Learn more

Refine search


Results (1-50 of 176 matches)

Next   Download to        
Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
57.1.h.a 57.h 57.h $2$ $0.028$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-2\) \(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{7}-\zeta_{6}q^{9}+q^{12}+\cdots\)
57.2.a.a 57.a 1.a $1$ $0.455$ \(\Q\) None None \(-2\) \(-1\) \(-3\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}-3q^{5}+2q^{6}+\cdots\)
57.2.a.b 57.a 1.a $1$ $0.455$ \(\Q\) None None \(-2\) \(1\) \(1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+3q^{7}+\cdots\)
57.2.a.c 57.a 1.a $1$ $0.455$ \(\Q\) None None \(1\) \(1\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}-3q^{8}+\cdots\)
57.2.d.a 57.d 57.d $4$ $0.455$ \(\Q(\sqrt{2}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-\beta _{1}q^{3}+\beta _{3}q^{5}+(-1-\beta _{3})q^{6}+\cdots\)
57.2.e.a 57.e 19.c $2$ $0.455$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(1\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
57.2.e.b 57.e 19.c $6$ $0.455$ 6.0.954288.1 None None \(1\) \(-3\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{4}+\beta _{5})q^{2}-\beta _{3}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots\)
57.2.f.a 57.f 57.f $8$ $0.455$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{24}+\zeta_{24}^{5}+\zeta_{24}^{7})q^{2}+(\zeta_{24}^{2}+\cdots)q^{3}+\cdots\)
57.2.i.a 57.i 19.e $6$ $0.455$ \(\Q(\zeta_{18})\) None None \(3\) \(0\) \(-6\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{5})q^{2}-\zeta_{18}^{4}q^{3}+\cdots\)
57.2.i.b 57.i 19.e $12$ $0.455$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-3\) \(0\) \(6\) \(-9\) $\mathrm{SU}(2)[C_{9}]$ \(q+(1-\beta _{1}-\beta _{2}+\beta _{5}-\beta _{9})q^{2}-\beta _{6}q^{3}+\cdots\)
57.2.j.a 57.j 57.j $6$ $0.455$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{18}]$ \(q+(-\zeta_{18}^{2}+2\zeta_{18}^{5})q^{3}+2\zeta_{18}q^{4}+\cdots\)
57.2.j.b 57.j 57.j $24$ $0.455$ None None \(0\) \(-9\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{18}]$
57.3.b.a 57.b 3.b $12$ $1.553$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(2\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(-2+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
57.3.c.a 57.c 19.b $2$ $1.553$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(8\) \(-20\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+q^{4}+4q^{5}-3q^{6}+\cdots\)
57.3.c.b 57.c 19.b $4$ $1.553$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None None \(0\) \(0\) \(-10\) \(34\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{3})q^{2}-\beta _{1}q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
57.3.g.a 57.g 19.d $6$ $1.553$ 6.0.6967728.1 None None \(-3\) \(9\) \(-2\) \(26\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{2}+(2-\beta _{1})q^{3}+(-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
57.3.g.b 57.g 19.d $6$ $1.553$ 6.0.92607408.1 None None \(3\) \(-9\) \(4\) \(-22\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{4}q^{2}+(-2-\beta _{3})q^{3}+(1+\beta _{1}+2\beta _{3}+\cdots)q^{4}+\cdots\)
57.3.h.a 57.h 57.h $8$ $1.553$ 8.0.\(\cdots\).5 None None \(0\) \(0\) \(0\) \(48\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(\beta _{2}+\beta _{6})q^{3}+(\beta _{3}+\beta _{6})q^{4}+\cdots\)
57.3.h.b 57.h 57.h $16$ $1.553$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(1\) \(0\) \(-68\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{3}q^{2}-\beta _{6}q^{3}+(-2\beta _{1}-3\beta _{8}-2\beta _{9}+\cdots)q^{4}+\cdots\)
57.3.k.a 57.k 19.f $18$ $1.553$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(9\) \(0\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{18}]$ \(q+(1+\beta _{8}+\beta _{9}-\beta _{13}+\beta _{14})q^{2}+(-2\beta _{3}+\cdots)q^{3}+\cdots\)
57.3.k.b 57.k 19.f $24$ $1.553$ None None \(-9\) \(0\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{18}]$
57.3.l.a 57.l 57.l $6$ $1.553$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{18}]$ \(q-3\zeta_{18}^{4}q^{3}+4\zeta_{18}^{2}q^{4}+(3\zeta_{18}+5\zeta_{18}^{2}+\cdots)q^{7}+\cdots\)
57.3.l.b 57.l 57.l $60$ $1.553$ None None \(0\) \(-12\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{18}]$
57.4.a.a 57.a 1.a $1$ $3.363$ \(\Q\) None None \(-1\) \(3\) \(-12\) \(-20\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}-7q^{4}-12q^{5}-3q^{6}+\cdots\)
57.4.a.b 57.a 1.a $2$ $3.363$ \(\Q(\sqrt{33}) \) None None \(1\) \(-6\) \(22\) \(36\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-3q^{3}+\beta q^{4}+(10+2\beta )q^{5}+\cdots\)
57.4.a.c 57.a 1.a $3$ $3.363$ 3.3.2700.1 None None \(-3\) \(-9\) \(-12\) \(-18\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}-3q^{3}+(3+4\beta _{1}+\beta _{2})q^{4}+\cdots\)
57.4.a.d 57.a 1.a $4$ $3.363$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None None \(3\) \(12\) \(-6\) \(38\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+3q^{3}+(6+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
57.4.d.a 57.d 57.d $2$ $3.363$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-40\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{6}q^{3}-8q^{4}-20q^{7}-3^{3}q^{9}+8\zeta_{6}q^{12}+\cdots\)
57.4.d.b 57.d 57.d $4$ $3.363$ \(\Q(\sqrt{-10}, \sqrt{17})\) None None \(0\) \(0\) \(0\) \(-80\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}+9q^{4}-\beta _{3}q^{5}+\cdots\)
57.4.d.c 57.d 57.d $12$ $3.363$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(124\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{7}q^{2}+(\beta _{1}-\beta _{7})q^{3}+(2+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
57.4.e.a 57.e 19.c $10$ $3.363$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(-1\) \(15\) \(-4\) \(30\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}-3\beta _{5}q^{3}+(-4-4\beta _{5}+\beta _{7}+\cdots)q^{4}+\cdots\)
57.4.e.b 57.e 19.c $10$ $3.363$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(1\) \(-15\) \(12\) \(-54\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-3-3\beta _{4})q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
57.4.f.a 57.f 57.f $2$ $3.363$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-9\) \(0\) \(74\) $\mathrm{U}(1)[D_{6}]$ \(q+(-3-3\zeta_{6})q^{3}+8\zeta_{6}q^{4}+37q^{7}+\cdots\)
57.4.f.b 57.f 57.f $2$ $3.363$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(9\) \(0\) \(-34\) $\mathrm{U}(1)[D_{6}]$ \(q+(3+3\zeta_{6})q^{3}+8\zeta_{6}q^{4}-17q^{7}+3^{3}\zeta_{6}q^{9}+\cdots\)
57.4.f.c 57.f 57.f $32$ $3.363$ None None \(0\) \(0\) \(0\) \(-56\) $\mathrm{SU}(2)[C_{6}]$
57.4.i.a 57.i 19.e $24$ $3.363$ None None \(-3\) \(0\) \(-12\) \(36\) $\mathrm{SU}(2)[C_{9}]$
57.4.i.b 57.i 19.e $36$ $3.363$ None None \(3\) \(0\) \(12\) \(-48\) $\mathrm{SU}(2)[C_{9}]$
57.4.j.a 57.j 57.j $108$ $3.363$ None None \(0\) \(-9\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{18}]$
57.5.b.a 57.b 3.b $24$ $5.892$ None None \(0\) \(-10\) \(0\) \(-80\) $\mathrm{SU}(2)[C_{2}]$
57.5.c.a 57.c 19.b $14$ $5.892$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None None \(0\) \(0\) \(18\) \(-54\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-11+\beta _{2})q^{4}+\cdots\)
57.5.g.a 57.g 19.d $14$ $5.892$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None None \(-3\) \(-63\) \(-30\) \(138\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{3}q^{2}+(-3-3\beta _{4})q^{3}+(8\beta _{4}+\beta _{10}+\cdots)q^{4}+\cdots\)
57.5.g.b 57.g 19.d $14$ $5.892$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None None \(3\) \(63\) \(12\) \(-174\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{2}+(3+3\beta _{7})q^{3}+(-\beta _{3}+8\beta _{7}+\cdots)q^{4}+\cdots\)
57.5.h.a 57.h 57.h $48$ $5.892$ None None \(0\) \(-5\) \(0\) \(68\) $\mathrm{SU}(2)[C_{6}]$
57.5.k.a 57.k 19.f $36$ $5.892$ None None \(-9\) \(0\) \(0\) \(45\) $\mathrm{SU}(2)[C_{18}]$
57.5.k.b 57.k 19.f $42$ $5.892$ None None \(9\) \(0\) \(0\) \(45\) $\mathrm{SU}(2)[C_{18}]$
57.5.l.a 57.l 57.l $6$ $5.892$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{18}]$ \(q+9\zeta_{18}^{4}q^{3}+2^{4}\zeta_{18}^{2}q^{4}+(39\zeta_{18}+\cdots)q^{7}+\cdots\)
57.5.l.b 57.l 57.l $144$ $5.892$ None None \(0\) \(6\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{18}]$
57.6.a.a 57.a 1.a $1$ $9.142$ \(\Q\) None None \(-2\) \(9\) \(-98\) \(240\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+9q^{3}-28q^{4}-98q^{5}-18q^{6}+\cdots\)
57.6.a.b 57.a 1.a $1$ $9.142$ \(\Q\) None None \(11\) \(9\) \(6\) \(-176\) $-$ $\mathrm{SU}(2)$ \(q+11q^{2}+9q^{3}+89q^{4}+6q^{5}+99q^{6}+\cdots\)
57.6.a.c 57.a 1.a $2$ $9.142$ \(\Q(\sqrt{17}) \) None None \(-3\) \(18\) \(-87\) \(-251\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+9q^{3}+(7+3\beta )q^{4}+\cdots\)
Next   Download to