Learn more

Refine search


Results (1-50 of 210 matches)

Next   Download to        
Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
171.1.c.a 171.c 19.b $1$ $0.085$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{57}) \) \(0\) \(0\) \(0\) \(-2\) \(q+q^{4}-2q^{7}+q^{16}-q^{19}-q^{25}+\cdots\)
171.1.o.a 171.o 171.o $4$ $0.085$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-2\) \(-2\) \(q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{5}+\cdots\)
171.1.p.a 171.p 19.d $2$ $0.085$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q-\zeta_{6}q^{4}+q^{7}+(-1+\zeta_{6}^{2})q^{13}+\zeta_{6}^{2}q^{16}+\cdots\)
171.2.a.a 171.a 1.a $1$ $1.365$ \(\Q\) None None \(-1\) \(0\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+2q^{5}+3q^{8}-2q^{10}+\cdots\)
171.2.a.b 171.a 1.a $1$ $1.365$ \(\Q\) None None \(0\) \(0\) \(-3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-3q^{5}-q^{7}-3q^{11}-4q^{13}+\cdots\)
171.2.a.c 171.a 1.a $1$ $1.365$ \(\Q\) None None \(2\) \(0\) \(-1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}+3q^{7}-2q^{10}+\cdots\)
171.2.a.d 171.a 1.a $1$ $1.365$ \(\Q\) None None \(2\) \(0\) \(3\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+3q^{5}-5q^{7}+6q^{10}+\cdots\)
171.2.a.e 171.a 1.a $4$ $1.365$ 4.4.13068.1 None None \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{3})q^{4}+(\beta _{1}+\beta _{2})q^{5}+\cdots\)
171.2.d.a 171.d 57.d $4$ $1.365$ \(\Q(\sqrt{-2}, \sqrt{19})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{4}+\beta _{1}q^{5}+\beta _{3}q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
171.2.d.b 171.d 57.d $4$ $1.365$ \(\Q(\sqrt{-2}, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+3q^{4}-\beta _{1}q^{5}-2q^{7}-\beta _{3}q^{8}+\cdots\)
171.2.e.a 171.e 9.c $18$ $1.365$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(-3\) \(-1\) \(-9\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{4})q^{2}+(\beta _{2}+\beta _{10})q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots\)
171.2.e.b 171.e 9.c $18$ $1.365$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(3\) \(-1\) \(7\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{8}+\beta _{11})q^{2}+(-\beta _{3}+\beta _{16})q^{3}+\cdots\)
171.2.f.a 171.f 19.c $2$ $1.365$ \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+q^{7}+3q^{8}+\cdots\)
171.2.f.b 171.f 19.c $6$ $1.365$ 6.0.954288.1 None None \(-1\) \(0\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{4}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots\)
171.2.f.c 171.f 19.c $8$ $1.365$ 8.0.764411904.5 None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{5}q^{2}+(-1-\beta _{3}+\beta _{4}-\beta _{6})q^{4}+\cdots\)
171.2.g.a 171.g 171.g $2$ $1.365$ \(\Q(\sqrt{-3}) \) None None \(1\) \(-3\) \(6\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
171.2.g.b 171.g 171.g $2$ $1.365$ \(\Q(\sqrt{-3}) \) None None \(1\) \(3\) \(-2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(2-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
171.2.g.c 171.g 171.g $32$ $1.365$ None None \(1\) \(-2\) \(-6\) \(1\) $\mathrm{SU}(2)[C_{3}]$
171.2.h.a 171.h 171.h $2$ $1.365$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-1+2\zeta_{6})q^{3}-q^{4}-3\zeta_{6}q^{5}+\cdots\)
171.2.h.b 171.h 171.h $2$ $1.365$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+\zeta_{6}q^{5}+\cdots\)
171.2.h.c 171.h 171.h $32$ $1.365$ None None \(-2\) \(1\) \(3\) \(1\) $\mathrm{SU}(2)[C_{3}]$
171.2.k.a 171.k 171.k $36$ $1.365$ None None \(-3\) \(-6\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{6}]$
171.2.l.a 171.l 171.l $36$ $1.365$ None None \(0\) \(0\) \(-6\) \(-4\) $\mathrm{SU}(2)[C_{6}]$
171.2.m.a 171.m 57.f $16$ $1.365$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{2}+(-\beta _{3}+2\beta _{4}+\beta _{10})q^{4}+\cdots\)
171.2.t.a 171.t 171.t $36$ $1.365$ None None \(-6\) \(-3\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{6}]$
171.2.u.a 171.u 19.e $6$ $1.365$ \(\Q(\zeta_{18})\) None None \(-3\) \(0\) \(6\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{5})q^{2}+(-1+\cdots)q^{4}+\cdots\)
171.2.u.b 171.u 19.e $6$ $1.365$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{9}]$ \(q-2\zeta_{18}^{2}q^{4}+(3\zeta_{18}-\zeta_{18}^{2}-2\zeta_{18}^{4}+\cdots)q^{7}+\cdots\)
171.2.u.c 171.u 19.e $6$ $1.365$ \(\Q(\zeta_{18})\) None None \(6\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(1-\zeta_{18}+\zeta_{18}^{2})q^{2}+(1-2\zeta_{18}+\cdots)q^{4}+\cdots\)
171.2.u.d 171.u 19.e $12$ $1.365$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{1}q^{2}+(-1+2\beta _{6}-\beta _{7}-\beta _{9})q^{4}+\cdots\)
171.2.u.e 171.u 19.e $12$ $1.365$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(3\) \(0\) \(-6\) \(-9\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-1+\beta _{1}+\beta _{2}-\beta _{5}+\beta _{9})q^{2}+(-1+\cdots)q^{4}+\cdots\)
171.2.v.a 171.v 171.v $108$ $1.365$ None None \(-3\) \(-12\) \(-3\) \(3\) $\mathrm{SU}(2)[C_{9}]$
171.2.w.a 171.w 171.w $108$ $1.365$ None None \(-3\) \(-3\) \(-3\) \(-6\) $\mathrm{SU}(2)[C_{9}]$
171.2.x.a 171.x 171.x $108$ $1.365$ None None \(-9\) \(0\) \(-9\) \(3\) $\mathrm{SU}(2)[C_{18}]$
171.2.y.a 171.y 57.j $36$ $1.365$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
171.2.bd.a 171.bd 171.ad $108$ $1.365$ None None \(-9\) \(-9\) \(-9\) \(-6\) $\mathrm{SU}(2)[C_{18}]$
171.3.b.a 171.b 3.b $12$ $4.659$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\)
171.3.c.a 171.c 19.b $1$ $4.659$ \(\Q\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(9\) \(-5\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{4}+9q^{5}-5q^{7}-3q^{11}+2^{4}q^{16}+\cdots\)
171.3.c.b 171.c 19.b $2$ $4.659$ \(\Q(\sqrt{-13}) \) None None \(0\) \(0\) \(-8\) \(-10\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-9q^{4}-4q^{5}-5q^{7}-5\beta q^{8}+\cdots\)
171.3.c.c 171.c 19.b $2$ $4.659$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-8\) \(-20\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{2}+q^{4}-4q^{5}-10q^{7}-5\zeta_{6}q^{8}+\cdots\)
171.3.c.d 171.c 19.b $2$ $4.659$ \(\Q(\sqrt{19}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(10\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{4}+\beta q^{5}+5q^{7}-5\beta q^{11}+2^{4}q^{16}+\cdots\)
171.3.c.e 171.c 19.b $4$ $4.659$ \(\Q(\sqrt{-7}, \sqrt{10})\) None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-3q^{4}+\beta _{2}q^{5}-2q^{7}-\beta _{1}q^{8}+\cdots\)
171.3.c.f 171.c 19.b $4$ $4.659$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None None \(0\) \(0\) \(10\) \(34\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(3-\beta _{2})q^{5}+\cdots\)
171.3.i.a 171.i 171.i $76$ $4.659$ None None \(0\) \(-3\) \(1\) \(-3\) $\mathrm{SU}(2)[C_{6}]$
171.3.j.a 171.j 171.j $76$ $4.659$ None None \(0\) \(-5\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{6}]$
171.3.n.a 171.n 171.n $76$ $4.659$ None None \(-3\) \(1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{6}]$
171.3.o.a 171.o 171.o $76$ $4.659$ None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
171.3.p.a 171.p 19.d $2$ $4.659$ \(\Q(\sqrt{-3}) \) None None \(-3\) \(0\) \(-4\) \(10\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-4+4\zeta_{6})q^{5}+\cdots\)
171.3.p.b 171.p 19.d $2$ $4.659$ \(\Q(\sqrt{-3}) \) None None \(3\) \(0\) \(4\) \(10\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(4-4\zeta_{6})q^{5}+\cdots\)
171.3.p.c 171.p 19.d $6$ $4.659$ 6.0.92607408.1 None None \(-3\) \(0\) \(-4\) \(-22\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{4}q^{2}+(1+\beta _{1}+2\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots\)
171.3.p.d 171.p 19.d $6$ $4.659$ 6.0.6967728.1 None None \(3\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\beta _{5})q^{2}+(-2\beta _{1}-2\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
Next   Download to