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Results (11 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
447.1.d.a	$447$	$1$	447.d	447.d	$2$	$3$	$3$	$0.223$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-447}) \)	None	✓	$2$	$0$	\(-1\)	\(3\)	\(0\)	\(-1\)	$1$		\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
447.1.d.b	$447$	$1$	447.d	447.d	$2$	$3$	$3$	$0.223$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-447}) \)	None	✓	$2$	$0$	\(1\)	\(-3\)	\(0\)	\(-1\)	$1$		\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
3129.1.o.a	$3129$	$1$	3129.o	3129.o	$6$	$2$	$1$	$1.562$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-447}) \)	None		$4$	$0$	\(-1\)	\(1\)	\(0\)	\(-1\)	$1$		\(q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-q^{6}+\zeta_{6}^{2}q^{7}+\cdots\)
3129.1.o.b	$3129$	$1$	3129.o	3129.o	$6$	$2$	$1$	$1.562$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-447}) \)	None		$4$	$0$	\(1\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-q^{6}+\zeta_{6}^{2}q^{7}+\cdots\)
3129.1.o.c	$3129$	$1$	3129.o	3129.o	$6$	$12$	$6$	$1.562$	\(\Q(\zeta_{21})\)	$D_{21}$	\(\Q(\sqrt{-447}) \)	None		$4$	$0$	\(-1\)	\(-6\)	\(0\)	\(1\)	$1$		\(q+(-\zeta_{42}^{3}+\zeta_{42}^{4})q^{2}-\zeta_{42}^{7}q^{3}+\cdots\)
3129.1.o.d	$3129$	$1$	3129.o	3129.o	$6$	$12$	$6$	$1.562$	\(\Q(\zeta_{21})\)	$D_{21}$	\(\Q(\sqrt{-447}) \)	None		$4$	$0$	\(1\)	\(6\)	\(0\)	\(1\)	$1$		\(q+(\zeta_{42}^{3}-\zeta_{42}^{4})q^{2}+\zeta_{42}^{7}q^{3}+(\zeta_{42}^{6}+\cdots)q^{4}+\cdots\)
3576.1.o.a	$3576$	$1$	3576.o	3576.o	$2$	$2$	$2$	$1.785$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-447}) \)	\(\Q(\sqrt{298}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$		\(q-iq^{2}-iq^{3}-q^{4}-q^{6}+q^{7}+iq^{8}+\cdots\)
3576.1.o.f	$3576$	$1$	3576.o	3576.o	$2$	$12$	$12$	$1.785$	\(\Q(\zeta_{28})\)	$D_{14}$	\(\Q(\sqrt{-447}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$		\(q+\zeta_{28}^{9}q^{2}-\zeta_{28}^{7}q^{3}-\zeta_{28}^{4}q^{4}+\cdots\)
1341.2.c.c	$1341$	$2$	1341.c	149.b	$2$	$14$	$14$	$10.708$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	$_{}$	\(\Q(\sqrt{-447}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}-\beta _{9}q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots\)
447.3.d.a	$447$	$3$	447.d	447.d	$2$	$7$	$7$	$12.180$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	$_{}$	\(\Q(\sqrt{-447}) \)	None	✓	$2$	$0$	\(0\)	\(-21\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{3})q^{4}+3\beta _{1}q^{6}+\cdots\)
447.3.d.b	$447$	$3$	447.d	447.d	$2$	$7$	$7$	$12.180$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	$_{}$	\(\Q(\sqrt{-447}) \)	None	✓	$2$	$0$	\(0\)	\(21\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}+3q^{3}+(4+\beta _{3})q^{4}+3\beta _{1}q^{6}+\cdots\)