↑

Learn more

The results below are complete, since the LMFDB contains all newforms with $Nk^2$ at most 4000

Refine search

Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad \(p\)	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

				Sort order	Select

Results (displaying both matches)

Download displayed columns for results to

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
159.1.d.a	$159$	$1$	159.d	159.d	$2$	$2$	$2$	$0.079$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-159}) \)	None	✓	✓			159.1.d.a	$2$	$0$	\(-1\)	\(2\)	\(-1\)	\(-1\)	$1$		\(q+(-1+\beta )q^{2}+q^{3}+(1-\beta )q^{4}-\beta q^{5}+\cdots\)
159.1.d.b	$159$	$1$	159.d	159.d	$2$	$2$	$2$	$0.079$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-159}) \)	None	✓	✓			159.1.d.a	$2$	$0$	\(1\)	\(-2\)	\(1\)	\(-1\)	$1$		\(q+(1-\beta )q^{2}-q^{3}+(1-\beta )q^{4}+\beta q^{5}+\cdots\)

Download displayed columns for results to