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Results (10 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3639.1.d.a	$3639$	$1$	3639.d	3639.d	$2$	$1$	$1$	$1.816$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-3639}) \)	None	✓	$2$	$0$	\(-2\)	\(1\)	\(1\)	\(-1\)	$1$		\(q-2q^{2}+q^{3}+3q^{4}+q^{5}-2q^{6}-q^{7}+\cdots\)
3639.1.d.b	$3639$	$1$	3639.d	3639.d	$2$	$1$	$1$	$1.816$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3639}) \)	\(\Q(\sqrt{1213}) \)	✓	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)	$1$		\(q-q^{3}-q^{4}-2q^{7}+q^{9}+q^{12}-2q^{13}+\cdots\)
3639.1.d.c	$3639$	$1$	3639.d	3639.d	$2$	$1$	$1$	$1.816$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-3639}) \)	None	✓	$2$	$0$	\(2\)	\(1\)	\(-1\)	\(-1\)	$1$		\(q+2q^{2}+q^{3}+3q^{4}-q^{5}+2q^{6}-q^{7}+\cdots\)
3639.1.d.d	$3639$	$1$	3639.d	3639.d	$2$	$2$	$2$	$1.816$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-3639}) \)	None	✓	$2$	$0$	\(-1\)	\(2\)	\(-1\)	\(-1\)	$1$		\(q+(-1+\beta )q^{2}+q^{3}+(1-\beta )q^{4}+(-1+\cdots)q^{5}+\cdots\)
3639.1.d.e	$3639$	$1$	3639.d	3639.d	$2$	$2$	$2$	$1.816$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-3639}) \)	None	✓	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)	$1$		\(q-q^{3}-q^{4}-\beta q^{5}+q^{7}+q^{9}+q^{12}+\cdots\)
3639.1.d.f	$3639$	$1$	3639.d	3639.d	$2$	$2$	$2$	$1.816$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-3639}) \)	None	✓	$2$	$0$	\(1\)	\(2\)	\(1\)	\(-1\)	$1$		\(q+(1-\beta )q^{2}+q^{3}+(1-\beta )q^{4}+(1-\beta )q^{5}+\cdots\)
3639.1.d.g	$3639$	$1$	3639.d	3639.d	$2$	$4$	$4$	$1.816$	\(\Q(\zeta_{15})^+\)	$D_{15}$	\(\Q(\sqrt{-3639}) \)	None	✓	$2$	$0$	\(-2\)	\(4\)	\(1\)	\(1\)	$1$		\(q+(-1-\beta _{3})q^{2}+q^{3}+(1+\beta _{3})q^{4}+\cdots\)
3639.1.d.h	$3639$	$1$	3639.d	3639.d	$2$	$4$	$4$	$1.816$	\(\Q(\zeta_{20})^+\)	$D_{10}$	\(\Q(\sqrt{-3639}) \)	None	✓	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(2\)	$1$		\(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots\)
3639.1.d.i	$3639$	$1$	3639.d	3639.d	$2$	$4$	$4$	$1.816$	\(\Q(\zeta_{15})^+\)	$D_{15}$	\(\Q(\sqrt{-3639}) \)	None	✓	$2$	$0$	\(2\)	\(4\)	\(-1\)	\(1\)	$1$		\(q+(1+\beta _{3})q^{2}+q^{3}+(1+\beta _{3})q^{4}-\beta _{1}q^{5}+\cdots\)
3639.1.d.j	$3639$	$1$	3639.d	3639.d	$2$	$8$	$8$	$1.816$	\(\Q(\zeta_{60})^+\)	$D_{30}$	\(\Q(\sqrt{-3639}) \)	None	✓	$4$	$0$	\(0\)	\(-8\)	\(0\)	\(-2\)	$1$		\(q+(\beta _{1}-\beta _{7})q^{2}-q^{3}+(1-\beta _{4})q^{4}-\beta _{1}q^{5}+\cdots\)