Learn more

Refine search


Results (50 matches)

  Download to        
Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
729.1.f.a 729.f 27.f $6$ $0.364$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{18}q^{4}-\zeta_{18}^{8}q^{7}-\zeta_{18}^{4}q^{13}+\cdots\)
729.2.a.a 729.a 1.a $6$ $5.821$ 6.6.1397493.1 None None \(-3\) \(0\) \(-6\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{5})q^{2}+(\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots\)
729.2.a.b 729.a 1.a $6$ $5.821$ 6.6.7459857.1 None None \(-3\) \(0\) \(3\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
729.2.a.c 729.a 1.a $6$ $5.821$ \(\Q(\zeta_{36})^+\) None None \(0\) \(0\) \(0\) \(-12\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
729.2.a.d 729.a 1.a $6$ $5.821$ 6.6.1397493.1 None None \(3\) \(0\) \(6\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{5})q^{2}+(\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots\)
729.2.a.e 729.a 1.a $6$ $5.821$ 6.6.7459857.1 None None \(3\) \(0\) \(-3\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
729.2.c.a 729.c 9.c $12$ $5.821$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(-3\) \(0\) \(3\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{6})q^{2}+(-1+\cdots)q^{4}+\cdots\)
729.2.c.b 729.c 9.c $12$ $5.821$ 12.0.\(\cdots\).1 None None \(-3\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{6}+\beta _{8}-\beta _{10})q^{2}+(-1+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
729.2.c.c 729.c 9.c $12$ $5.821$ \(\Q(\zeta_{36})\) None None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\zeta_{36}^{7}-\zeta_{36}^{8}+\zeta_{36}^{10})q^{2}-\zeta_{36}^{11}q^{4}+\cdots\)
729.2.c.d 729.c 9.c $12$ $5.821$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(3\) \(0\) \(-3\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{2}-\beta _{3}+\beta _{5}-\beta _{6}+\beta _{9})q^{2}+(-1+\cdots)q^{4}+\cdots\)
729.2.c.e 729.c 9.c $12$ $5.821$ 12.0.\(\cdots\).1 None None \(3\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{6}-\beta _{8}+\beta _{10})q^{2}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
729.2.e.a 729.e 27.e $6$ $5.821$ \(\Q(\zeta_{18})\) None None \(-6\) \(0\) \(-3\) \(-9\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-1-\zeta_{18}+\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)
729.2.e.b 729.e 27.e $6$ $5.821$ \(\Q(\zeta_{18})\) None None \(-3\) \(0\) \(-6\) \(9\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-1+\zeta_{18}-\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{4}+\cdots)q^{2}+\cdots\)
729.2.e.c 729.e 27.e $6$ $5.821$ \(\Q(\zeta_{18})\) None None \(-3\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3}-\zeta_{18}^{4})q^{2}+\cdots\)
729.2.e.d 729.e 27.e $6$ $5.821$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{9}]$ \(q+2\zeta_{18}^{5}q^{4}+5\zeta_{18}^{4}q^{7}+2\zeta_{18}^{2}q^{13}+\cdots\)
729.2.e.e 729.e 27.e $6$ $5.821$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{9}]$ \(q+2\zeta_{18}^{5}q^{4}-4\zeta_{18}^{4}q^{7}-7\zeta_{18}^{2}q^{13}+\cdots\)
729.2.e.f 729.e 27.e $6$ $5.821$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{9}]$ \(q+2\zeta_{18}^{5}q^{4}-\zeta_{18}^{4}q^{7}+5\zeta_{18}^{2}q^{13}+\cdots\)
729.2.e.g 729.e 27.e $6$ $5.821$ \(\Q(\zeta_{18})\) None None \(3\) \(0\) \(6\) \(9\) $\mathrm{SU}(2)[C_{9}]$ \(q+(1-\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{2}+\cdots\)
729.2.e.h 729.e 27.e $6$ $5.821$ \(\Q(\zeta_{18})\) None None \(3\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{2}+\cdots\)
729.2.e.i 729.e 27.e $6$ $5.821$ \(\Q(\zeta_{18})\) None None \(6\) \(0\) \(3\) \(-9\) $\mathrm{SU}(2)[C_{9}]$ \(q+(1+\zeta_{18}-\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+(1+\cdots)q^{4}+\cdots\)
729.2.e.j 729.e 27.e $12$ $5.821$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(-6\) \(0\) \(6\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-1-\beta _{6}-\beta _{7}+\beta _{11})q^{2}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
729.2.e.k 729.e 27.e $12$ $5.821$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(-3\) \(0\) \(-6\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\beta _{5}-\beta _{7}+\beta _{10})q^{2}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
729.2.e.l 729.e 27.e $12$ $5.821$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(-3\) \(0\) \(12\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q+\beta _{2}q^{2}+(-2\beta _{1}-\beta _{2}+\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots\)
729.2.e.m 729.e 27.e $12$ $5.821$ \(\Q(\zeta_{36})\) None None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{36}^{2}+\zeta_{36}^{7}-\zeta_{36}^{9}+\zeta_{36}^{11})q^{2}+\cdots\)
729.2.e.n 729.e 27.e $12$ $5.821$ \(\Q(\zeta_{36})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q-\zeta_{36}^{8}q^{2}+(-\zeta_{36}^{2}+\zeta_{36}^{7})q^{4}+\cdots\)
729.2.e.o 729.e 27.e $12$ $5.821$ \(\Q(\zeta_{36})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q-\zeta_{36}^{8}q^{2}+(-\zeta_{36}^{2}+\zeta_{36}^{7})q^{4}+\cdots\)
729.2.e.p 729.e 27.e $12$ $5.821$ 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+\beta _{4}q^{2}+4\beta _{5}q^{4}+\beta _{11}q^{5}-2\beta _{7}q^{7}+\cdots\)
729.2.e.q 729.e 27.e $12$ $5.821$ \(\Q(\zeta_{36})\) None None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{9}]$ \(q+\zeta_{36}^{9}q^{2}+(1+\zeta_{36}-\zeta_{36}^{4})q^{4}+\cdots\)
729.2.e.r 729.e 27.e $12$ $5.821$ \(\Q(\zeta_{36})\) None None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{36}^{9}+\zeta_{36}^{10})q^{2}+(1+\zeta_{36}^{3}+\cdots)q^{4}+\cdots\)
729.2.e.s 729.e 27.e $12$ $5.821$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(3\) \(0\) \(-12\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(1-\beta _{5}+\beta _{6}+\beta _{10}-\beta _{11})q^{2}+(\beta _{1}+\cdots)q^{4}+\cdots\)
729.2.e.t 729.e 27.e $12$ $5.821$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(3\) \(0\) \(6\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\beta _{1}+\beta _{2}+\beta _{5}-\beta _{6}-\beta _{8})q^{2}+(1+\cdots)q^{4}+\cdots\)
729.2.e.u 729.e 27.e $12$ $5.821$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(6\) \(0\) \(-6\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\beta _{1}+\beta _{5}-\beta _{6}-\beta _{8})q^{2}+(-1+2\beta _{1}+\cdots)q^{4}+\cdots\)
729.2.g.a 729.g 81.g $144$ $5.821$ None None \(-9\) \(0\) \(-9\) \(9\) $\mathrm{SU}(2)[C_{27}]$
729.2.g.b 729.g 81.g $144$ $5.821$ None None \(-9\) \(0\) \(-9\) \(9\) $\mathrm{SU}(2)[C_{27}]$
729.2.g.c 729.g 81.g $144$ $5.821$ None None \(9\) \(0\) \(9\) \(9\) $\mathrm{SU}(2)[C_{27}]$
729.2.g.d 729.g 81.g $144$ $5.821$ None None \(9\) \(0\) \(9\) \(9\) $\mathrm{SU}(2)[C_{27}]$
729.2.i.a 729.i 243.i $1404$ $5.821$ None None \(54\) \(0\) \(54\) \(-54\) $\mathrm{SU}(2)[C_{81}]$
729.2.k.a 729.k 729.k $12960$ $5.821$ None None \(-162\) \(-162\) \(-162\) \(-162\) $\mathrm{SU}(2)[C_{243}]$
729.3.b.a 729.b 3.b $30$ $19.864$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
729.3.b.b 729.b 3.b $36$ $19.864$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
729.4.a.a 729.a 1.a $12$ $43.012$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-6\) \(0\) \(-12\) \(-42\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(3+\beta _{2}+\beta _{3})q^{4}+\cdots\)
729.4.a.b 729.a 1.a $12$ $43.012$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(6\) \(0\) \(12\) \(-42\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(3+\beta _{2}+\beta _{3})q^{4}+(1+\cdots)q^{5}+\cdots\)
729.4.a.c 729.a 1.a $24$ $43.012$ None None \(-6\) \(0\) \(-30\) \(0\) $-$ $\mathrm{SU}(2)$
729.4.a.d 729.a 1.a $24$ $43.012$ None None \(6\) \(0\) \(30\) \(0\) $+$ $\mathrm{SU}(2)$
729.4.a.e 729.a 1.a $30$ $43.012$ None None \(0\) \(0\) \(0\) \(84\) $+$ $\mathrm{SU}(2)$
729.6.a.a 729.a 1.a $24$ $116.920$ None None \(-12\) \(0\) \(-33\) \(294\) $-$ $\mathrm{SU}(2)$
729.6.a.b 729.a 1.a $24$ $116.920$ None None \(12\) \(0\) \(33\) \(294\) $-$ $\mathrm{SU}(2)$
729.6.a.c 729.a 1.a $42$ $116.920$ None None \(-12\) \(0\) \(-150\) \(0\) $+$ $\mathrm{SU}(2)$
729.6.a.d 729.a 1.a $42$ $116.920$ None None \(0\) \(0\) \(0\) \(-588\) $+$ $\mathrm{SU}(2)$
729.6.a.e 729.a 1.a $42$ $116.920$ None None \(12\) \(0\) \(150\) \(0\) $-$ $\mathrm{SU}(2)$
  Download to