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Results (46 matches)

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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3971.1.c.a 3971.c 11.b $1$ $1.982$ \(\Q\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{209}) \) \(0\) \(0\) \(-2\) \(0\) \(q+q^{4}-2q^{5}-q^{9}-q^{11}+q^{16}-2q^{20}+\cdots\)
3971.1.c.b 3971.c 11.b $2$ $1.982$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(2\) \(0\) \(q-iq^{2}-q^{3}+q^{5}+iq^{6}-iq^{8}-iq^{10}+\cdots\)
3971.1.c.c 3971.c 11.b $2$ $1.982$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(-1\) \(0\) \(q+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{5}+\cdots\)
3971.1.c.d 3971.c 11.b $2$ $1.982$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(-1\) \(0\) \(q+(1-\beta )q^{3}+q^{4}+(-1+\beta )q^{5}+(1+\cdots)q^{9}+\cdots\)
3971.1.c.e 3971.c 11.b $2$ $1.982$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(2\) \(0\) \(q-iq^{2}+q^{3}+q^{5}-iq^{6}-iq^{8}-iq^{10}+\cdots\)
3971.1.c.f 3971.c 11.b $4$ $1.982$ \(\Q(\zeta_{20})^+\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}+(2+\beta _{2})q^{9}+\cdots\)
3971.1.h.a 3971.h 209.h $2$ $1.982$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{209}) \) \(0\) \(0\) \(2\) \(0\) \(q+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{9}-q^{11}+\cdots\)
3971.1.h.b 3971.h 209.h $4$ $1.982$ \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(1\) \(0\) \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-1-\beta _{3})q^{4}+\cdots\)
3971.1.h.c 3971.h 209.h $4$ $1.982$ \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(1\) \(0\) \(q+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-1-\beta _{3})q^{4}+\cdots\)
3971.1.h.d 3971.h 209.h $4$ $1.982$ \(\Q(\zeta_{12})\) None None \(0\) \(2\) \(-2\) \(0\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{5}q^{6}+\cdots\)
3971.1.h.e 3971.h 209.h $8$ $1.982$ 8.0.324000000.2 \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-\beta _{1}-\beta _{5})q^{3}+(-1-\beta _{4})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
3971.1.l.a 3971.l 11.d $4$ $1.982$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(-5\) \(q+\zeta_{10}^{4}q^{4}+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{5}+\cdots\)
3971.1.q.a 3971.q 209.q $6$ $1.982$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{209}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{2}q^{4}+\zeta_{18}^{7}q^{5}-\zeta_{18}^{8}q^{9}+\cdots\)
3971.1.q.b 3971.q 209.q $12$ $1.982$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{3}+\beta _{3}q^{4}+(\beta _{4}+\beta _{10})q^{5}+(\beta _{1}+\cdots)q^{9}+\cdots\)
3971.1.q.c 3971.q 209.q $12$ $1.982$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{4}-\beta _{5})q^{3}+\beta _{3}q^{4}+(-\beta _{4}-\beta _{10}+\cdots)q^{5}+\cdots\)
3971.1.q.d 3971.q 209.q $12$ $1.982$ \(\Q(\zeta_{36})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{36}^{11}q^{2}-\zeta_{36}^{8}q^{3}-\zeta_{36}^{14}q^{5}+\cdots\)
3971.1.q.e 3971.q 209.q $12$ $1.982$ \(\Q(\zeta_{36})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{36}^{11}q^{2}+\zeta_{36}^{8}q^{3}-\zeta_{36}^{14}q^{5}+\cdots\)
3971.1.q.f 3971.q 209.q $24$ $1.982$ 24.0.\(\cdots\).3 \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{11}+\beta _{23})q^{3}-\beta _{8}q^{4}-\beta _{16}q^{5}+\cdots\)
3971.1.s.a 3971.s 209.r $8$ $1.982$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(6\) \(q-\zeta_{30}^{13}q^{4}+(\zeta_{30}^{8}+\zeta_{30}^{14})q^{5}+\cdots\)
3971.1.t.a 3971.t 209.s $8$ $1.982$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-2\) \(-10\) \(q-\zeta_{30}^{11}q^{4}+(\zeta_{30}+\zeta_{30}^{13})q^{5}+(-1+\cdots)q^{7}+\cdots\)
3971.1.ba.a 3971.ba 209.v $24$ $1.982$ \(\Q(\zeta_{45})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(15\) \(q+\zeta_{90}^{22}q^{4}+(-\zeta_{90}^{32}+\zeta_{90}^{41}+\cdots)q^{5}+\cdots\)
3971.1.bc.a 3971.bc 209.x $24$ $1.982$ \(\Q(\zeta_{45})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(-9\) \(q+\zeta_{90}^{28}q^{4}+(\zeta_{90}^{8}+\zeta_{90}^{44})q^{5}+\cdots\)
3971.2.a.a 3971.a 1.a $1$ $31.709$ \(\Q\) None None \(0\) \(-1\) \(-3\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-3q^{5}-4q^{7}-2q^{9}+\cdots\)
3971.2.a.b 3971.a 1.a $1$ $31.709$ \(\Q\) None None \(2\) \(1\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots\)
3971.2.a.c 3971.a 1.a $2$ $31.709$ \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(-2\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2q^{4}-q^{5}-4q^{7}+4q^{9}+\cdots\)
3971.2.a.d 3971.a 1.a $2$ $31.709$ \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(-2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1-\beta )q^{3}-q^{5}+(-2+\beta )q^{6}+\cdots\)
3971.2.a.e 3971.a 1.a $3$ $31.709$ \(\Q(\zeta_{18})^+\) None None \(-3\) \(-6\) \(-6\) \(-6\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-2q^{3}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
3971.2.a.f 3971.a 1.a $3$ $31.709$ \(\Q(\zeta_{18})^+\) None None \(3\) \(6\) \(-6\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+2q^{3}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
3971.2.a.g 3971.a 1.a $4$ $31.709$ \(\Q(\sqrt{3}, \sqrt{7})\) None None \(0\) \(0\) \(2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{3})q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}+\cdots\)
3971.2.a.h 3971.a 1.a $5$ $31.709$ 5.5.246832.1 None None \(-2\) \(-1\) \(-5\) \(6\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-\beta _{3}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
3971.2.a.i 3971.a 1.a $7$ $31.709$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(1\) \(-2\) \(2\) \(10\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(2+\beta _{2}+\beta _{3})q^{4}+\cdots\)
3971.2.a.j 3971.a 1.a $9$ $31.709$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(-1\) \(-4\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+\beta _{8}q^{5}+\cdots\)
3971.2.a.k 3971.a 1.a $9$ $31.709$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(-1\) \(0\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
3971.2.a.l 3971.a 1.a $9$ $31.709$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(1\) \(0\) \(0\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
3971.2.a.m 3971.a 1.a $9$ $31.709$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(1\) \(4\) \(0\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+\beta _{8}q^{5}+\cdots\)
3971.2.a.n 3971.a 1.a $10$ $31.709$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(-2\) \(1\) \(-8\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{7}q^{3}+(-\beta _{5}+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
3971.2.a.o 3971.a 1.a $10$ $31.709$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(0\) \(2\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(2+\beta _{2})q^{4}+\beta _{8}q^{5}+\cdots\)
3971.2.a.p 3971.a 1.a $10$ $31.709$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(2\) \(-1\) \(-8\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(-\beta _{5}+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
3971.2.a.q 3971.a 1.a $18$ $31.709$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(-2\) \(0\) \(5\) \(7\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
3971.2.a.r 3971.a 1.a $18$ $31.709$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(2\) \(0\) \(5\) \(7\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
3971.2.a.s 3971.a 1.a $21$ $31.709$ None None \(-6\) \(-15\) \(6\) \(6\) $+$ $\mathrm{SU}(2)$
3971.2.a.t 3971.a 1.a $21$ $31.709$ None None \(6\) \(15\) \(6\) \(6\) $-$ $\mathrm{SU}(2)$
3971.2.a.u 3971.a 1.a $24$ $31.709$ None None \(-3\) \(-3\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$
3971.2.a.v 3971.a 1.a $24$ $31.709$ None None \(0\) \(0\) \(-10\) \(-14\) $+$ $\mathrm{SU}(2)$
3971.2.a.w 3971.a 1.a $24$ $31.709$ None None \(3\) \(3\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$
3971.2.a.x 3971.a 1.a $40$ $31.709$ None None \(0\) \(0\) \(28\) \(14\) $-$ $\mathrm{SU}(2)$
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