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Results (12 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3999.1.g.a	$3999$	$1$	3999.g	3999.g	$2$	$1$	$1$	$1.996$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-3999}) \)	None	✓	$2$	$0$	\(-1\)	\(-1\)	\(2\)	\(0\)	$1$		\(q-q^{2}-q^{3}+2q^{5}+q^{6}+q^{8}+q^{9}+\cdots\)
3999.1.g.b	$3999$	$1$	3999.g	3999.g	$2$	$1$	$1$	$1.996$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-3999}) \)	None	✓	$2$	$0$	\(-1\)	\(1\)	\(2\)	\(0\)	$1$		\(q-q^{2}+q^{3}+2q^{5}-q^{6}+q^{8}+q^{9}+\cdots\)
3999.1.g.c	$3999$	$1$	3999.g	3999.g	$2$	$1$	$1$	$1.996$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3999}) \)	\(\Q(\sqrt{1333}) \)	✓	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$		\(q-q^{3}-q^{4}+q^{9}+q^{12}+q^{16}-q^{25}+\cdots\)
3999.1.g.d	$3999$	$1$	3999.g	3999.g	$2$	$1$	$1$	$1.996$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3999}) \)	\(\Q(\sqrt{1333}) \)	✓	$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$		\(q+q^{3}-q^{4}+q^{9}-q^{12}+q^{16}-q^{25}+\cdots\)
3999.1.g.e	$3999$	$1$	3999.g	3999.g	$2$	$1$	$1$	$1.996$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-3999}) \)	None	✓	$2$	$0$	\(1\)	\(-1\)	\(-2\)	\(0\)	$1$		\(q+q^{2}-q^{3}-2q^{5}-q^{6}-q^{8}+q^{9}+\cdots\)
3999.1.g.f	$3999$	$1$	3999.g	3999.g	$2$	$1$	$1$	$1.996$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-3999}) \)	None	✓	$2$	$0$	\(1\)	\(1\)	\(-2\)	\(0\)	$1$		\(q+q^{2}+q^{3}-2q^{5}+q^{6}-q^{8}+q^{9}+\cdots\)
3999.1.g.g	$3999$	$1$	3999.g	3999.g	$2$	$2$	$2$	$1.996$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-3999}) \)	None	✓	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-\beta q^{2}-q^{3}+q^{4}-\beta q^{5}+\beta q^{6}+q^{9}+\cdots\)
3999.1.g.h	$3999$	$1$	3999.g	3999.g	$2$	$2$	$2$	$1.996$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-3999}) \)	None	✓	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-\beta q^{2}-q^{3}+2q^{4}+\beta q^{6}-\beta q^{8}+\cdots\)
3999.1.g.i	$3999$	$1$	3999.g	3999.g	$2$	$2$	$2$	$1.996$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-3999}) \)	None	✓	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q-\beta q^{2}+q^{3}+q^{4}-\beta q^{5}-\beta q^{6}+q^{9}+\cdots\)
3999.1.g.j	$3999$	$1$	3999.g	3999.g	$2$	$2$	$2$	$1.996$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-3999}) \)	None	✓	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q-\beta q^{2}+q^{3}+2q^{4}-\beta q^{6}-\beta q^{8}+\cdots\)
3999.1.g.k	$3999$	$1$	3999.g	3999.g	$2$	$4$	$4$	$1.996$	\(\Q(\zeta_{24})^+\)	$D_{12}$	\(\Q(\sqrt{-3999}) \)	None	✓	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
3999.1.g.l	$3999$	$1$	3999.g	3999.g	$2$	$4$	$4$	$1.996$	\(\Q(\zeta_{24})^+\)	$D_{12}$	\(\Q(\sqrt{-3999}) \)	None	✓	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)