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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
232.2.a.a 232.a 1.a $1$ $1.853$ \(\Q\) None \(0\) \(-1\) \(-3\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}+2q^{7}-2q^{9}-3q^{11}+\cdots\)
232.2.a.b 232.a 1.a $1$ $1.853$ \(\Q\) None \(0\) \(1\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+2q^{7}-2q^{9}+3q^{11}+\cdots\)
232.2.a.c 232.a 1.a $2$ $1.853$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+(-1-2\beta )q^{5}-4q^{7}+\cdots\)
232.2.a.d 232.a 1.a $3$ $1.853$ 3.3.568.1 None \(0\) \(2\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(1-\beta _{2})q^{5}+(2+\beta _{2})q^{9}+\cdots\)
232.2.c.a 232.c 8.b $28$ $1.853$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
232.2.e.a 232.e 29.b $8$ $1.853$ 8.0.4589249536.2 None \(0\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+\beta _{4}q^{5}+(1-\beta _{6})q^{7}+(-1+\cdots)q^{9}+\cdots\)
232.2.g.a 232.g 232.g $4$ $1.853$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-1+\beta _{3})q^{4}+(1+\cdots)q^{6}+\cdots\)
232.2.g.b 232.g 232.g $24$ $1.853$ None \(0\) \(0\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{2}]$
232.2.k.a 232.k 232.k $56$ $1.853$ None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
232.2.m.a 232.m 29.d $6$ $1.853$ \(\Q(\zeta_{14})\) None \(0\) \(-3\) \(2\) \(-3\) $\mathrm{SU}(2)[C_{7}]$ \(q+(-1+\zeta_{14}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{3}+\cdots\)
232.2.m.b 232.m 29.d $6$ $1.853$ \(\Q(\zeta_{14})\) None \(0\) \(-1\) \(-1\) \(5\) $\mathrm{SU}(2)[C_{7}]$ \(q+(-1-2\zeta_{14}^{2}+2\zeta_{14}^{3}+\zeta_{14}^{5})q^{3}+\cdots\)
232.2.m.c 232.m 29.d $6$ $1.853$ \(\Q(\zeta_{14})\) None \(0\) \(5\) \(7\) \(-3\) $\mathrm{SU}(2)[C_{7}]$ \(q+(1-\zeta_{14}^{5})q^{3}+(1-\zeta_{14}-2\zeta_{14}^{4}+\cdots)q^{5}+\cdots\)
232.2.m.d 232.m 29.d $24$ $1.853$ None \(0\) \(-1\) \(-8\) \(5\) $\mathrm{SU}(2)[C_{7}]$
232.2.o.a 232.o 232.o $168$ $1.853$ None \(-7\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{14}]$
232.2.q.a 232.q 29.e $48$ $1.853$ None \(0\) \(0\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{14}]$
232.2.s.a 232.s 232.s $168$ $1.853$ None \(-7\) \(0\) \(0\) \(-14\) $\mathrm{SU}(2)[C_{14}]$
232.2.v.a 232.v 232.v $336$ $1.853$ None \(-14\) \(-24\) \(0\) \(0\) $\mathrm{SU}(2)[C_{28}]$
232.3.b.a 232.b 232.b $1$ $6.322$ \(\Q\) \(\Q(\sqrt{-58}) \) \(-2\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}+4q^{4}-8q^{8}+9q^{9}+2^{4}q^{16}+\cdots\)
232.3.b.b 232.b 232.b $1$ $6.322$ \(\Q\) \(\Q(\sqrt{-58}) \) \(2\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}+4q^{4}+8q^{8}+9q^{9}+2^{4}q^{16}+\cdots\)
232.3.b.c 232.b 232.b $56$ $6.322$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
232.3.f.a 232.f 8.d $56$ $6.322$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
232.3.j.a 232.j 29.c $14$ $6.322$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{3}+(-\beta _{4}+\beta _{7})q^{5}+(1+\beta _{6}+\cdots)q^{7}+\cdots\)
232.3.j.b 232.j 29.c $16$ $6.322$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{3}+(\beta _{5}+\beta _{6})q^{5}+(-1+\beta _{11}+\cdots)q^{7}+\cdots\)
232.3.l.a 232.l 232.l $116$ $6.322$ None \(-4\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$
232.3.p.a 232.p 232.p $348$ $6.322$ None \(-3\) \(-10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{14}]$
232.3.t.a 232.t 232.t $348$ $6.322$ None \(-7\) \(-14\) \(0\) \(0\) $\mathrm{SU}(2)[C_{14}]$
232.3.u.a 232.u 232.u $696$ $6.322$ None \(-10\) \(0\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{28}]$
232.3.w.a 232.w 29.f $84$ $6.322$ None \(0\) \(-4\) \(-28\) \(34\) $\mathrm{SU}(2)[C_{28}]$
232.3.w.b 232.w 29.f $96$ $6.322$ None \(0\) \(4\) \(28\) \(-34\) $\mathrm{SU}(2)[C_{28}]$
232.4.a.a 232.a 1.a $3$ $13.688$ 3.3.4481.1 None \(0\) \(3\) \(11\) \(-38\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(4+\beta _{1}+\beta _{2})q^{5}+(-13+\cdots)q^{7}+\cdots\)
232.4.a.b 232.a 1.a $3$ $13.688$ 3.3.229.1 None \(0\) \(6\) \(4\) \(16\) $+$ $\mathrm{SU}(2)$ \(q+(1-3\beta _{2})q^{3}+(1+3\beta _{1}-4\beta _{2})q^{5}+\cdots\)
232.4.a.c 232.a 1.a $4$ $13.688$ 4.4.225792.1 None \(0\) \(0\) \(-20\) \(-8\) $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{3})q^{3}+(-5+\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots\)
232.4.a.d 232.a 1.a $5$ $13.688$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(4\) \(10\) \(32\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(2+\beta _{3})q^{5}+(6+\beta _{2}+\cdots)q^{7}+\cdots\)
232.4.a.e 232.a 1.a $6$ $13.688$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-5\) \(-5\) \(-38\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{3}+(-1-\beta _{3}-\beta _{4})q^{5}+\cdots\)
232.4.c.a 232.c 8.b $84$ $13.688$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
232.4.e.a 232.e 29.b $22$ $13.688$ None \(0\) \(0\) \(18\) \(-12\) $\mathrm{SU}(2)[C_{2}]$
232.4.g.a 232.g 232.g $88$ $13.688$ None \(0\) \(0\) \(0\) \(24\) $\mathrm{SU}(2)[C_{2}]$
232.4.k.a 232.k 232.k $176$ $13.688$ None \(-4\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
232.4.m.a 232.m 29.d $66$ $13.688$ None \(0\) \(1\) \(16\) \(-71\) $\mathrm{SU}(2)[C_{7}]$
232.4.m.b 232.m 29.d $72$ $13.688$ None \(0\) \(-1\) \(-12\) \(59\) $\mathrm{SU}(2)[C_{7}]$
232.4.o.a 232.o 232.o $528$ $13.688$ None \(-7\) \(0\) \(0\) \(-38\) $\mathrm{SU}(2)[C_{14}]$
232.4.q.a 232.q 29.e $132$ $13.688$ None \(0\) \(0\) \(-18\) \(12\) $\mathrm{SU}(2)[C_{14}]$
232.4.s.a 232.s 232.s $528$ $13.688$ None \(-3\) \(0\) \(0\) \(18\) $\mathrm{SU}(2)[C_{14}]$
232.4.v.a 232.v 232.v $1056$ $13.688$ None \(-10\) \(-24\) \(0\) \(0\) $\mathrm{SU}(2)[C_{28}]$
232.5.j.a 232.j 29.c $30$ $23.982$ None \(0\) \(-16\) \(0\) \(96\) $\mathrm{SU}(2)[C_{4}]$
232.5.j.b 232.j 29.c $30$ $23.982$ None \(0\) \(16\) \(0\) \(-96\) $\mathrm{SU}(2)[C_{4}]$
232.6.a.a 232.a 1.a $1$ $37.209$ \(\Q\) None \(0\) \(16\) \(54\) \(112\) $-$ $\mathrm{SU}(2)$ \(q+2^{4}q^{3}+54q^{5}+112q^{7}+13q^{9}+\cdots\)
232.6.a.b 232.a 1.a $8$ $37.209$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-23\) \(-75\) \(74\) $+$ $\mathrm{SU}(2)$ \(q+(-3+\beta _{1})q^{3}+(-10+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
232.6.a.c 232.a 1.a $8$ $37.209$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(3\) \(25\) \(282\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+(3-\beta _{2})q^{5}+(35+\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
232.6.a.d 232.a 1.a $9$ $37.209$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-24\) \(-50\) \(-208\) $+$ $\mathrm{SU}(2)$ \(q+(-3+\beta _{1})q^{3}+(-6-\beta _{4})q^{5}+(-23+\cdots)q^{7}+\cdots\)
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