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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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
699.1.c.a	$699$	$1$	699.c	699.c	$2$	$2$	$2$	$0.349$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-699}) \)	None	✓	$2$	$0$	\(0\)	\(-2\)	\(1\)	\(-1\)	$1$		\(q-q^{3}+q^{4}+(1-\beta )q^{5}-\beta q^{7}+q^{9}+\cdots\)
699.1.c.b	$699$	$1$	699.c	699.c	$2$	$2$	$2$	$0.349$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-699}) \)	None	✓	$2$	$0$	\(0\)	\(2\)	\(-1\)	\(-1\)	$1$		\(q+q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{7}+q^{9}+\cdots\)
2796.1.h.a	$2796$	$1$	2796.h	699.c	$2$	$1$	$1$	$1.395$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-699}) \)	None	✓	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(-1\)	$1$		\(q-q^{3}+q^{5}-q^{7}+q^{9}-2q^{11}-q^{13}+\cdots\)
2796.1.h.b	$2796$	$1$	2796.h	699.c	$2$	$1$	$1$	$1.395$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-699}) \)	None	✓	$2$	$0$	\(0\)	\(1\)	\(-1\)	\(-1\)	$1$		\(q+q^{3}-q^{5}-q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
2796.1.h.c	$2796$	$1$	2796.h	699.c	$2$	$4$	$4$	$1.395$	\(\Q(\zeta_{15})^+\)	$D_{15}$	\(\Q(\sqrt{-699}) \)	None	✓	$2$	$0$	\(0\)	\(-4\)	\(-1\)	\(1\)	$1$		\(q-q^{3}-\beta _{1}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+q^{9}+\cdots\)
2796.1.h.d	$2796$	$1$	2796.h	699.c	$2$	$4$	$4$	$1.395$	\(\Q(\zeta_{15})^+\)	$D_{15}$	\(\Q(\sqrt{-699}) \)	None	✓	$2$	$0$	\(0\)	\(4\)	\(1\)	\(1\)	$1$		\(q+q^{3}+\beta _{1}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+q^{9}+\cdots\)
3495.1.g.e	$3495$	$1$	3495.g	3495.g	$2$	$2$	$2$	$1.744$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-699}) \)	\(\Q(\sqrt{1165}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{3}-q^{4}-iq^{5}-q^{9}+iq^{12}+\cdots\)
3495.1.g.j	$3495$	$1$	3495.g	3495.g	$2$	$8$	$8$	$1.744$	\(\Q(\zeta_{20})\)	$D_{10}$	\(\Q(\sqrt{-699}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{20}^{5}q^{3}-q^{4}-\zeta_{20}q^{5}+(-\zeta_{20}^{2}+\cdots)q^{7}+\cdots\)
2097.2.d.a	$2097$	$2$	2097.d	233.b	$2$	$10$	$10$	$16.745$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	$_{}$	\(\Q(\sqrt{-699}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{4}-\beta _{1}q^{5}-\beta _{9}q^{7}-\beta _{2}q^{11}+\cdots\)
8388.2.e.c	$8388$	$2$	8388.e	233.b	$2$	$20$	$20$	$66.979$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	$_{}$	\(\Q(\sqrt{-699}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{6}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{5}+\beta _{16}q^{7}+\beta _{9}q^{11}-\beta _{11}q^{13}+\cdots\)