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Results (5 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
687.1.d.a	$687$	$1$	687.d	687.d	$2$	$1$	$1$	$0.343$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-687}) \)	None	✓	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(0\)	$1$		\(q-q^{2}+q^{3}-q^{6}+q^{8}+q^{9}-q^{16}+\cdots\)
687.1.d.b	$687$	$1$	687.d	687.d	$2$	$1$	$1$	$0.343$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-687}) \)	\(\Q(\sqrt{229}) \)	✓	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$		\(q-q^{3}-q^{4}+q^{9}+q^{12}+q^{16}+2q^{19}+\cdots\)
687.1.d.c	$687$	$1$	687.d	687.d	$2$	$1$	$1$	$0.343$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-687}) \)	None	✓	$2$	$0$	\(1\)	\(1\)	\(0\)	\(0\)	$1$		\(q+q^{2}+q^{3}+q^{6}-q^{8}+q^{9}-q^{16}+\cdots\)
687.1.d.d	$687$	$1$	687.d	687.d	$2$	$2$	$2$	$0.343$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-687}) \)	None	✓	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-\beta q^{2}-q^{3}+2q^{4}+\beta q^{6}-\beta q^{8}+\cdots\)
2061.2.c.c	$2061$	$2$	2061.c	229.b	$2$	$12$	$12$	$16.457$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	$_{}$	\(\Q(\sqrt{-687}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{7}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{3}q^{2}+(-2-\beta _{2})q^{4}+(-\beta _{1}+2\beta _{3}+\cdots)q^{8}+\cdots\)