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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
475.1.c.a 475.c 19.b $1$ $0.237$ \(\Q\) \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{4}+q^{9}-2q^{11}+q^{16}-q^{19}+\cdots\)
475.1.c.b 475.c 19.b $2$ $0.237$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{2}-\beta q^{3}-q^{4}-2q^{6}-q^{9}+\beta q^{12}+\cdots\)
475.1.m.a 475.m 475.m $4$ $0.237$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(0\) \(q+\zeta_{10}^{3}q^{4}-\zeta_{10}q^{5}+(\zeta_{10}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots\)
475.1.o.a 475.o 475.o $4$ $0.237$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(-2\) \(q+\zeta_{10}^{2}q^{4}+\zeta_{10}^{4}q^{5}+(-\zeta_{10}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots\)
475.2.a.a 475.a 1.a $1$ $3.793$ \(\Q\) None None \(-1\) \(0\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+2q^{7}+3q^{8}-3q^{9}-4q^{11}+\cdots\)
475.2.a.b 475.a 1.a $1$ $3.793$ \(\Q\) None None \(0\) \(2\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{4}+q^{7}+q^{9}+3q^{11}+\cdots\)
475.2.a.c 475.a 1.a $1$ $3.793$ \(\Q\) None None \(1\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-2q^{7}-3q^{8}-3q^{9}-4q^{11}+\cdots\)
475.2.a.d 475.a 1.a $3$ $3.793$ \(\Q(\zeta_{14})^+\) None None \(-4\) \(-2\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
475.2.a.e 475.a 1.a $3$ $3.793$ 3.3.169.1 None None \(-2\) \(-2\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(2+\cdots)q^{4}+\cdots\)
475.2.a.f 475.a 1.a $3$ $3.793$ 3.3.148.1 None None \(-1\) \(-2\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
475.2.a.g 475.a 1.a $3$ $3.793$ 3.3.169.1 None None \(2\) \(2\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
475.2.a.h 475.a 1.a $3$ $3.793$ \(\Q(\zeta_{14})^+\) None None \(4\) \(2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}+(\beta _{1}-\beta _{2})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
475.2.a.i 475.a 1.a $4$ $3.793$ 4.4.11344.1 None None \(2\) \(-2\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)
475.2.a.j 475.a 1.a $6$ $3.793$ 6.6.66064384.1 None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{2}+(-\beta _{1}-\beta _{5})q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots\)
475.2.b.a 475.b 5.b $2$ $3.793$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}+2q^{4}-iq^{7}-q^{9}+3q^{11}+\cdots\)
475.2.b.b 475.b 5.b $6$ $3.793$ 6.0.1827904.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{4}+\beta _{5})q^{2}+(\beta _{1}+\beta _{4})q^{3}+(-1+\cdots)q^{4}+\cdots\)
475.2.b.c 475.b 5.b $6$ $3.793$ 6.0.153664.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}-\beta _{5})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(-3+\cdots)q^{4}+\cdots\)
475.2.b.d 475.b 5.b $6$ $3.793$ 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(\beta _{2}-\beta _{4})q^{3}+\beta _{1}q^{4}+(-1+\cdots)q^{6}+\cdots\)
475.2.b.e 475.b 5.b $8$ $3.793$ 8.0.2058981376.2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}+\beta _{1}q^{3}+(-2-\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
475.2.e.a 475.e 19.c $2$ $3.793$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-4q^{7}+\cdots\)
475.2.e.b 475.e 19.c $2$ $3.793$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(0\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+4q^{7}+\cdots\)
475.2.e.c 475.e 19.c $2$ $3.793$ \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+4q^{7}+3\zeta_{6}q^{9}+\cdots\)
475.2.e.d 475.e 19.c $6$ $3.793$ 6.0.3518667.1 None None \(1\) \(1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3}+\beta _{5})q^{3}+(-3+\cdots)q^{4}+\cdots\)
475.2.e.e 475.e 19.c $8$ $3.793$ 8.0.4601315889.1 None None \(1\) \(3\) \(0\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{7}q^{2}+(-\beta _{1}+\beta _{5})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
475.2.e.f 475.e 19.c $12$ $3.793$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-2\) \(-3\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{7}+\beta _{8})q^{2}+(1-\beta _{1}+\beta _{2}+\beta _{9}+\cdots)q^{3}+\cdots\)
475.2.e.g 475.e 19.c $12$ $3.793$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{5}q^{2}+(\beta _{4}-\beta _{5})q^{3}+(\beta _{2}-\beta _{3}+\beta _{8}+\cdots)q^{4}+\cdots\)
475.2.e.h 475.e 19.c $12$ $3.793$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(2\) \(3\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{7}-\beta _{8})q^{2}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
475.2.g.a 475.g 95.g $4$ $3.793$ \(\Q(i, \sqrt{19})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(-6\) $\mathrm{U}(1)[D_{4}]$ \(q-2\beta _{1}q^{4}+(-2+2\beta _{1}+\beta _{3})q^{7}+3\beta _{1}q^{9}+\cdots\)
475.2.g.b 475.g 95.g $12$ $3.793$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{7}q^{2}+\beta _{5}q^{3}+(-\beta _{6}-\beta _{8})q^{4}+\cdots\)
475.2.g.c 475.g 95.g $16$ $3.793$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q-\beta _{9}q^{2}-\beta _{3}q^{3}+(-2\beta _{7}-\beta _{10})q^{4}+\cdots\)
475.2.g.d 475.g 95.g $24$ $3.793$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
475.2.h.a 475.h 25.d $84$ $3.793$ None None \(-1\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{5}]$
475.2.h.b 475.h 25.d $100$ $3.793$ None None \(-1\) \(-2\) \(1\) \(-10\) $\mathrm{SU}(2)[C_{5}]$
475.2.j.a 475.j 95.i $4$ $3.793$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{3}-2\zeta_{12}^{2}q^{4}+2\zeta_{12}^{3}q^{7}+\cdots\)
475.2.j.b 475.j 95.i $12$ $3.793$ 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}-\beta _{11}q^{3}+(2-\beta _{2}+3\beta _{3}+\cdots)q^{4}+\cdots\)
475.2.j.c 475.j 95.i $16$ $3.793$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{14}q^{2}+(\beta _{7}+\beta _{13})q^{3}+(-\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots\)
475.2.j.d 475.j 95.i $24$ $3.793$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
475.2.l.a 475.l 19.e $6$ $3.793$ \(\Q(\zeta_{18})\) None None \(6\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(1+\zeta_{18}-\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+(1+\cdots)q^{3}+\cdots\)
475.2.l.b 475.l 19.e $18$ $3.793$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(-3\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+\beta _{14}q^{2}+(\beta _{4}-\beta _{6}+\beta _{7}+\beta _{15})q^{3}+\cdots\)
475.2.l.c 475.l 19.e $18$ $3.793$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(3\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\beta _{4}-\beta _{15})q^{2}+(-\beta _{5}-\beta _{6}-\beta _{8}+\cdots)q^{3}+\cdots\)
475.2.l.d 475.l 19.e $42$ $3.793$ None None \(0\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
475.2.l.e 475.l 19.e $42$ $3.793$ None None \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
475.2.l.f 475.l 19.e $48$ $3.793$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
475.2.n.a 475.n 25.e $80$ $3.793$ None None \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{10}]$
475.2.n.b 475.n 25.e $96$ $3.793$ None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{10}]$
475.2.p.a 475.p 95.l $4$ $3.793$ \(\Q(\zeta_{12})\) None None \(-2\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(2+2\zeta_{12}+\cdots)q^{3}+\cdots\)
475.2.p.b 475.p 95.l $4$ $3.793$ \(\Q(\zeta_{12})\) None None \(0\) \(6\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1+\zeta_{12}+\zeta_{12}^{2}-2\zeta_{12}^{3})q^{3}+(2\zeta_{12}+\cdots)q^{4}+\cdots\)
475.2.p.c 475.p 95.l $4$ $3.793$ \(\Q(\zeta_{12})\) None None \(2\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2-2\zeta_{12}+\cdots)q^{3}+\cdots\)
475.2.p.d 475.p 95.l $4$ $3.793$ \(\Q(\zeta_{12})\) None None \(6\) \(6\) \(0\) \(8\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\zeta_{12}+\zeta_{12}^{2}+2\zeta_{12}^{3})q^{2}+(1+\cdots)q^{3}+\cdots\)
475.2.p.e 475.p 95.l $16$ $3.793$ 16.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+\beta _{14}q^{2}+(\beta _{1}+\beta _{3})q^{3}-\beta _{5}q^{4}-\beta _{6}q^{6}+\cdots\)
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