LMFDB - Newform search results

Refine search

Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
		Only for weight 1:

				Sort order	Select

Results (1-50 of 81 matches)

Next Download displayed columns for results to

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1944.1.e.a	$1944$	$1$	1944.e	3.b	$2$	$2$	$2$	$0.970$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{5}-\beta q^{11}+q^{13}+\beta q^{17}-q^{19}+\cdots$
1944.1.h.a	$1944$	$1$	1944.h	24.h	$2$	$3$	$3$	$0.970$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-6}) $	None	✓	$2$	$0$	$-3$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots$
1944.1.h.b	$1944$	$1$	1944.h	24.h	$2$	$3$	$3$	$0.970$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-6}) $	None	✓	$2$	$0$	$3$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}-\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots$
1944.1.h.c	$1944$	$1$	1944.h	24.h	$2$	$4$	$4$	$0.970$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
1944.1.j.a	$1944$	$1$	1944.j	72.j	$6$	$6$	$3$	$0.970$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$		$3$		$q-\zeta_{18}^{3}q^{2}+\zeta_{18}^{6}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{8}+\cdots)q^{5}+\cdots$
1944.1.j.b	$1944$	$1$	1944.j	72.j	$6$	$6$	$3$	$0.970$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$3$	$0$	$0$	$0$		$3$		$q+\zeta_{18}^{3}q^{2}+\zeta_{18}^{6}q^{4}+(\zeta_{18}-\zeta_{18}^{2}+\cdots)q^{5}+\cdots$
1944.1.j.c	$1944$	$1$	1944.j	72.j	$6$	$8$	$4$	$0.970$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{5}-\zeta_{24}^{11}+\cdots)q^{5}+\cdots$
1944.1.m.a	$1944$	$1$	1944.m	9.d	$6$	$4$	$2$	$0.970$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\beta _{1}-\beta _{3})q^{5}-\beta _{1}q^{11}-\beta _{2}q^{13}+\cdots$
1944.1.r.a	$1944$	$1$	1944.r	216.r	$18$	$6$	$1$	$0.970$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}-\zeta_{18}^{3}q^{8}+\cdots$
1944.1.r.b	$1944$	$1$	1944.r	216.r	$18$	$6$	$1$	$0.970$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}-\zeta_{18}^{3}q^{8}+\cdots$
1944.1.r.c	$1944$	$1$	1944.r	216.r	$18$	$6$	$1$	$0.970$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+\zeta_{18}^{3}q^{8}+\cdots$
1944.1.r.d	$1944$	$1$	1944.r	216.r	$18$	$6$	$1$	$0.970$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+\zeta_{18}^{3}q^{8}+\cdots$
1944.1.bf.a	$1944$	$1$	1944.bf	648.af	$54$	$18$	$1$	$0.970$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{54}^{7}q^{2}+\zeta_{54}^{14}q^{4}+\zeta_{54}^{21}q^{8}+\cdots$
1944.1.bh.a	$1944$	$1$	1944.bh	1944.ah	$162$	$54$	$1$	$0.970$	$\Q(\zeta_{162})$	$D_{81}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{162}^{32}q^{2}-\zeta_{162}^{29}q^{3}+\zeta_{162}^{64}q^{4}+\cdots$
1944.2.a.a	$1944$	$2$	1944.a	1.a	$1$	$1$	$1$	$15.523$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-4$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+3q^{7}+2q^{11}-5q^{13}-2q^{17}+\cdots$
1944.2.a.b	$1944$	$2$	1944.a	1.a	$1$	$1$	$1$	$15.523$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-3q^{7}-2q^{11}+q^{13}+8q^{17}+\cdots$
1944.2.a.c	$1944$	$2$	1944.a	1.a	$1$	$1$	$1$	$15.523$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-2q^{11}+q^{13}+2q^{17}+5q^{19}+\cdots$
1944.2.a.d	$1944$	$2$	1944.a	1.a	$1$	$1$	$1$	$15.523$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+3q^{7}-2q^{11}+q^{13}-4q^{17}+\cdots$
1944.2.a.e	$1944$	$2$	1944.a	1.a	$1$	$1$	$1$	$15.523$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{11}-2q^{13}+4q^{17}-q^{19}+\cdots$
1944.2.a.f	$1944$	$2$	1944.a	1.a	$1$	$1$	$1$	$15.523$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{11}-2q^{13}-4q^{17}-q^{19}+\cdots$
1944.2.a.g	$1944$	$2$	1944.a	1.a	$1$	$1$	$1$	$15.523$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-3q^{7}+2q^{11}+q^{13}-8q^{17}+\cdots$
1944.2.a.h	$1944$	$2$	1944.a	1.a	$1$	$1$	$1$	$15.523$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+2q^{11}+q^{13}-2q^{17}+5q^{19}+\cdots$
1944.2.a.i	$1944$	$2$	1944.a	1.a	$1$	$1$	$1$	$15.523$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+3q^{7}+2q^{11}+q^{13}+4q^{17}+\cdots$
1944.2.a.j	$1944$	$2$	1944.a	1.a	$1$	$1$	$1$	$15.523$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$4$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+3q^{7}-2q^{11}-5q^{13}+2q^{17}+\cdots$
1944.2.a.k	$1944$	$2$	1944.a	1.a	$1$	$2$	$2$	$15.523$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{5}+2\beta q^{7}+(-1-3\beta )q^{11}+\cdots$
1944.2.a.l	$1944$	$2$	1944.a	1.a	$1$	$2$	$2$	$15.523$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{5}+(-1-\beta )q^{7}+4q^{11}+(2-2\beta )q^{13}+\cdots$
1944.2.a.m	$1944$	$2$	1944.a	1.a	$1$	$2$	$2$	$15.523$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-1-\beta )q^{7}-4q^{11}+(2-2\beta )q^{13}+\cdots$
1944.2.a.n	$1944$	$2$	1944.a	1.a	$1$	$2$	$2$	$15.523$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}-2\beta q^{7}+(1-3\beta )q^{11}+\cdots$
1944.2.a.o	$1944$	$2$	1944.a	1.a	$1$	$3$	$3$	$15.523$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+(-1+\beta _{1})q^{7}+(-1+2\beta _{1}+\cdots)q^{11}+\cdots$
1944.2.a.p	$1944$	$2$	1944.a	1.a	$1$	$3$	$3$	$15.523$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+(-1+\beta _{1})q^{7}+(1-2\beta _{1}+\cdots)q^{11}+\cdots$
1944.2.a.q	$1944$	$2$	1944.a	1.a	$1$	$6$	$6$	$15.523$	6.6.9926793.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$3$	$-$	$3^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{5}+(1-\beta _{4})q^{7}+(-\beta _{1}-\beta _{3}+\cdots)q^{11}+\cdots$
1944.2.a.r	$1944$	$2$	1944.a	1.a	$1$	$6$	$6$	$15.523$	6.6.9926793.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$3$	$-$	$3^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{5}+(1-\beta _{4})q^{7}+(\beta _{1}+\beta _{3}+\beta _{5})q^{11}+\cdots$
1944.2.i.a	$1944$	$2$	1944.i	9.c	$3$	$2$	$1$	$15.523$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-4\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots$
1944.2.i.b	$1944$	$2$	1944.i	9.c	$3$	$2$	$1$	$15.523$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots$
1944.2.i.c	$1944$	$2$	1944.i	9.c	$3$	$2$	$1$	$15.523$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{11}-\zeta_{6}q^{13}+\cdots$
1944.2.i.d	$1944$	$2$	1944.i	9.c	$3$	$2$	$1$	$15.523$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$0$	$-2$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots$
1944.2.i.e	$1944$	$2$	1944.i	9.c	$3$	$2$	$1$	$15.523$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{5}+(2-2\zeta_{6})q^{11}+2\zeta_{6}q^{13}+\cdots$
1944.2.i.f	$1944$	$2$	1944.i	9.c	$3$	$2$	$1$	$15.523$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{11}+2\zeta_{6}q^{13}+\cdots$
1944.2.i.g	$1944$	$2$	1944.i	9.c	$3$	$2$	$1$	$15.523$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots$
1944.2.i.h	$1944$	$2$	1944.i	9.c	$3$	$2$	$1$	$15.523$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{5}+(2-2\zeta_{6})q^{11}-\zeta_{6}q^{13}+\cdots$
1944.2.i.i	$1944$	$2$	1944.i	9.c	$3$	$2$	$1$	$15.523$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots$
1944.2.i.j	$1944$	$2$	1944.i	9.c	$3$	$2$	$1$	$15.523$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+4\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots$
1944.2.i.k	$1944$	$2$	1944.i	9.c	$3$	$4$	$2$	$15.523$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\zeta_{12}+\zeta_{12}^{2})q^{5}+(2\zeta_{12}^{2}-2\zeta_{12}^{3})q^{7}+\cdots$
1944.2.i.l	$1944$	$2$	1944.i	9.c	$3$	$4$	$2$	$15.523$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{3})q^{5}+(1-2\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots$
1944.2.i.m	$1944$	$2$	1944.i	9.c	$3$	$4$	$2$	$15.523$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$1$	$3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{5}+(2-\beta _{1}+\beta _{2}-\beta _{3})q^{7}+(-4+\cdots)q^{11}+\cdots$
1944.2.i.n	$1944$	$2$	1944.i	9.c	$3$	$4$	$2$	$15.523$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{5}+(2\zeta_{12}^{2}-2\zeta_{12}^{3})q^{7}+\cdots$
1944.2.i.o	$1944$	$2$	1944.i	9.c	$3$	$6$	$3$	$15.523$	$\Q(\zeta_{18})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}-\zeta_{18}^{5})q^{5}+\cdots$
1944.2.i.p	$1944$	$2$	1944.i	9.c	$3$	$6$	$3$	$15.523$	$\Q(\zeta_{18})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\zeta_{18}^{2}-\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{5}+\cdots$
1944.2.i.q	$1944$	$2$	1944.i	9.c	$3$	$12$	$6$	$15.523$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-3$		$3^{6}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{6}q^{5}+(-\beta _{1}-\beta _{2}-\beta _{8}+\beta _{9})q^{7}+\cdots$
1944.2.i.r	$1944$	$2$	1944.i	9.c	$3$	$12$	$6$	$15.523$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-3$		$3^{6}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{6}q^{5}+(-\beta _{1}+\beta _{2}-\beta _{8}-\beta _{9})q^{7}+\cdots$

Next Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 81 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.