2$ $1.868$ \(\Q(\sqrt{-1}) \) None 26.2.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}-3iq^{5}-3iq^{7}-iq^{8}+\cdots\)
234.2.e.a 234.e 9.c $2$ $1.868$ \(\Q(\sqrt{-3}) \) None 234.2.e.a \(-1\) \(3\) \(2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
234.2.e.b 234.e 9.c $4$ $1.868$ \(\Q(\zeta_{12})\) None 234.2.e.b \(2\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{12}q^{2}-\zeta_{12}^{2}q^{3}+(-1+\zeta_{12}+\cdots)q^{4}+\cdots\)
234.2.e.c 234.e 9.c $4$ $1.868$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 234.2.e.c \(2\) \(2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
234.2.e.d 234.e 9.c $6$ $1.868$ 6.0.309123.1 None 234.2.e.d \(3\) \(-2\) \(2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{2}+(\beta _{2}+\beta _{4})q^{3}+(-1-\beta _{4}+\cdots)q^{4}+\cdots\)
234.2.e.e 234.e 9.c $8$ $1.868$ 8.0.508277025.1 None 234.2.e.e \(-4\) \(3\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{7})q^{2}+(-\beta _{3}+\beta _{4})q^{3}-\beta _{7}q^{4}+\cdots\)
234.2.f.a 234.f 117.h $2$ $1.868$ \(\Q(\sqrt{-3}) \) None 234.2.f.a \(-2\) \(0\) \(3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(1-2\zeta_{6})q^{3}+q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
234.2.f.b 234.f 117.h $2$ $1.868$ \(\Q(\sqrt{-3}) \) None 234.2.f.b \(2\) \(0\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-1+2\zeta_{6})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
234.2.f.c 234.f 117.h $12$ $1.868$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 234.2.f.c \(-12\) \(0\) \(-3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-\beta _{3}-\beta _{6})q^{3}+q^{4}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
234.2.f.d 234.f 117.h $12$ $1.868$ 12.0.\(\cdots\).1 None 234.2.f.d \(12\) \(0\) \(1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(\beta _{9}+\beta _{10})q^{3}+q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
234.2.g.a 234.g 117.f $2$ $1.868$ \(\Q(\sqrt{-3}) \) None 234.2.f.b \(-1\) \(-3\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
234.2.g.b 234.g 117.f $2$ $1.868$ \(\Q(\sqrt{-3}) \) None 234.2.f.a \(1\) \(3\) \(3\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(2-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
234.2.g.c 234.g 117.f $12$ $1.868$ 12.0.\(\cdots\).1 None 234.2.f.d \(-6\) \(3\) \(1\) \(10\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}-\beta _{10}q^{3}+(-1-\beta _{1})q^{4}+\cdots\)
234.2.g.d 234.g 117.f $12$ $1.868$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 234.2.f.c \(6\) \(-3\) \(-3\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{8}q^{2}+\beta _{6}q^{3}+(-1+\beta _{8})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
234.2.h.a 234.h 13.c $2$ $1.868$ \(\Q(\sqrt{-3}) \) None 78.2.e.a \(-1\) \(0\) \(-6\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3q^{5}-2\zeta_{6}q^{7}+\cdots\)
234.2.h.b 234.h 13.c $2$ $1.868$ \(\Q(\sqrt{-3}) \) None 78.2.e.b \(-1\) \(0\) \(2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+2\zeta_{6}q^{7}+\cdots\)
234.2.h.c 234.h 13.c $2$ $1.868$ \(\Q(\sqrt{-3}) \) None 26.2.c.a \(1\) \(0\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}-4\zeta_{6}q^{7}+\cdots\)
234.2.h.d 234.h 13.c $4$ $1.868$ \(\Q(\sqrt{-3}, \sqrt{10})\) None 234.2.h.d \(-2\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(1+\beta _{3})q^{5}+\cdots\)
234.2.h.e 234.h 13.c $4$ $1.868$ \(\Q(\sqrt{-3}, \sqrt{10})\) None 234.2.h.d \(2\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+(-1+\beta _{3})q^{5}+\cdots\)
234.2.j.a 234.j 39.f $4$ $1.868$ \(\Q(\zeta_{8})\) None 234.2.j.a \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(2+2\zeta_{8}^{2})q^{7}+\cdots\)
234.2.l.a 234.l 13.e $4$ $1.868$ \(\Q(\zeta_{12})\) None 78.2.i.b \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-1+2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
234.2.l.b 234.l 13.e $4$ $1.868$ \(\Q(\zeta_{12})\) None 234.2.l.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+3\zeta_{12}^{3}q^{5}+\cdots\)
234.2.l.c 234.l 13.e $4$ $1.868$ \(\Q(\zeta_{12})\) None 78.2.i.a \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(1-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
234.2.p.a 234.p 117.r $28$ $1.868$ None 234.2.p.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
234.2.s.a 234.s 117.l $28$ $1.868$ None 234.2.p.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
234.2.t.a 234.t 117.t $28$ $1.868$ None 234.2.t.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
234.2.x.a 234.x 39.k $8$ $1.868$ \(\Q(\zeta_{24})\) None 234.2.x.a \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{12}]$ \(q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}-\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
234.2.x.b 234.x 39.k $16$ $1.868$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 234.2.x.b \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{12}]$ \(q-\beta _{3}q^{2}+\beta _{4}q^{4}+\beta _{14}q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
234.2.y.a 234.y 117.x $56$ $1.868$ None 234.2.y.a \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{12}]$
234.2.z.a 234.z 117.ac $56$ $1.868$ None 234.2.y.a \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{12}]$
234.2.bd.a 234.bd 117.z $56$ $1.868$ None 234.2.bd.a \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{12}]$
234.3.c.a 234.c 3.b $4$ $6.376$ \(\Q(\sqrt{-2}, \sqrt{13})\) None 234.3.c.a \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-2q^{4}+(-\beta _{1}-3\beta _{2})q^{5}+\cdots\)
234.3.c.b 234.c 3.b $4$ $6.376$ \(\Q(\sqrt{-2}, \sqrt{13})\) None 234.3.c.b \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-2q^{4}+(-\beta _{1}-\beta _{2})q^{5}+(3+\cdots)q^{7}+\cdots\)
234.3.d.a 234.d 39.d $4$ $6.376$ \(\Q(\zeta_{8})\) None 234.3.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{2}+2q^{4}-6\zeta_{8}^{2}q^{5}-2\zeta_{8}q^{7}+\cdots\)
234.3.d.b 234.d 39.d $4$ $6.376$ \(\Q(\zeta_{8})\) None 234.3.d.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}^{3}q^{2}+2q^{4}+\zeta_{8}^{3}q^{5}+8\zeta_{8}q^{7}+\cdots\)
234.3.d.c 234.d 39.d $4$ $6.376$ \(\Q(\zeta_{8})\) None 234.3.d.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}^{2}q^{2}+2q^{4}-6\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+\cdots\)
234.3.i.a 234.i 13.d $2$ $6.376$ \(\Q(\sqrt{-1}) \) None 26.3.d.a \(-2\) \(0\) \(6\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{2}+2iq^{4}+(3+3i)q^{5}+\cdots\)
234.3.i.b 234.i 13.d $4$ $6.376$ \(\Q(\zeta_{12})\) None 78.3.f.a \(-4\) \(0\) \(-12\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\zeta_{12})q^{2}+2\zeta_{12}q^{4}+(-3+\cdots)q^{5}+\cdots\)
234.3.i.c 234.i 13.d $6$ $6.376$ 6.0.353139264.2 None 234.3.i.c \(-6\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\beta _{1})q^{2}+2\beta _{1}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
234.3.i.d 234.i 13.d $6$ $6.376$ 6.0.353139264.2 None 234.3.i.c \(6\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-\beta _{1})q^{2}-2\beta _{1}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
234.3.i.e 234.i 13.d $8$ $6.376$ 8.0.\(\cdots\).1 None 78.3.f.b \(8\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{3})q^{2}+2\beta _{3}q^{4}+\beta _{1}q^{5}+(1+\cdots)q^{7}+\cdots\)
234.3.k.a 234.k 39.i $4$ $6.376$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 234.3.k.a \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+\beta _{3}q^{5}+5\beta _{2}q^{7}+\cdots\)
234.3.k.b 234.k 39.i $12$ $6.376$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 234.3.k.b \(0\) \(0\) \(0\) \(-14\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{5}+\beta _{8})q^{2}+(2+2\beta _{2})q^{4}-\beta _{9}q^{5}+\cdots\)
234.3.m.a 234.m 117.m $56$ $6.376$ None 234.3.m.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
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