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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2128.1.c.a 2128.c 532.b $1$ $1.062$ \(\Q\) \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-133}) \) \(\Q(\sqrt{7}) \) 2128.1.c.a \(0\) \(0\) \(0\) \(-1\) \(q-q^{7}+q^{9}+q^{19}+q^{25}+2q^{47}+\cdots\)
2128.1.c.b 2128.c 532.b $1$ $1.062$ \(\Q\) \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-133}) \) \(\Q(\sqrt{7}) \) 2128.1.c.a \(0\) \(0\) \(0\) \(1\) \(q+q^{7}+q^{9}-q^{19}+q^{25}-2q^{47}+\cdots\)
2128.1.c.c 2128.c 532.b $2$ $1.062$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-19}) \) None 2128.1.c.c \(0\) \(0\) \(0\) \(-1\) \(q+(\zeta_{6}+\zeta_{6}^{2})q^{5}+\zeta_{6}^{2}q^{7}+q^{9}+(\zeta_{6}+\cdots)q^{11}+\cdots\)
2128.1.c.d 2128.c 532.b $2$ $1.062$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-19}) \) None 2128.1.c.c \(0\) \(0\) \(0\) \(1\) \(q+(\zeta_{6}+\zeta_{6}^{2})q^{5}-\zeta_{6}^{2}q^{7}+q^{9}+(-\zeta_{6}+\cdots)q^{11}+\cdots\)
2128.1.cl.a 2128.cl 133.r $2$ $1.062$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-19}) \) None 532.1.bc.a \(0\) \(0\) \(-2\) \(1\) \(q+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{11}+\cdots\)
2128.1.cl.b 2128.cl 133.r $2$ $1.062$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-19}) \) None 532.1.bc.b \(0\) \(0\) \(1\) \(-2\) \(q-\zeta_{6}^{2}q^{5}-q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{11}+\cdots\)
2128.1.cl.c 2128.cl 133.r $2$ $1.062$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-19}) \) None 133.1.r.a \(0\) \(0\) \(1\) \(1\) \(q-\zeta_{6}^{2}q^{5}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{11}+\cdots\)
2128.1.cl.d 2128.cl 133.r $4$ $1.062$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None 1064.1.cd.a \(0\) \(0\) \(0\) \(2\) \(q+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{7}+(1-\beta _{2})q^{9}+\cdots\)
2128.1.cw.a 2128.cw 532.ah $2$ $1.062$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-19}) \) None 2128.1.cw.a \(0\) \(0\) \(-3\) \(-2\) \(q+(-1-\zeta_{6})q^{5}-q^{7}+\zeta_{6}^{2}q^{9}+(1+\cdots)q^{17}+\cdots\)
2128.1.cw.b 2128.cw 532.ah $2$ $1.062$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-19}) \) None 2128.1.cw.a \(0\) \(0\) \(-3\) \(2\) \(q+(-1-\zeta_{6})q^{5}+q^{7}+\zeta_{6}^{2}q^{9}+(1+\cdots)q^{17}+\cdots\)
2128.1.cw.c 2128.cw 532.ah $2$ $1.062$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-19}) \) None 2128.1.cw.c \(0\) \(0\) \(0\) \(-1\) \(q-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+(-1+\zeta_{6}^{2})q^{11}+\cdots\)
2128.1.cw.d 2128.cw 532.ah $2$ $1.062$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-19}) \) None 2128.1.cw.c \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+(1-\zeta_{6}^{2})q^{11}+\cdots\)
2128.1.cw.e 2128.cw 532.ah $2$ $1.062$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-19}) \) None 2128.1.cw.e \(0\) \(0\) \(3\) \(-1\) \(q+(1+\zeta_{6})q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+(1+\cdots)q^{11}+\cdots\)
2128.1.cw.f 2128.cw 532.ah $2$ $1.062$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-19}) \) None 2128.1.cw.e \(0\) \(0\) \(3\) \(1\) \(q+(1+\zeta_{6})q^{5}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+(-1+\cdots)q^{11}+\cdots\)
2128.1.cy.a 2128.cy 133.m $4$ $1.062$ \(\Q(\zeta_{12})\) None None 133.1.m.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}-\zeta_{12}q^{5}+\zeta_{12}^{3}q^{7}+\zeta_{12}^{5}q^{13}+\cdots\)
2128.2.a.a 2128.a 1.a $1$ $16.992$ \(\Q\) None None 532.2.a.a \(0\) \(0\) \(-2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}-3q^{9}-4q^{11}+4q^{13}+\cdots\)
2128.2.a.b 2128.a 1.a $2$ $16.992$ \(\Q(\sqrt{5}) \) None None 266.2.a.b \(0\) \(-3\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(2-3\beta )q^{5}-q^{7}+(-1+\cdots)q^{9}+\cdots\)
2128.2.a.c 2128.a 1.a $2$ $16.992$ \(\Q(\sqrt{5}) \) None None 133.2.a.c \(0\) \(-3\) \(2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+q^{5}-q^{7}+(-1+3\beta )q^{9}+\cdots\)
2128.2.a.d 2128.a 1.a $2$ $16.992$ \(\Q(\sqrt{5}) \) None None 1064.2.a.e \(0\) \(-3\) \(5\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(2+\beta )q^{5}-q^{7}+(-1+\cdots)q^{9}+\cdots\)
2128.2.a.e 2128.a 1.a $2$ $16.992$ \(\Q(\sqrt{5}) \) None None 532.2.a.d \(0\) \(-1\) \(-4\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-1-2\beta )q^{5}+q^{7}+(-2+\cdots)q^{9}+\cdots\)
2128.2.a.f 2128.a 1.a $2$ $16.992$ \(\Q(\sqrt{5}) \) None None 1064.2.a.d \(0\) \(-1\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-q^{5}+q^{7}+(-2+\beta )q^{9}+(-1+\cdots)q^{11}+\cdots\)
2128.2.a.g 2128.a 1.a $2$ $16.992$ \(\Q(\sqrt{29}) \) None None 266.2.a.a \(0\) \(-1\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-1+\beta )q^{5}+q^{7}+(4+\beta )q^{9}+\cdots\)
2128.2.a.h 2128.a 1.a $2$ $16.992$ \(\Q(\sqrt{13}) \) None None 266.2.a.c \(0\) \(-1\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1-\beta )q^{5}-q^{7}+\beta q^{9}+(2+\cdots)q^{11}+\cdots\)
2128.2.a.i 2128.a 1.a $2$ $16.992$ \(\Q(\sqrt{13}) \) None None 1064.2.a.b \(0\) \(1\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+q^{7}+\beta q^{9}+(1-\beta )q^{11}+\cdots\)
2128.2.a.j 2128.a 1.a $2$ $16.992$ \(\Q(\sqrt{5}) \) None None 1064.2.a.c \(0\) \(1\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1+2\beta )q^{5}-q^{7}+(-2+\cdots)q^{9}+\cdots\)
2128.2.a.k 2128.a 1.a $2$ $16.992$ \(\Q(\sqrt{21}) \) None None 532.2.a.c \(0\) \(1\) \(6\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+3q^{5}-q^{7}+(2+\beta )q^{9}+(1+\cdots)q^{11}+\cdots\)
2128.2.a.l 2128.a 1.a $2$ $16.992$ \(\Q(\sqrt{13}) \) None None 133.2.a.b \(0\) \(3\) \(-6\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-3q^{5}-q^{7}+(1+3\beta )q^{9}+\cdots\)
2128.2.a.m 2128.a 1.a $2$ $16.992$ \(\Q(\sqrt{5}) \) None None 532.2.a.b \(0\) \(3\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-q^{5}-q^{7}+(-1+3\beta )q^{9}+\cdots\)
2128.2.a.n 2128.a 1.a $2$ $16.992$ \(\Q(\sqrt{5}) \) None None 1064.2.a.a \(0\) \(3\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(1-2\beta )q^{5}-q^{7}+(-1+\cdots)q^{9}+\cdots\)
2128.2.a.o 2128.a 1.a $2$ $16.992$ \(\Q(\sqrt{5}) \) None None 133.2.a.a \(0\) \(3\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-1+2\beta )q^{5}+q^{7}+(-1+\cdots)q^{9}+\cdots\)
2128.2.a.p 2128.a 1.a $3$ $16.992$ 3.3.229.1 None None 133.2.a.d \(0\) \(-3\) \(-2\) \(3\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
2128.2.a.q 2128.a 1.a $3$ $16.992$ 3.3.1101.1 None None 1064.2.a.f \(0\) \(1\) \(2\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{2})q^{5}-q^{7}+(4-\beta _{1}+\cdots)q^{9}+\cdots\)
2128.2.a.r 2128.a 1.a $3$ $16.992$ 3.3.733.1 None None 532.2.a.e \(0\) \(1\) \(2\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+q^{7}+(2+\cdots)q^{9}+\cdots\)
2128.2.a.s 2128.a 1.a $3$ $16.992$ 3.3.469.1 None None 266.2.a.d \(0\) \(1\) \(5\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(2-\beta _{1})q^{5}+q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
2128.2.a.t 2128.a 1.a $4$ $16.992$ 4.4.25857.1 None None 1064.2.a.h \(0\) \(-2\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
2128.2.a.u 2128.a 1.a $4$ $16.992$ 4.4.18097.1 None None 1064.2.a.g \(0\) \(0\) \(-3\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+(-1-\beta _{2}+\beta _{3})q^{5}+q^{7}+\cdots\)
2128.2.a.v 2128.a 1.a $5$ $16.992$ 5.5.10463409.1 None None 1064.2.a.i \(0\) \(0\) \(3\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1-\beta _{4})q^{5}+q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
2128.2.j.a 2128.j 28.d $2$ $16.992$ \(\Q(\sqrt{-3}) \) None None 2128.2.j.a \(0\) \(-4\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{2}]$ \(q-2q^{3}+(-1+2\zeta_{6})q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
2128.2.j.b 2128.j 28.d $2$ $16.992$ \(\Q(\sqrt{-3}) \) None None 2128.2.j.b \(0\) \(-2\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(2-4\zeta_{6})q^{5}+(-2+3\zeta_{6})q^{7}+\cdots\)
2128.2.j.c 2128.j 28.d $2$ $16.992$ \(\Q(\sqrt{-3}) \) None None 2128.2.j.b \(0\) \(2\) \(0\) \(1\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(2-4\zeta_{6})q^{5}+(2-3\zeta_{6})q^{7}+\cdots\)
2128.2.j.d 2128.j 28.d $2$ $16.992$ \(\Q(\sqrt{-3}) \) None None 2128.2.j.a \(0\) \(4\) \(0\) \(5\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{3}+(1-2\zeta_{6})q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
2128.2.j.e 2128.j 28.d $12$ $16.992$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None 2128.2.j.e \(0\) \(0\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}-\beta _{6}q^{5}+\beta _{8}q^{7}+(1-\beta _{3}+\cdots)q^{9}+\cdots\)
2128.2.j.f 2128.j 28.d $12$ $16.992$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None 2128.2.j.e \(0\) \(0\) \(0\) \(5\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}-\beta _{6}q^{5}-\beta _{8}q^{7}+(1-\beta _{3}+\cdots)q^{9}+\cdots\)
2128.2.j.g 2128.j 28.d $20$ $16.992$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None 2128.2.j.g \(0\) \(-2\) \(0\) \(1\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+\beta _{15}q^{5}+\beta _{13}q^{7}+(1-\beta _{3}+\cdots)q^{9}+\cdots\)
2128.2.j.h 2128.j 28.d $20$ $16.992$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None 2128.2.j.g \(0\) \(2\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{15}q^{5}-\beta _{13}q^{7}+(1-\beta _{3}+\cdots)q^{9}+\cdots\)
2128.2.m.a 2128.m 133.c $2$ $16.992$ \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{-19}) \) None 133.2.c.a \(0\) \(0\) \(0\) \(3\) $\mathrm{U}(1)[D_{2}]$ \(q+(-1+2\beta )q^{5}+(1+\beta )q^{7}-3q^{9}+\cdots\)
2128.2.m.b 2128.m 133.c $4$ $16.992$ \(\Q(i, \sqrt{13})\) None None 133.2.c.b \(0\) \(-2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{3})q^{3}+\beta _{2}q^{5}+(1-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
2128.2.m.c 2128.m 133.c $4$ $16.992$ \(\Q(\sqrt{-3}, \sqrt{-19})\) \(\Q(\sqrt{-19}) \) None 532.2.g.a \(0\) \(0\) \(0\) \(-3\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}-\beta _{3})q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
2128.2.m.d 2128.m 133.c $4$ $16.992$ \(\Q(i, \sqrt{13})\) None None 133.2.c.b \(0\) \(2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{3})q^{3}-\beta _{2}q^{5}+(1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
2128.2.m.e 2128.m 133.c $8$ $16.992$ 8.0.\(\cdots\).5 None None 532.2.g.b \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{3}-\beta _{3}q^{5}+(1+\beta _{2}+\beta _{4})q^{7}+\cdots\)
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