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Results (16 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
311.1.b.a	$311$	$1$	311.b	311.b	$2$	$9$	$9$	$0.155$	\(\Q(\zeta_{38})^+\)	$D_{19}$	\(\Q(\sqrt{-311}) \)	None	✓	$2$	$0$	\(-1\)	\(-1\)	\(-1\)	\(-1\)	$1$		\(q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots\)
1555.1.b.a	$1555$	$1$	1555.b	1555.b	$2$	$1$	$1$	$0.776$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-311}) \), \(\Q(\sqrt{-1555}) \)	\(\Q(\sqrt{5}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+q^{4}-q^{5}+q^{9}+q^{16}-q^{20}+q^{25}+\cdots\)
1555.1.b.b	$1555$	$1$	1555.b	1555.b	$2$	$18$	$18$	$0.776$	\(\Q(\zeta_{38})\)	$D_{38}$	\(\Q(\sqrt{-311}) \)	None		$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q+(-\zeta_{38}^{3}-\zeta_{38}^{16})q^{2}+(-\zeta_{38}^{2}+\cdots)q^{3}+\cdots\)
2177.1.g.a	$2177$	$1$	2177.g	2177.g	$6$	$2$	$1$	$1.086$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-311}) \)	None		$4$	$0$	\(1\)	\(1\)	\(-2\)	\(-1\)	$1$		\(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}+q^{6}+\cdots\)
2177.1.g.b	$2177$	$1$	2177.g	2177.g	$6$	$36$	$18$	$1.086$	\(\Q(\zeta_{57})\)	$D_{57}$	\(\Q(\sqrt{-311}) \)	None		$4$	$0$	\(-1\)	\(-1\)	\(2\)	\(1\)	$1$		\(q+(-\zeta_{114}^{9}+\zeta_{114}^{10})q^{2}+(\zeta_{114}^{44}-\zeta_{114}^{51}+\cdots)q^{3}+\cdots\)
2488.1.c.a	$2488$	$1$	2488.c	2488.c	$2$	$1$	$1$	$1.242$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-311}) \), \(\Q(\sqrt{-622}) \)	\(\Q(\sqrt{2}) \)	✓	$4$	$0$	\(-1\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-q^{2}+q^{4}-2q^{7}-q^{8}+q^{9}+2q^{14}+\cdots\)
2488.1.c.e	$2488$	$1$	2488.c	2488.c	$2$	$18$	$18$	$1.242$	\(\Q(\zeta_{38})\)	$D_{38}$	\(\Q(\sqrt{-311}) \)	None		$4$	$0$	\(1\)	\(0\)	\(0\)	\(2\)	$1$		\(q+\zeta_{38}^{13}q^{2}+(\zeta_{38}^{4}+\zeta_{38}^{15})q^{3}+\cdots\)
2799.1.d.a	$2799$	$1$	2799.d	311.b	$2$	$9$	$9$	$1.397$	\(\Q(\zeta_{38})^+\)	$D_{19}$	\(\Q(\sqrt{-311}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(1\)	\(-1\)	$1$		\(q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots\)
2799.1.g.a	$2799$	$1$	2799.g	2799.g	$6$	$2$	$1$	$1.397$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-311}) \)	None		$4$	$0$	\(-2\)	\(2\)	\(1\)	\(-2\)	$1$		\(q-\zeta_{6}q^{2}+q^{3}+3\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\cdots\)
2799.1.g.c	$2799$	$1$	2799.g	2799.g	$6$	$36$	$18$	$1.397$	\(\Q(\zeta_{57})\)	$D_{57}$	\(\Q(\sqrt{-311}) \)	None		$4$	$0$	\(2\)	\(-2\)	\(-1\)	\(2\)	$1$		\(q+(-\zeta_{114}^{43}+\zeta_{114}^{52})q^{2}-\zeta_{114}^{3}q^{3}+\cdots\)
3732.1.b.a	$3732$	$1$	3732.b	3732.b	$2$	$1$	$1$	$1.863$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-311}) \), \(\Q(\sqrt{-933}) \)	\(\Q(\sqrt{3}) \)	✓	$4$	$0$	\(-1\)	\(-1\)	\(0\)	\(0\)	$1$		\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
3732.1.b.b	$3732$	$1$	3732.b	3732.b	$2$	$1$	$1$	$1.863$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-311}) \), \(\Q(\sqrt{-933}) \)	\(\Q(\sqrt{3}) \)	✓	$4$	$0$	\(1\)	\(1\)	\(0\)	\(0\)	$1$		\(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
3732.1.b.e	$3732$	$1$	3732.b	3732.b	$2$	$18$	$18$	$1.863$	\(\Q(\zeta_{38})\)	$D_{38}$	\(\Q(\sqrt{-311}) \)	None		$4$	$0$	\(-1\)	\(-1\)	\(0\)	\(0\)	$1$		\(q-\zeta_{38}^{13}q^{2}+\zeta_{38}^{4}q^{3}-\zeta_{38}^{7}q^{4}+\cdots\)
3732.1.b.f	$3732$	$1$	3732.b	3732.b	$2$	$18$	$18$	$1.863$	\(\Q(\zeta_{38})\)	$D_{38}$	\(\Q(\sqrt{-311}) \)	None		$4$	$0$	\(1\)	\(1\)	\(0\)	\(0\)	$1$		\(q+\zeta_{38}^{13}q^{2}+\zeta_{38}^{15}q^{3}-\zeta_{38}^{7}q^{4}+\cdots\)
933.2.c.b	$933$	$2$	933.c	933.c	$2$	$38$	$38$	$7.450$		$_{}$	\(\Q(\sqrt{-311}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{2}]$
311.3.b.a	$311$	$3$	311.b	311.b	$2$	$19$	$19$	$8.474$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	$_{}$	\(\Q(\sqrt{-311}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{2}-\beta _{14}q^{3}+(4+\beta _{4})q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots\)