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Results (6 matches)

 

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
471.1.d.a	$471$	$1$	471.d	471.d	$2$	$1$	$1$	$0.235$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-471}) \)	\(\Q(\sqrt{157}) \)	✓	$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$		\(q+q^{3}-q^{4}+q^{9}-q^{12}+2q^{13}+q^{16}+\cdots\)
471.1.d.b	$471$	$1$	471.d	471.d	$2$	$2$	$2$	$0.235$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-471}) \)	None	✓	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q-\beta q^{2}+q^{3}+q^{4}+\beta q^{5}-\beta q^{6}+q^{9}+\cdots\)
471.1.d.c	$471$	$1$	471.d	471.d	$2$	$4$	$4$	$0.235$	\(\Q(\zeta_{16})^+\)	$D_{8}$	\(\Q(\sqrt{-471}) \)	None	✓	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
2355.1.d.e	$2355$	$1$	2355.d	2355.d	$2$	$16$	$16$	$1.175$	\(\Q(\zeta_{32})\)	$D_{16}$	\(\Q(\sqrt{-471}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{32}^{5}+\zeta_{32}^{11})q^{2}+\zeta_{32}^{8}q^{3}+(-1+\cdots)q^{4}+\cdots\)
3768.1.b.e	$3768$	$1$	3768.b	3768.b	$2$	$16$	$16$	$1.880$	\(\Q(\zeta_{32})\)	$D_{16}$	\(\Q(\sqrt{-471}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{32}^{3}q^{2}-\zeta_{32}^{8}q^{3}+\zeta_{32}^{6}q^{4}+\cdots\)
1413.2.b.f	$1413$	$2$	1413.b	157.b	$2$	$16$	$16$	$11.283$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	$_{}$	\(\Q(\sqrt{-471}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{5}q^{2}+(-2+\beta _{9})q^{4}-\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{8}+\cdots\)