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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
230.2.a.a 230.a 1.a $2$ $1.837$ \(\Q(\sqrt{21}) \) None \(-2\) \(-1\) \(-2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(1+\cdots)q^{7}+\cdots\)
230.2.a.b 230.a 1.a $2$ $1.837$ \(\Q(\sqrt{13}) \) None \(-2\) \(3\) \(2\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
230.2.a.c 230.a 1.a $2$ $1.837$ \(\Q(\sqrt{5}) \) None \(2\) \(1\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+(1+\cdots)q^{7}+\cdots\)
230.2.a.d 230.a 1.a $3$ $1.837$ 3.3.1101.1 None \(3\) \(1\) \(-3\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
230.2.b.a 230.b 5.b $4$ $1.837$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}+(1+2\beta _{2})q^{5}+\cdots\)
230.2.b.b 230.b 5.b $8$ $1.837$ 8.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(\beta _{2}-\beta _{5})q^{3}-q^{4}+(\beta _{1}-\beta _{6}+\cdots)q^{5}+\cdots\)
230.2.e.a 230.e 115.e $8$ $1.837$ 8.0.110166016.2 None \(0\) \(-4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{2}+(-1-\beta _{2}-\beta _{6}-\beta _{7})q^{3}+\cdots\)
230.2.e.b 230.e 115.e $8$ $1.837$ 8.0.110166016.2 None \(0\) \(-4\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{2}+(-1-\beta _{2}-\beta _{6}-\beta _{7})q^{3}+\cdots\)
230.2.e.c 230.e 115.e $8$ $1.837$ \(\Q(\zeta_{16})\) None \(0\) \(16\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{16}^{6}q^{2}+(2+2\zeta_{16}^{4})q^{3}-\zeta_{16}^{4}q^{4}+\cdots\)
230.2.g.a 230.g 23.c $10$ $1.837$ \(\Q(\zeta_{22})\) None \(-1\) \(3\) \(-1\) \(-15\) $\mathrm{SU}(2)[C_{11}]$ \(q+\zeta_{22}^{4}q^{2}+(1-\zeta_{22}+\zeta_{22}^{2}+\zeta_{22}^{4}+\cdots)q^{3}+\cdots\)
230.2.g.b 230.g 23.c $20$ $1.837$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(2\) \(-3\) \(-2\) \(19\) $\mathrm{SU}(2)[C_{11}]$ \(q+\beta _{6}q^{2}+(\beta _{1}-\beta _{2}+\beta _{5}-\beta _{13}+\beta _{18}+\cdots)q^{3}+\cdots\)
230.2.g.c 230.g 23.c $20$ $1.837$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(2\) \(1\) \(2\) \(-12\) $\mathrm{SU}(2)[C_{11}]$ \(q+\beta _{3}q^{2}+(\beta _{5}+\beta _{18})q^{3}+\beta _{12}q^{4}+\cdots\)
230.2.g.d 230.g 23.c $30$ $1.837$ None \(-3\) \(-1\) \(3\) \(8\) $\mathrm{SU}(2)[C_{11}]$
230.2.j.a 230.j 115.j $120$ $1.837$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
230.2.l.a 230.l 115.l $240$ $1.837$ None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{44}]$
230.3.c.a 230.c 115.c $24$ $6.267$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
230.3.d.a 230.d 23.b $16$ $6.267$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{2}-\beta _{5}q^{3}+2q^{4}+\beta _{2}q^{5}-\beta _{10}q^{6}+\cdots\)
230.3.f.a 230.f 5.c $20$ $6.267$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-20\) \(0\) \(4\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\beta _{8})q^{2}+\beta _{1}q^{3}+2\beta _{8}q^{4}+\cdots\)
230.3.f.b 230.f 5.c $24$ $6.267$ None \(24\) \(0\) \(4\) \(8\) $\mathrm{SU}(2)[C_{4}]$
230.3.h.a 230.h 23.d $160$ $6.267$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
230.3.i.a 230.i 115.i $240$ $6.267$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
230.3.k.a 230.k 115.k $240$ $6.267$ None \(-24\) \(0\) \(-4\) \(-74\) $\mathrm{SU}(2)[C_{44}]$
230.3.k.b 230.k 115.k $240$ $6.267$ None \(24\) \(8\) \(-4\) \(50\) $\mathrm{SU}(2)[C_{44}]$
230.4.a.a 230.a 1.a $1$ $13.570$ \(\Q\) None \(-2\) \(-5\) \(-5\) \(12\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-5q^{3}+4q^{4}-5q^{5}+10q^{6}+\cdots\)
230.4.a.b 230.a 1.a $1$ $13.570$ \(\Q\) None \(-2\) \(4\) \(-5\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
230.4.a.c 230.a 1.a $1$ $13.570$ \(\Q\) None \(-2\) \(7\) \(5\) \(20\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+7q^{3}+4q^{4}+5q^{5}-14q^{6}+\cdots\)
230.4.a.d 230.a 1.a $1$ $13.570$ \(\Q\) None \(2\) \(-1\) \(5\) \(-32\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+4q^{4}+5q^{5}-2q^{6}+\cdots\)
230.4.a.e 230.a 1.a $1$ $13.570$ \(\Q\) None \(2\) \(1\) \(-5\) \(-18\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+4q^{4}-5q^{5}+2q^{6}+\cdots\)
230.4.a.f 230.a 1.a $2$ $13.570$ \(\Q(\sqrt{73}) \) None \(-4\) \(-3\) \(10\) \(-17\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-1-\beta )q^{3}+4q^{4}+5q^{5}+\cdots\)
230.4.a.g 230.a 1.a $3$ $13.570$ 3.3.318165.1 None \(-6\) \(-1\) \(15\) \(7\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+5q^{5}+2\beta _{1}q^{6}+\cdots\)
230.4.a.h 230.a 1.a $4$ $13.570$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-8\) \(-4\) \(-20\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots\)
230.4.a.i 230.a 1.a $4$ $13.570$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(8\) \(4\) \(-20\) \(26\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots\)
230.4.a.j 230.a 1.a $4$ $13.570$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(8\) \(14\) \(20\) \(8\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(4-\beta _{1})q^{3}+4q^{4}+5q^{5}+\cdots\)
230.4.b.a 230.b 5.b $14$ $13.570$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta _{8}q^{2}+(\beta _{1}-\beta _{8})q^{3}-4q^{4}+(-\beta _{7}+\cdots)q^{5}+\cdots\)
230.4.b.b 230.b 5.b $18$ $13.570$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta _{5}q^{2}+\beta _{1}q^{3}-4q^{4}+(-\beta _{5}-\beta _{12}+\cdots)q^{5}+\cdots\)
230.4.e.a 230.e 115.e $72$ $13.570$ None \(0\) \(-16\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
230.4.g.a 230.g 23.c $50$ $13.570$ None \(-10\) \(-5\) \(25\) \(-19\) $\mathrm{SU}(2)[C_{11}]$
230.4.g.b 230.g 23.c $60$ $13.570$ None \(12\) \(-3\) \(-30\) \(100\) $\mathrm{SU}(2)[C_{11}]$
230.4.g.c 230.g 23.c $60$ $13.570$ None \(12\) \(5\) \(30\) \(-3\) $\mathrm{SU}(2)[C_{11}]$
230.4.g.d 230.g 23.c $70$ $13.570$ None \(-14\) \(3\) \(-35\) \(-78\) $\mathrm{SU}(2)[C_{11}]$
230.4.j.a 230.j 115.j $360$ $13.570$ None \(0\) \(0\) \(32\) \(0\) $\mathrm{SU}(2)[C_{22}]$
230.4.l.a 230.l 115.l $720$ $13.570$ None \(0\) \(16\) \(0\) \(0\) $\mathrm{SU}(2)[C_{44}]$
230.5.c.a 230.c 115.c $48$ $23.775$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
230.5.d.a 230.d 23.b $32$ $23.775$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
230.5.f.a 230.f 5.c $44$ $23.775$ None \(-88\) \(0\) \(24\) \(-80\) $\mathrm{SU}(2)[C_{4}]$
230.5.f.b 230.f 5.c $44$ $23.775$ None \(88\) \(0\) \(24\) \(-80\) $\mathrm{SU}(2)[C_{4}]$
230.6.a.a 230.a 1.a $1$ $36.888$ \(\Q\) None \(-4\) \(8\) \(-25\) \(199\) $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+8q^{3}+2^{4}q^{4}-5^{2}q^{5}-2^{5}q^{6}+\cdots\)
230.6.a.b 230.a 1.a $2$ $36.888$ \(\Q(\sqrt{2}) \) None \(-8\) \(6\) \(-50\) \(-164\) $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+(3+6\beta )q^{3}+2^{4}q^{4}-5^{2}q^{5}+\cdots\)
230.6.a.c 230.a 1.a $3$ $36.888$ 3.3.27980.1 None \(-12\) \(-26\) \(75\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+(-9+\beta _{2})q^{3}+2^{4}q^{4}+5^{2}q^{5}+\cdots\)
230.6.a.d 230.a 1.a $3$ $36.888$ 3.3.27980.1 None \(12\) \(-34\) \(75\) \(-121\) $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+(-11-\beta _{2})q^{3}+2^{4}q^{4}+5^{2}q^{5}+\cdots\)
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