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Results (13 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
415.1.d.a	$415$	$1$	415.d	415.d	$2$	$2$	$2$	$0.207$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-415}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(2\)	\(0\)	$1$		\(q+(-1+\beta )q^{2}+(1-\beta )q^{4}+q^{5}-q^{8}+\cdots\)
415.1.d.b	$415$	$1$	415.d	415.d	$2$	$2$	$2$	$0.207$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-415}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(-2\)	\(0\)	$1$		\(q+(1-\beta )q^{2}+(1-\beta )q^{4}-q^{5}+q^{8}+\cdots\)
2075.1.c.h	$2075$	$1$	2075.c	83.b	$2$	$4$	$4$	$1.036$	\(\Q(i, \sqrt{5})\)	$D_{5}$	\(\Q(\sqrt{-415}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{3}q^{8}-q^{9}+\beta _{2}q^{11}+\cdots\)
3320.1.j.c	$3320$	$1$	3320.j	3320.j	$2$	$2$	$2$	$1.657$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-415}) \), \(\Q(\sqrt{-166}) \)	\(\Q(\sqrt{10}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+iq^{2}-q^{4}-iq^{5}-iq^{8}-q^{9}+q^{10}+\cdots\)
3320.1.j.i	$3320$	$1$	3320.j	3320.j	$2$	$8$	$8$	$1.657$	\(\Q(\zeta_{20})\)	$D_{10}$	\(\Q(\sqrt{-415}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}+\zeta_{20}^{5}q^{5}-\zeta_{20}^{3}q^{8}+\cdots\)
3735.1.g.a	$3735$	$1$	3735.g	415.d	$2$	$1$	$1$	$1.864$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-415}) \)	\(\Q(\sqrt{249}) \)	✓	$4$	$0$	\(-2\)	\(0\)	\(1\)	\(0\)	$1$		\(q-2q^{2}+3q^{4}+q^{5}-4q^{8}-2q^{10}+\cdots\)
3735.1.g.b	$3735$	$1$	3735.g	415.d	$2$	$1$	$1$	$1.864$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-415}) \)	\(\Q(\sqrt{249}) \)	✓	$4$	$0$	\(2\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+2q^{2}+3q^{4}-q^{5}+4q^{8}-2q^{10}+\cdots\)
3735.1.g.c	$3735$	$1$	3735.g	415.d	$2$	$2$	$2$	$1.864$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-415}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(2\)	\(0\)	$1$		\(q+(-1+\beta )q^{2}+(1-\beta )q^{4}+q^{5}-q^{8}+\cdots\)
3735.1.g.d	$3735$	$1$	3735.g	415.d	$2$	$2$	$2$	$1.864$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-415}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(-2\)	\(0\)	$1$		\(q+(1-\beta )q^{2}+(1-\beta )q^{4}-q^{5}+q^{8}+\cdots\)
3735.1.g.e	$3735$	$1$	3735.g	415.d	$2$	$4$	$4$	$1.864$	\(\Q(\zeta_{20})^+\)	$D_{10}$	\(\Q(\sqrt{-415}) \)	None	✓	$4$	$0$	\(-2\)	\(0\)	\(-4\)	\(0\)	$1$		\(q+\beta _{2}q^{2}-\beta _{2}q^{4}-q^{5}-q^{8}-\beta _{2}q^{10}+\cdots\)
3735.1.g.f	$3735$	$1$	3735.g	415.d	$2$	$4$	$4$	$1.864$	\(\Q(\zeta_{20})^+\)	$D_{10}$	\(\Q(\sqrt{-415}) \)	None	✓	$4$	$0$	\(2\)	\(0\)	\(4\)	\(0\)	$1$		\(q-\beta _{2}q^{2}-\beta _{2}q^{4}+q^{5}+q^{8}-\beta _{2}q^{10}+\cdots\)
415.3.d.a	$415$	$3$	415.d	415.d	$2$	$5$	$5$	$11.308$	5.5.538203125.1	$_{}$	\(\Q(\sqrt{-415}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(-25\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}+(4+\beta _{2}-\beta _{3})q^{4}-5q^{5}+\cdots\)
415.3.d.b	$415$	$3$	415.d	415.d	$2$	$5$	$5$	$11.308$	5.5.538203125.1	$_{}$	\(\Q(\sqrt{-415}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(25\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{2}+(4+\beta _{2}-\beta _{3})q^{4}+5q^{5}+\cdots\)