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Results (22 matches)

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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1028.1.d.a 1028.d 1028.d $1$ $0.513$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-257}) \) \(\Q(\sqrt{257}) \) \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}-q^{9}+2q^{13}+q^{16}+\cdots\)
1028.1.d.b 1028.d 1028.d $2$ $0.513$ \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{257}) \) \(-1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{8}-q^{9}+(\zeta_{6}+\cdots)q^{11}+\cdots\)
1028.1.d.c 1028.d 1028.d $2$ $0.513$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-257}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}-\beta q^{3}+q^{4}-\beta q^{6}+\beta q^{7}+q^{8}+\cdots\)
1028.1.d.d 1028.d 1028.d $4$ $0.513$ \(\Q(\zeta_{16})^+\) \(\Q(\sqrt{-257}) \) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+\beta _{3}q^{7}+\cdots\)
1028.1.e.a 1028.e 1028.e $2$ $0.513$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-2\) \(0\) \(q+q^{2}+q^{4}+(-1+i)q^{5}+q^{8}+iq^{9}+\cdots\)
1028.1.h.a 1028.h 1028.h $4$ $0.513$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(4\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}+q^{8}+\cdots\)
1028.1.j.a 1028.j 1028.j $8$ $0.513$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-1}) \) None \(-8\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}+(\zeta_{16}^{6}+\zeta_{16}^{7})q^{5}-q^{8}+\cdots\)
1028.1.l.a 1028.l 1028.l $16$ $0.513$ \(\Q(\zeta_{32})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{32}^{8}q^{2}-q^{4}+(\zeta_{32}^{2}+\zeta_{32}^{13}+\cdots)q^{5}+\cdots\)
1028.1.m.a 1028.m 1028.m $32$ $0.513$ \(\Q(\zeta_{64})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{64}^{8}q^{2}+\zeta_{64}^{16}q^{4}+(-\zeta_{64}^{11}+\cdots)q^{5}+\cdots\)
1028.2.a.a 1028.a 1.a $1$ $8.209$ \(\Q\) None None \(0\) \(-2\) \(-4\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-4q^{5}-4q^{7}+q^{9}-5q^{11}+\cdots\)
1028.2.a.b 1028.a 1.a $1$ $8.209$ \(\Q\) None None \(0\) \(0\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+2q^{7}-3q^{9}-q^{11}+q^{13}+\cdots\)
1028.2.a.c 1028.a 1.a $1$ $8.209$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-3q^{9}+3q^{11}+q^{13}-3q^{17}+\cdots\)
1028.2.a.d 1028.a 1.a $5$ $8.209$ 5.5.288385.1 None None \(0\) \(-3\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{4})q^{3}+\beta _{2}q^{5}+(\beta _{3}-\beta _{4})q^{7}+\cdots\)
1028.2.a.e 1028.a 1.a $14$ $8.209$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(5\) \(7\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1-\beta _{4})q^{5}+\beta _{13}q^{7}+(2+\cdots)q^{9}+\cdots\)
1028.2.b.a 1028.b 257.b $22$ $8.209$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1028.2.f.a 1028.f 257.c $44$ $8.209$ None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
1028.2.g.a 1028.g 257.d $88$ $8.209$ None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$
1028.4.a.a 1028.a 1.a $28$ $60.654$ None None \(0\) \(-6\) \(-14\) \(0\) $-$ $\mathrm{SU}(2)$
1028.4.a.b 1028.a 1.a $36$ $60.654$ None None \(0\) \(12\) \(16\) \(0\) $+$ $\mathrm{SU}(2)$
1028.4.b.a 1028.b 257.b $64$ $60.654$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1028.6.a.a 1028.a 1.a $49$ $164.875$ None None \(0\) \(-27\) \(-89\) \(88\) $+$ $\mathrm{SU}(2)$
1028.6.a.b 1028.a 1.a $57$ $164.875$ None None \(0\) \(27\) \(61\) \(88\) $-$ $\mathrm{SU}(2)$
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