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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
231.1.h.a 231.h 231.h $1$ $0.115$ \(\Q\) \(\Q(\sqrt{-231}) \) None 231.1.h.a \(-1\) \(-1\) \(1\) \(-1\) \(q-q^{2}-q^{3}+q^{5}+q^{6}-q^{7}+q^{8}+\cdots\)
231.1.h.b 231.h 231.h $1$ $0.115$ \(\Q\) \(\Q(\sqrt{-231}) \) None 231.1.h.a \(-1\) \(1\) \(-1\) \(1\) \(q-q^{2}+q^{3}-q^{5}-q^{6}+q^{7}+q^{8}+\cdots\)
231.1.h.c 231.h 231.h $1$ $0.115$ \(\Q\) \(\Q(\sqrt{-231}) \) None 231.1.h.a \(1\) \(-1\) \(1\) \(1\) \(q+q^{2}-q^{3}+q^{5}-q^{6}+q^{7}-q^{8}+\cdots\)
231.1.h.d 231.h 231.h $1$ $0.115$ \(\Q\) \(\Q(\sqrt{-231}) \) None 231.1.h.a \(1\) \(1\) \(-1\) \(-1\) \(q+q^{2}+q^{3}-q^{5}+q^{6}-q^{7}-q^{8}+\cdots\)
231.2.a.a 231.a 1.a $1$ $1.845$ \(\Q\) None None 231.2.a.a \(-1\) \(-1\) \(-2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
231.2.a.b 231.a 1.a $2$ $1.845$ \(\Q(\sqrt{21}) \) None None 231.2.a.b \(-1\) \(-2\) \(6\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(3+\beta )q^{4}+3q^{5}+\beta q^{6}+\cdots\)
231.2.a.c 231.a 1.a $2$ $1.845$ \(\Q(\sqrt{5}) \) None None 231.2.a.c \(1\) \(2\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
231.2.a.d 231.a 1.a $3$ $1.845$ 3.3.837.1 None None 231.2.a.d \(0\) \(-3\) \(0\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
231.2.a.e 231.a 1.a $3$ $1.845$ 3.3.229.1 None None 231.2.a.e \(2\) \(3\) \(4\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+q^{3}+(2+\beta _{1})q^{4}+(1+\cdots)q^{5}+\cdots\)
231.2.c.a 231.c 77.b $16$ $1.845$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None 231.2.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{2}-\beta _{8}q^{3}+(-1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
231.2.e.a 231.e 21.c $28$ $1.845$ None None 231.2.e.a \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$
231.2.g.a 231.g 33.d $24$ $1.845$ None None 231.2.g.a \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
231.2.i.a 231.i 7.c $2$ $1.845$ \(\Q(\sqrt{-3}) \) None None 231.2.i.a \(-1\) \(1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
231.2.i.b 231.i 7.c $2$ $1.845$ \(\Q(\sqrt{-3}) \) None None 231.2.i.b \(1\) \(1\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
231.2.i.c 231.i 7.c $2$ $1.845$ \(\Q(\sqrt{-3}) \) None None 231.2.i.c \(2\) \(1\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
231.2.i.d 231.i 7.c $4$ $1.845$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None 231.2.i.d \(2\) \(-2\) \(4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{2}+\beta _{2}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
231.2.i.e 231.i 7.c $8$ $1.845$ 8.0.\(\cdots\).5 None None 231.2.i.e \(-2\) \(-4\) \(-4\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
231.2.i.f 231.i 7.c $10$ $1.845$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None 231.2.i.f \(-2\) \(5\) \(4\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{3}q^{2}+(1+\beta _{2})q^{3}+(-2-2\beta _{2}+\cdots)q^{4}+\cdots\)
231.2.j.a 231.j 11.c $4$ $1.845$ \(\Q(\zeta_{10})\) None None 231.2.j.a \(-4\) \(1\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-2+\zeta_{10}-\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots\)
231.2.j.b 231.j 11.c $4$ $1.845$ \(\Q(\zeta_{10})\) None None 231.2.j.b \(-2\) \(1\) \(3\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}-\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots\)
231.2.j.c 231.j 11.c $4$ $1.845$ \(\Q(\zeta_{10})\) None None 231.2.j.c \(1\) \(1\) \(7\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
231.2.j.d 231.j 11.c $4$ $1.845$ \(\Q(\zeta_{10})\) None None 231.2.j.d \(2\) \(-1\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots\)
231.2.j.e 231.j 11.c $4$ $1.845$ \(\Q(\zeta_{10})\) None None 231.2.j.e \(5\) \(1\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1+\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
231.2.j.f 231.j 11.c $8$ $1.845$ 8.0.13140625.1 None None 231.2.j.f \(2\) \(2\) \(2\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{3}+\beta _{5}+\beta _{6})q^{2}+(1-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
231.2.j.g 231.j 11.c $20$ $1.845$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None 231.2.j.g \(0\) \(-5\) \(-5\) \(5\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{7}q^{2}-\beta _{4}q^{3}+(\beta _{3}-\beta _{6}-\beta _{8}-2\beta _{9}+\cdots)q^{4}+\cdots\)
231.2.l.a 231.l 231.l $8$ $1.845$ 8.0.\(\cdots\).5 None None 231.2.l.a \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}+\beta _{4})q^{3}+2\beta _{4}q^{4}+(-\beta _{2}-\beta _{7})q^{5}+\cdots\)
231.2.l.b 231.l 231.l $48$ $1.845$ None None 231.2.l.b \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
231.2.n.a 231.n 21.g $52$ $1.845$ None None 231.2.n.a \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$
231.2.p.a 231.p 77.i $32$ $1.845$ None None 231.2.p.a \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{6}]$
231.2.s.a 231.s 33.f $96$ $1.845$ None None 231.2.s.a \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
231.2.u.a 231.u 231.u $112$ $1.845$ None None 231.2.u.a \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{10}]$
231.2.w.a 231.w 77.l $64$ $1.845$ None None 231.2.w.a \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{10}]$
231.2.y.a 231.y 77.m $64$ $1.845$ None None 231.2.y.a \(0\) \(-8\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{15}]$
231.2.y.b 231.y 77.m $64$ $1.845$ None None 231.2.y.b \(4\) \(8\) \(-4\) \(-1\) $\mathrm{SU}(2)[C_{15}]$
231.2.ba.a 231.ba 77.n $128$ $1.845$ None None 231.2.ba.a \(0\) \(0\) \(12\) \(-10\) $\mathrm{SU}(2)[C_{30}]$
231.2.bc.a 231.bc 231.ac $224$ $1.845$ None None 231.2.bc.a \(0\) \(-9\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{30}]$
231.2.be.a 231.be 231.ae $224$ $1.845$ None None 231.2.be.a \(0\) \(-3\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{30}]$
231.3.b.a 231.b 3.b $40$ $6.294$ None None 231.3.b.a \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
231.3.d.a 231.d 11.b $24$ $6.294$ None None 231.3.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
231.3.f.a 231.f 7.b $28$ $6.294$ None None 231.3.f.a \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$
231.3.h.a 231.h 231.h $3$ $6.294$ 3.3.6237.1 \(\Q(\sqrt{-231}) \) None 231.3.h.a \(0\) \(-9\) \(0\) \(-21\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots\)
231.3.h.b 231.h 231.h $3$ $6.294$ 3.3.6237.1 \(\Q(\sqrt{-231}) \) None 231.3.h.a \(0\) \(-9\) \(0\) \(21\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots\)
231.3.h.c 231.h 231.h $3$ $6.294$ 3.3.6237.1 \(\Q(\sqrt{-231}) \) None 231.3.h.a \(0\) \(9\) \(0\) \(-21\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{2}+3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots\)
231.3.h.d 231.h 231.h $3$ $6.294$ 3.3.6237.1 \(\Q(\sqrt{-231}) \) None 231.3.h.a \(0\) \(9\) \(0\) \(21\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}+3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots\)
231.3.h.e 231.h 231.h $48$ $6.294$ None None 231.3.h.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
231.3.k.a 231.k 231.k $120$ $6.294$ None None 231.3.k.a \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
231.3.m.a 231.m 7.d $24$ $6.294$ None None 231.3.m.a \(0\) \(-36\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{6}]$
231.3.m.b 231.m 7.d $28$ $6.294$ None None 231.3.m.b \(0\) \(42\) \(0\) \(16\) $\mathrm{SU}(2)[C_{6}]$
231.3.o.a 231.o 77.h $64$ $6.294$ None None 231.3.o.a \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$
231.3.q.a 231.q 21.h $108$ $6.294$ None None 231.3.q.a \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$
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