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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
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
869.1.j.a 869.j 869.j $20$ $0.434$ \(\Q(\zeta_{50})\) \(\Q(\sqrt{-79}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{2}+(-\zeta_{50}^{5}+\cdots)q^{4}+\cdots\)
869.2.a.a 869.a 1.a $1$ $6.939$ \(\Q\) None None \(-2\) \(1\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}-2q^{7}+\cdots\)
869.2.a.b 869.a 1.a $1$ $6.939$ \(\Q\) None None \(-1\) \(-2\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}-q^{4}+2q^{5}+2q^{6}+4q^{7}+\cdots\)
869.2.a.c 869.a 1.a $1$ $6.939$ \(\Q\) None None \(1\) \(-1\) \(1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
869.2.a.d 869.a 1.a $1$ $6.939$ \(\Q\) None None \(1\) \(1\) \(1\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}-5q^{7}+\cdots\)
869.2.a.e 869.a 1.a $11$ $6.939$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(-3\) \(-3\) \(-8\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(\beta _{1}+\beta _{7}+\beta _{8})q^{4}+\cdots\)
869.2.a.f 869.a 1.a $11$ $6.939$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(1\) \(-9\) \(-8\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1-\beta _{7})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
869.2.a.g 869.a 1.a $18$ $6.939$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(4\) \(8\) \(-3\) \(10\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{15}q^{3}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)
869.2.a.h 869.a 1.a $21$ $6.939$ None None \(0\) \(7\) \(6\) \(10\) $-$ $\mathrm{SU}(2)$
869.2.b.a 869.b 869.b $10$ $6.939$ 10.0.\(\cdots\).1 \(\Q(\sqrt{-79}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{8}q^{2}+(-2+\beta _{1}+\beta _{5}-\beta _{6}-\beta _{8}+\cdots)q^{4}+\cdots\)
869.2.b.b 869.b 869.b $68$ $6.939$ None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$
869.2.e.a 869.e 79.c $66$ $6.939$ None None \(0\) \(-3\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$
869.2.e.b 869.e 79.c $66$ $6.939$ None None \(0\) \(1\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$
869.2.f.a 869.f 11.c $4$ $6.939$ \(\Q(\zeta_{10})\) None None \(-3\) \(-1\) \(-3\) \(-5\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}^{3})q^{2}+(-\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
869.2.f.b 869.f 11.c $132$ $6.939$ None None \(2\) \(4\) \(16\) \(8\) $\mathrm{SU}(2)[C_{5}]$
869.2.f.c 869.f 11.c $176$ $6.939$ None None \(-1\) \(-9\) \(-19\) \(3\) $\mathrm{SU}(2)[C_{5}]$
869.2.i.a 869.i 869.i $156$ $6.939$ None None \(0\) \(-6\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
869.2.l.a 869.l 869.l $8$ $6.939$ 8.0.484000000.9 None None \(10\) \(0\) \(14\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(2+\beta _{2}+\beta _{3}-\beta _{5})q^{2}+(-\beta _{1}-\beta _{4}+\cdots)q^{3}+\cdots\)
869.2.l.b 869.l 869.l $40$ $6.939$ \(\Q(\sqrt{-79}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{10}]$
869.2.l.c 869.l 869.l $264$ $6.939$ None None \(-20\) \(0\) \(-20\) \(0\) $\mathrm{SU}(2)[C_{10}]$
869.2.m.a 869.m 79.e $408$ $6.939$ None None \(0\) \(-4\) \(0\) \(1\) $\mathrm{SU}(2)[C_{13}]$
869.2.m.b 869.m 79.e $408$ $6.939$ None None \(0\) \(0\) \(0\) \(-13\) $\mathrm{SU}(2)[C_{13}]$
869.2.n.a 869.n 869.n $8$ $6.939$ \(\Q(\zeta_{15})\) None None \(-3\) \(-1\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{15}]$ \(q+(\zeta_{15}^{2}+\zeta_{15}^{5})q^{2}+(1-\zeta_{15}+\zeta_{15}^{3}+\cdots)q^{3}+\cdots\)
869.2.n.b 869.n 869.n $616$ $6.939$ None None \(2\) \(-2\) \(-1\) \(-7\) $\mathrm{SU}(2)[C_{15}]$
869.2.q.a 869.q 869.q $936$ $6.939$ None None \(0\) \(-26\) \(-22\) \(0\) $\mathrm{SU}(2)[C_{26}]$
869.2.r.a 869.r 869.r $624$ $6.939$ None None \(-5\) \(-9\) \(-3\) \(-15\) $\mathrm{SU}(2)[C_{30}]$
869.2.u.a 869.u 79.g $792$ $6.939$ None None \(0\) \(-1\) \(0\) \(11\) $\mathrm{SU}(2)[C_{39}]$
869.2.u.b 869.u 79.g $792$ $6.939$ None None \(0\) \(3\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{39}]$
869.2.v.a 869.v 869.v $3744$ $6.939$ None None \(-37\) \(-33\) \(-33\) \(-45\) $\mathrm{SU}(2)[C_{65}]$
869.2.w.a 869.w 869.w $1872$ $6.939$ None None \(0\) \(-46\) \(-50\) \(0\) $\mathrm{SU}(2)[C_{78}]$
869.2.z.a 869.z 869.z $3744$ $6.939$ None None \(-55\) \(-39\) \(-33\) \(-65\) $\mathrm{SU}(2)[C_{130}]$
869.2.bc.a 869.bc 869.ac $7488$ $6.939$ None None \(-77\) \(-75\) \(-75\) \(-75\) $\mathrm{SU}(2)[C_{195}]$
869.2.bf.a 869.bf 869.af $7488$ $6.939$ None None \(-125\) \(-69\) \(-75\) \(-115\) $\mathrm{SU}(2)[C_{390}]$
869.4.a.a 869.a 1.a $44$ $51.273$ None None \(-2\) \(-16\) \(-32\) \(-70\) $-$ $\mathrm{SU}(2)$
869.4.a.b 869.a 1.a $46$ $51.273$ None None \(-8\) \(-24\) \(-30\) \(-98\) $-$ $\mathrm{SU}(2)$
869.4.a.c 869.a 1.a $52$ $51.273$ None None \(-2\) \(26\) \(28\) \(70\) $+$ $\mathrm{SU}(2)$
869.4.a.d 869.a 1.a $54$ $51.273$ None None \(8\) \(18\) \(30\) \(98\) $+$ $\mathrm{SU}(2)$
869.6.a.a 869.a 1.a $76$ $139.374$ None None \(-16\) \(-79\) \(-174\) \(-686\) $+$ $\mathrm{SU}(2)$
869.6.a.b 869.a 1.a $78$ $139.374$ None None \(4\) \(-48\) \(-131\) \(-490\) $+$ $\mathrm{SU}(2)$
869.6.a.c 869.a 1.a $84$ $139.374$ None None \(16\) \(47\) \(126\) \(686\) $-$ $\mathrm{SU}(2)$
869.6.a.d 869.a 1.a $86$ $139.374$ None None \(4\) \(78\) \(169\) \(490\) $-$ $\mathrm{SU}(2)$
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