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Results (41 matches)

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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3871.1.c.a 3871.c 79.b $1$ $1.932$ \(\Q\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-79}) \) \(\Q(\sqrt{553}) \) \(2\) \(0\) \(0\) \(0\) \(q+2q^{2}+3q^{4}+4q^{8}+q^{9}-2q^{11}+\cdots\)
3871.1.c.b 3871.c 79.b $2$ $1.932$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-79}) \) None \(-4\) \(0\) \(0\) \(0\) \(q-2q^{2}+3q^{4}-\beta q^{5}-4q^{8}+q^{9}+\cdots\)
3871.1.c.c 3871.c 79.b $2$ $1.932$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-79}) \) None \(-1\) \(0\) \(1\) \(0\) \(q-\beta q^{2}+\beta q^{4}+(1-\beta )q^{5}-q^{8}+q^{9}+\cdots\)
3871.1.c.d 3871.c 79.b $4$ $1.932$ \(\Q(\zeta_{20})^+\) \(\Q(\sqrt{-79}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+(-1-\beta _{2})q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots\)
3871.1.c.e 3871.c 79.b $8$ $1.932$ \(\Q(\zeta_{40})^+\) \(\Q(\sqrt{-79}) \) None \(4\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}-\beta _{4}q^{4}+\beta _{7}q^{5}+q^{8}+q^{9}+\cdots\)
3871.1.i.a 3871.i 553.i $2$ $1.932$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}+q^{8}+q^{9}+\zeta_{6}q^{11}-\zeta_{6}^{2}q^{16}+\cdots\)
3871.1.i.b 3871.i 553.i $4$ $1.932$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(-2\) \(0\) \(0\) \(0\) \(q+(-1+\beta _{2})q^{2}-\beta _{3}q^{3}+\beta _{1}q^{6}-q^{8}+\cdots\)
3871.1.j.a 3871.j 553.j $2$ $1.932$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{2}+q^{8}+q^{9}+\zeta_{6}^{2}q^{11}+\zeta_{6}q^{16}+\cdots\)
3871.1.m.a 3871.m 553.m $2$ $1.932$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-79}) \) \(\Q(\sqrt{553}) \) \(-2\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{2}+3\zeta_{6}^{2}q^{4}-2q^{8}-\zeta_{6}q^{9}+\cdots\)
3871.1.m.b 3871.m 553.m $4$ $1.932$ \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-79}) \) None \(1\) \(0\) \(-1\) \(0\) \(q+(-\beta _{1}-\beta _{2})q^{2}-\beta _{1}q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
3871.1.m.c 3871.m 553.m $4$ $1.932$ \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-79}) \) None \(1\) \(0\) \(1\) \(0\) \(q+(-\beta _{1}-\beta _{2})q^{2}-\beta _{1}q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
3871.1.m.d 3871.m 553.m $4$ $1.932$ \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-79}) \) None \(4\) \(0\) \(0\) \(0\) \(q-2\beta _{2}q^{2}+(-3-3\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
3871.1.m.e 3871.m 553.m $8$ $1.932$ 8.0.324000000.2 \(\Q(\sqrt{-79}) \) None \(2\) \(0\) \(0\) \(0\) \(q+(\beta _{2}+\beta _{6})q^{2}+\beta _{6}q^{4}+(-\beta _{1}-\beta _{5}+\cdots)q^{5}+\cdots\)
3871.1.m.f 3871.m 553.m $16$ $1.932$ 16.0.\(\cdots\).5 \(\Q(\sqrt{-79}) \) None \(-4\) \(0\) \(0\) \(0\) \(q+(\beta _{4}+\beta _{7}+\beta _{8})q^{2}+(-\beta _{7}-\beta _{8})q^{4}+\cdots\)
3871.1.n.a 3871.n 79.d $2$ $1.932$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{2}+q^{8}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{11}+\cdots\)
3871.1.s.a 3871.s 553.s $2$ $1.932$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{8}+\zeta_{6}^{2}q^{9}+q^{11}-q^{16}+\cdots\)
3871.1.t.a 3871.t 553.t $2$ $1.932$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{8}-\zeta_{6}q^{9}-q^{11}-q^{16}+\cdots\)
3871.1.t.b 3871.t 553.t $4$ $1.932$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(4\) \(0\) \(0\) \(0\) \(q+q^{2}+\beta _{1}q^{3}+\beta _{1}q^{6}-q^{8}+\beta _{2}q^{9}+\cdots\)
3871.1.be.a 3871.be 79.f $12$ $1.932$ \(\Q(\zeta_{26})\) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+(\zeta_{26}^{2}-\zeta_{26}^{9})q^{2}+(\zeta_{26}^{4}-\zeta_{26}^{5}+\cdots)q^{4}+\cdots\)
3871.1.bw.a 3871.bw 553.ac $24$ $1.932$ \(\Q(\zeta_{39})\) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(0\) \(q+(-\zeta_{78}^{17}-\zeta_{78}^{37})q^{2}+(-\zeta_{78}^{15}+\cdots)q^{4}+\cdots\)
3871.1.bx.a 3871.bx 553.ad $24$ $1.932$ \(\Q(\zeta_{39})\) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(0\) \(q+(\zeta_{78}^{4}-\zeta_{78}^{11})q^{2}+(\zeta_{78}^{8}-\zeta_{78}^{15}+\cdots)q^{4}+\cdots\)
3871.1.cb.a 3871.cb 553.ah $24$ $1.932$ \(\Q(\zeta_{39})\) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(0\) \(q+(-\zeta_{78}-\zeta_{78}^{37})q^{2}+(\zeta_{78}^{2}-\zeta_{78}^{35}+\cdots)q^{4}+\cdots\)
3871.1.cc.a 3871.cc 79.h $24$ $1.932$ \(\Q(\zeta_{39})\) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(0\) \(q+(-\zeta_{78}^{19}+\zeta_{78}^{36})q^{2}+(\zeta_{78}^{16}+\cdots)q^{4}+\cdots\)
3871.1.cd.a 3871.cd 553.aj $24$ $1.932$ \(\Q(\zeta_{39})\) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(0\) \(q+(\zeta_{78}^{22}+\zeta_{78}^{28})q^{2}+(-\zeta_{78}^{5}-\zeta_{78}^{11}+\cdots)q^{4}+\cdots\)
3871.1.cg.a 3871.cg 553.am $24$ $1.932$ \(\Q(\zeta_{39})\) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(0\) \(q+(\zeta_{78}^{34}+\zeta_{78}^{36})q^{2}+(-\zeta_{78}^{29}+\cdots)q^{4}+\cdots\)
3871.1.ch.a 3871.ch 553.an $24$ $1.932$ \(\Q(\zeta_{39})\) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(0\) \(q+(-\zeta_{78}^{29}-\zeta_{78}^{33})q^{2}+(-\zeta_{78}^{19}+\cdots)q^{4}+\cdots\)
3871.2.a.a 3871.a 1.a $1$ $30.910$ \(\Q\) None None \(-1\) \(1\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}+3q^{5}-q^{6}+3q^{8}+\cdots\)
3871.2.a.b 3871.a 1.a $2$ $30.910$ \(\Q(\sqrt{2}) \) None None \(-2\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2\beta q^{3}-q^{4}+\beta q^{5}+2\beta q^{6}+\cdots\)
3871.2.a.c 3871.a 1.a $5$ $30.910$ 5.5.81589.1 None None \(0\) \(-1\) \(-7\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots\)
3871.2.a.d 3871.a 1.a $7$ $30.910$ 7.7.99230049.1 None None \(-6\) \(3\) \(4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{6})q^{2}-\beta _{4}q^{3}+(1+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
3871.2.a.e 3871.a 1.a $8$ $30.910$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(3\) \(-3\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
3871.2.a.f 3871.a 1.a $11$ $30.910$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(-5\) \(5\) \(10\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
3871.2.a.g 3871.a 1.a $13$ $30.910$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None None \(7\) \(-1\) \(-4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+\beta _{4}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
3871.2.a.h 3871.a 1.a $14$ $30.910$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(-4\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1-\beta _{5})q^{4}+\beta _{4}q^{5}+\cdots\)
3871.2.a.i 3871.a 1.a $24$ $30.910$ None None \(4\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$
3871.2.a.j 3871.a 1.a $26$ $30.910$ None None \(0\) \(-6\) \(-17\) \(0\) $+$ $\mathrm{SU}(2)$
3871.2.a.k 3871.a 1.a $26$ $30.910$ None None \(0\) \(-6\) \(-15\) \(0\) $+$ $\mathrm{SU}(2)$
3871.2.a.l 3871.a 1.a $26$ $30.910$ None None \(0\) \(6\) \(15\) \(0\) $-$ $\mathrm{SU}(2)$
3871.2.a.m 3871.a 1.a $26$ $30.910$ None None \(0\) \(6\) \(17\) \(0\) $-$ $\mathrm{SU}(2)$
3871.2.a.n 3871.a 1.a $28$ $30.910$ None None \(-4\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$
3871.2.a.o 3871.a 1.a $50$ $30.910$ None None \(10\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$
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