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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1900.1.e.a 1900.e 19.b $1$ $0.948$ \(\Q\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(1\) \(q+q^{7}+q^{9}-q^{11}+q^{17}+q^{19}-2q^{23}+\cdots\)
1900.1.e.b 1900.e 19.b $2$ $0.948$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{7}+q^{9}+q^{11}+\beta q^{17}-q^{19}+\cdots\)
1900.1.g.a 1900.g 95.d $2$ $0.948$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{7}-q^{9}-q^{11}-iq^{17}-q^{19}+\cdots\)
1900.1.j.a 1900.j 380.j $8$ $0.948$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{5}q^{2}+(-\zeta_{16}^{5}+\zeta_{16}^{7})q^{3}+\cdots\)
1900.1.j.b 1900.j 380.j $8$ $0.948$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{3}q^{2}+(\zeta_{16}+\zeta_{16}^{3})q^{3}+\zeta_{16}^{6}q^{4}+\cdots\)
1900.1.u.a 1900.u 19.d $2$ $0.948$ \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{9}+q^{11}+\zeta_{6}q^{19}+(1-\zeta_{6}^{2}+\cdots)q^{29}+\cdots\)
1900.1.w.a 1900.w 475.m $8$ $0.948$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{30}^{8}q^{5}+(\zeta_{30}^{2}+\zeta_{30}^{13})q^{7}+\zeta_{30}^{3}q^{9}+\cdots\)
1900.1.bb.a 1900.bb 475.o $8$ $0.948$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(1\) \(2\) \(q-\zeta_{30}^{7}q^{5}+(\zeta_{30}^{2}-\zeta_{30}^{13})q^{7}+\zeta_{30}^{12}q^{9}+\cdots\)
1900.1.bf.a 1900.bf 95.m $4$ $0.948$ \(\Q(\zeta_{12})\) None None \(0\) \(2\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{4})q^{3}-\zeta_{12}^{5}q^{9}+q^{11}+\cdots\)
1900.2.a.a 1900.a 1.a $1$ $15.172$ \(\Q\) None None \(0\) \(-2\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{7}+q^{9}-6q^{13}-2q^{17}+\cdots\)
1900.2.a.b 1900.a 1.a $1$ $15.172$ \(\Q\) None None \(0\) \(-2\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+3q^{7}+q^{9}+5q^{11}+4q^{13}+\cdots\)
1900.2.a.c 1900.a 1.a $1$ $15.172$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+2q^{7}-3q^{9}-4q^{11}+4q^{13}-6q^{17}+\cdots\)
1900.2.a.d 1900.a 1.a $2$ $15.172$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}-2q^{7}+(1-2\beta )q^{9}+\cdots\)
1900.2.a.e 1900.a 1.a $2$ $15.172$ \(\Q(\sqrt{2}) \) None None \(0\) \(4\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{3}+(2-2\beta )q^{7}+(3+4\beta )q^{9}+\cdots\)
1900.2.a.f 1900.a 1.a $3$ $15.172$ 3.3.257.1 None None \(0\) \(-2\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{1})q^{7}+(1+\cdots)q^{9}+\cdots\)
1900.2.a.g 1900.a 1.a $3$ $15.172$ 3.3.321.1 None None \(0\) \(-2\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(-1+2\beta _{1}+\beta _{2})q^{7}+\cdots\)
1900.2.a.h 1900.a 1.a $3$ $15.172$ 3.3.257.1 None None \(0\) \(2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(1-\beta _{1})q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots\)
1900.2.a.i 1900.a 1.a $3$ $15.172$ 3.3.321.1 None None \(0\) \(2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(1-2\beta _{1}-\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots\)
1900.2.a.j 1900.a 1.a $4$ $15.172$ \(\Q(\sqrt{2}, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
1900.2.a.k 1900.a 1.a $6$ $15.172$ 6.6.56310016.1 None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}-\beta _{4}q^{7}+(2-\beta _{1}+\beta _{5})q^{9}+\cdots\)
1900.2.c.a 1900.c 5.b $2$ $15.172$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-iq^{7}-q^{9}+3iq^{13}-iq^{17}+\cdots\)
1900.2.c.b 1900.c 5.b $2$ $15.172$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}+3iq^{7}-q^{9}+5q^{11}-4iq^{13}+\cdots\)
1900.2.c.c 1900.c 5.b $2$ $15.172$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{7}+3q^{9}-4q^{11}+2iq^{13}+3iq^{17}+\cdots\)
1900.2.c.d 1900.c 5.b $4$ $15.172$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}-\zeta_{8}^{2})q^{3}+(-\zeta_{8}-2\zeta_{8}^{2})q^{7}+\cdots\)
1900.2.c.e 1900.c 5.b $4$ $15.172$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{2}q^{3}+(-\zeta_{12}+\zeta_{12}^{2})q^{7}+(-1+\cdots)q^{9}+\cdots\)
1900.2.c.f 1900.c 5.b $6$ $15.172$ 6.0.6594624.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{4}-\beta _{5})q^{3}+(2\beta _{1}-\beta _{4}-\beta _{5})q^{7}+\cdots\)
1900.2.c.g 1900.c 5.b $6$ $15.172$ 6.0.4227136.2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+\beta _{1}q^{7}+\beta _{5}q^{9}-\beta _{2}q^{11}+\cdots\)
1900.2.i.a 1900.i 19.c $2$ $15.172$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{9}-4q^{11}+\cdots\)
1900.2.i.b 1900.i 19.c $2$ $15.172$ \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(0\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}+4q^{7}-\zeta_{6}q^{9}-3q^{11}+\cdots\)
1900.2.i.c 1900.i 19.c $6$ $15.172$ 6.0.1783323.2 None None \(0\) \(-1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{3}+\beta _{5})q^{3}+(-1+\beta _{3})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
1900.2.i.d 1900.i 19.c $8$ $15.172$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}-\beta _{7}q^{7}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
1900.2.i.e 1900.i 19.c $12$ $15.172$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{6})q^{3}+\beta _{4}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
1900.2.i.f 1900.i 19.c $12$ $15.172$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1}+\beta _{6})q^{3}-\beta _{4}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
1900.2.i.g 1900.i 19.c $20$ $15.172$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{14}q^{3}+(\beta _{15}+\beta _{18})q^{7}+(-1+\beta _{4}+\cdots)q^{9}+\cdots\)
1900.2.l.a 1900.l 95.g $8$ $15.172$ 8.0.2702336256.1 \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(6\) $\mathrm{U}(1)[D_{4}]$ \(q+(1+\beta _{1}+\beta _{5})q^{7}-3\beta _{1}q^{9}+(-1+\cdots)q^{11}+\cdots\)
1900.2.l.b 1900.l 95.g $12$ $15.172$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}-\beta _{6}q^{7}+(\beta _{3}+4\beta _{5}-\beta _{6}+\cdots)q^{9}+\cdots\)
1900.2.l.c 1900.l 95.g $16$ $15.172$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{4}q^{3}+\beta _{9}q^{7}+(-\beta _{2}-\beta _{11})q^{9}+\cdots\)
1900.2.l.d 1900.l 95.g $24$ $15.172$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
1900.2.s.a 1900.s 95.i $4$ $15.172$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{3}-2\zeta_{12}^{2}q^{9}-4q^{11}+(-\zeta_{12}+\cdots)q^{13}+\cdots\)
1900.2.s.b 1900.s 95.i $4$ $15.172$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{3}-2\zeta_{12}^{3}q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
1900.2.s.c 1900.s 95.i $12$ $15.172$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{6}+\beta _{11})q^{3}+(\beta _{10}+\beta _{11})q^{7}+(-2\beta _{1}+\cdots)q^{9}+\cdots\)
1900.2.s.d 1900.s 95.i $16$ $15.172$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{6}q^{3}+\beta _{14}q^{7}+(\beta _{4}-\beta _{5}+\beta _{10}+\cdots)q^{9}+\cdots\)
1900.2.s.e 1900.s 95.i $24$ $15.172$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
1900.3.e.a 1900.e 19.b $2$ $51.771$ \(\Q(\sqrt{57}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(-5\) $\mathrm{U}(1)[D_{2}]$ \(q+(-1-3\beta )q^{7}+9q^{9}+(1-5\beta )q^{11}+\cdots\)
1900.3.e.b 1900.e 19.b $2$ $51.771$ \(\Q(\sqrt{-29}) \) None None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+q^{7}-20q^{9}+14q^{11}+3\beta q^{13}+\cdots\)
1900.3.e.c 1900.e 19.b $4$ $51.771$ \(\Q(\sqrt{6}, \sqrt{-14})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+\beta _{2}q^{7}-5q^{9}+4q^{11}-3\beta _{1}q^{13}+\cdots\)
1900.3.e.d 1900.e 19.b $4$ $51.771$ \(\Q(\sqrt{3}, \sqrt{19})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{7}+9q^{9}+(1-\beta _{3})q^{11}+(\beta _{1}+\cdots)q^{17}+\cdots\)
1900.3.e.e 1900.e 19.b $12$ $51.771$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{3}+\beta _{8}q^{7}+(-6-\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots\)
1900.3.e.f 1900.e 19.b $12$ $51.771$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(1+\beta _{9})q^{7}+(-1+\beta _{2})q^{9}+\cdots\)
1900.3.e.g 1900.e 19.b $14$ $51.771$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{7}q^{7}+(-4+\beta _{2})q^{9}-\beta _{3}q^{11}+\cdots\)
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