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 105 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
116.1.d.a	$116$	$1$	116.d	116.d	$2$	$1$	$1$	$0.058$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	✓	$2$	$0$	$-1$	$1$	$-1$	$0$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
116.1.d.b	$116$	$1$	116.d	116.d	$2$	$1$	$1$	$0.058$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	✓	$2$	$0$	$1$	$-1$	$-1$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
464.1.h.a	$464$	$1$	464.h	116.d	$2$	$1$	$1$	$0.232$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-29}) $	$\Q(\sqrt{29}) $	✓	$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+2q^{5}-q^{9}-2q^{13}+3q^{25}-q^{29}+\cdots$
464.1.h.b	$464$	$1$	464.h	116.d	$2$	$2$	$2$	$0.232$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-29}) $	None	✓	$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-\beta q^{3}-q^{5}+2q^{9}+\beta q^{11}+q^{13}+\cdots$
580.1.e.c	$580$	$1$	580.e	580.e	$2$	$2$	$2$	$0.289$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-29}) $	$\Q(\sqrt{145}) $		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q-iq^{2}-iq^{3}-q^{4}+q^{5}-2q^{6}+iq^{8}+\cdots$
580.1.e.d	$580$	$1$	580.e	580.e	$2$	$4$	$4$	$0.289$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-29}) $	None		$8$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+\zeta_{12}^{3}q^{2}-\zeta_{12}^{3}q^{3}-q^{4}+\zeta_{12}^{4}q^{5}+\cdots$
1044.1.g.a	$1044$	$1$	1044.g	116.d	$2$	$1$	$1$	$0.521$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$0$	$1$		$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+q^{11}+\cdots$
1044.1.g.b	$1044$	$1$	1044.g	116.d	$2$	$1$	$1$	$0.521$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$0$	$1$		$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-q^{11}+\cdots$
1044.1.o.a	$1044$	$1$	1044.o	1044.o	$6$	$6$	$3$	$0.521$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{6}q^{2}+\zeta_{18}^{4}q^{3}-\zeta_{18}^{3}q^{4}+\cdots$
1044.1.o.b	$1044$	$1$	1044.o	1044.o	$6$	$6$	$3$	$0.521$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{6}q^{2}+\zeta_{18}^{7}q^{3}-\zeta_{18}^{3}q^{4}+\cdots$
1276.1.p.a	$1276$	$1$	1276.p	1276.p	$10$	$4$	$1$	$0.637$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$-1$	$3$	$3$	$0$	$1$		$q+\zeta_{10}^{4}q^{2}+(1+\zeta_{10}^{4})q^{3}-\zeta_{10}^{3}q^{4}+\cdots$
1276.1.p.b	$1276$	$1$	1276.p	1276.p	$10$	$4$	$1$	$0.637$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$1$	$-3$	$3$	$0$	$1$		$q-\zeta_{10}^{4}q^{2}+(-1-\zeta_{10}^{4})q^{3}-\zeta_{10}^{3}q^{4}+\cdots$
1276.1.p.c	$1276$	$1$	1276.p	1276.p	$10$	$8$	$2$	$0.637$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$-2$	$-3$	$-3$	$0$	$1$		$q+\zeta_{30}^{12}q^{2}+(\zeta_{30}^{2}+\zeta_{30}^{10})q^{3}+\cdots$
1276.1.p.d	$1276$	$1$	1276.p	1276.p	$10$	$8$	$2$	$0.637$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$2$	$3$	$-3$	$0$	$1$		$q-\zeta_{30}^{12}q^{2}+(\zeta_{30}^{5}+\zeta_{30}^{7})q^{3}-\zeta_{30}^{9}q^{4}+\cdots$
1508.1.g.d	$1508$	$1$	1508.g	1508.g	$2$	$2$	$2$	$0.753$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-13}) $, $\Q(\sqrt{-29}) $	$\Q(\sqrt{377}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}+iq^{8}-q^{9}+iq^{11}+\cdots$
1508.1.g.f	$1508$	$1$	1508.g	1508.g	$2$	$4$	$4$	$0.753$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-29}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}^{3}q^{2}+(-\zeta_{12}+\zeta_{12}^{5})q^{3}-q^{4}+\cdots$
1508.1.v.c	$1508$	$1$	1508.v	1508.v	$6$	$12$	$6$	$0.753$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-29}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{36}^{15}q^{2}+(\zeta_{36}^{5}+\zeta_{36}^{7})q^{3}-\zeta_{36}^{12}q^{4}+\cdots$
1508.1.x.a	$1508$	$1$	1508.x	1508.x	$6$	$6$	$3$	$0.753$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{3}q^{2}+(-\zeta_{18}-\zeta_{18}^{5})q^{3}+\zeta_{18}^{6}q^{4}+\cdots$
1508.1.x.b	$1508$	$1$	1508.x	1508.x	$6$	$6$	$3$	$0.753$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{3}q^{2}+(-\zeta_{18}^{2}-\zeta_{18}^{4})q^{3}+\cdots$
1740.1.v.a	$1740$	$1$	1740.v	1740.v	$4$	$4$	$2$	$0.868$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-29}) $	None		$8$	$0$	$0$	$0$	$-4$	$0$	$1$		$q+\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}-q^{5}-\zeta_{8}^{2}q^{6}+\cdots$
1740.1.v.b	$1740$	$1$	1740.v	1740.v	$4$	$4$	$2$	$0.868$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-29}) $	None		$8$	$0$	$0$	$0$	$4$	$0$	$1$		$q-\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+q^{5}+\zeta_{8}^{2}q^{6}+\cdots$
1740.1.v.c	$1740$	$1$	1740.v	1740.v	$4$	$8$	$4$	$0.868$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-29}) $	None		$8$	$0$	$0$	$0$	$-4$	$0$	$1$		$q+\zeta_{24}^{9}q^{2}-\zeta_{24}^{5}q^{3}-\zeta_{24}^{6}q^{4}+\cdots$
1740.1.v.d	$1740$	$1$	1740.v	1740.v	$4$	$8$	$4$	$0.868$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-29}) $	None		$8$	$0$	$0$	$0$	$4$	$0$	$1$		$q-\zeta_{24}^{3}q^{2}-\zeta_{24}^{7}q^{3}+\zeta_{24}^{6}q^{4}+\cdots$
1856.1.h.a	$1856$	$1$	1856.h	116.d	$2$	$1$	$1$	$0.926$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	✓	$2$	$0$	$0$	$-1$	$1$	$0$	$1$		$q-q^{3}+q^{5}-q^{11}+q^{13}-q^{15}+2q^{19}+\cdots$
1856.1.h.b	$1856$	$1$	1856.h	116.d	$2$	$1$	$1$	$0.926$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-29}) $	$\Q(\sqrt{29}) $	✓	$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-2q^{5}-q^{9}+2q^{13}+3q^{25}+q^{29}+\cdots$
1856.1.h.c	$1856$	$1$	1856.h	116.d	$2$	$1$	$1$	$0.926$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	✓	$2$	$0$	$0$	$1$	$1$	$0$	$1$		$q+q^{3}+q^{5}+q^{11}+q^{13}+q^{15}-2q^{19}+\cdots$
1856.1.h.d	$1856$	$1$	1856.h	116.d	$2$	$2$	$2$	$0.926$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-29}) $	None	✓	$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-\beta q^{3}+q^{5}+2q^{9}+\beta q^{11}-q^{13}+\cdots$
2204.1.o.a	$2204$	$1$	2204.o	2204.o	$6$	$6$	$3$	$1.100$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$3$		$q+\zeta_{18}^{6}q^{2}+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{3}-\zeta_{18}^{3}q^{4}+\cdots$
2204.1.o.b	$2204$	$1$	2204.o	2204.o	$6$	$6$	$3$	$1.100$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$3$		$q-\zeta_{18}^{6}q^{2}+(\zeta_{18}-\zeta_{18}^{2})q^{3}-\zeta_{18}^{3}q^{4}+\cdots$
2204.1.bk.a	$2204$	$1$	2204.bk	2204.ak	$18$	$18$	$3$	$1.100$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$3$		$q+\zeta_{54}^{6}q^{2}+(-\zeta_{54}+\zeta_{54}^{20})q^{3}+\cdots$
2204.1.bk.b	$2204$	$1$	2204.bk	2204.ak	$18$	$18$	$3$	$1.100$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$3$		$q-\zeta_{54}^{6}q^{2}+(\zeta_{54}-\zeta_{54}^{20})q^{3}+\zeta_{54}^{12}q^{4}+\cdots$
2320.1.h.c	$2320$	$1$	2320.h	580.e	$2$	$1$	$1$	$1.158$	$\Q$	$D_{2}$	$\Q(\sqrt{-29}) $, $\Q(\sqrt{-145}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+q^{5}+q^{9}-2q^{11}+2q^{19}+q^{25}+\cdots$
2320.1.h.d	$2320$	$1$	2320.h	580.e	$2$	$1$	$1$	$1.158$	$\Q$	$D_{2}$	$\Q(\sqrt{-29}) $, $\Q(\sqrt{-145}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+q^{5}+q^{9}+2q^{11}-2q^{19}+q^{25}+\cdots$
2320.1.h.e	$2320$	$1$	2320.h	580.e	$2$	$2$	$2$	$1.158$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+\zeta_{6}^{2}q^{5}+(-1-\zeta_{6}+\cdots)q^{9}+\cdots$
2320.1.h.f	$2320$	$1$	2320.h	580.e	$2$	$2$	$2$	$1.158$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}-\zeta_{6}q^{5}+(-1-\zeta_{6}+\cdots)q^{9}+\cdots$
2784.1.i.a	$2784$	$1$	2784.i	87.d	$2$	$4$	$4$	$1.389$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-29}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{9}+(-\zeta_{8}+\zeta_{8}^{3})q^{11}+\cdots$
2784.1.i.b	$2784$	$1$	2784.i	87.d	$2$	$8$	$8$	$1.389$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-29}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}q^{3}+(\zeta_{24}^{4}+\zeta_{24}^{8})q^{5}+\zeta_{24}^{2}q^{9}+\cdots$
2900.1.e.a	$2900$	$1$	2900.e	580.e	$2$	$2$	$2$	$1.447$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{8}-q^{11}+\cdots$
2900.1.e.b	$2900$	$1$	2900.e	580.e	$2$	$2$	$2$	$1.447$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{8}+q^{11}+\cdots$
2900.1.g.a	$2900$	$1$	2900.g	116.d	$2$	$1$	$1$	$1.447$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	✓	$2$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-q^{11}+\cdots$
2900.1.g.b	$2900$	$1$	2900.g	116.d	$2$	$1$	$1$	$1.447$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-29}) $	$\Q(\sqrt{145}) $	✓	$4$	$0$	$-1$	$2$	$0$	$0$	$1$		$q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+3q^{9}+\cdots$
2900.1.g.c	$2900$	$1$	2900.g	116.d	$2$	$1$	$1$	$1.447$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-29}) $	$\Q(\sqrt{145}) $	✓	$4$	$0$	$1$	$-2$	$0$	$0$	$1$		$q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+3q^{9}+\cdots$
2900.1.g.d	$2900$	$1$	2900.g	116.d	$2$	$1$	$1$	$1.447$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	✓	$2$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{11}+\cdots$
2900.1.g.e	$2900$	$1$	2900.g	116.d	$2$	$2$	$2$	$1.447$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-29}) $	None	✓	$4$	$0$	$-2$	$-2$	$0$	$0$	$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}-\beta q^{11}+\cdots$
2900.1.g.g	$2900$	$1$	2900.g	116.d	$2$	$2$	$2$	$1.447$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-29}) $	None	✓	$4$	$0$	$2$	$2$	$0$	$0$	$1$		$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}-\beta q^{11}+\cdots$
2900.1.w.a	$2900$	$1$	2900.w	2900.w	$10$	$4$	$1$	$1.447$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$-1$	$3$	$-1$	$0$	$1$		$q+\zeta_{10}^{2}q^{2}+(1-\zeta_{10}^{3})q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
2900.1.w.b	$2900$	$1$	2900.w	2900.w	$10$	$4$	$1$	$1.447$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$1$	$-3$	$-1$	$0$	$1$		$q-\zeta_{10}^{2}q^{2}+(-1+\zeta_{10}^{3})q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
2900.1.w.c	$2900$	$1$	2900.w	2900.w	$10$	$8$	$2$	$1.447$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$-2$	$-3$	$1$	$0$	$1$		$q+\zeta_{30}^{6}q^{2}+(\zeta_{30}^{4}-\zeta_{30}^{5})q^{3}+\zeta_{30}^{12}q^{4}+\cdots$
2900.1.w.d	$2900$	$1$	2900.w	2900.w	$10$	$8$	$2$	$1.447$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$2$	$3$	$1$	$0$	$1$		$q-\zeta_{30}^{6}q^{2}+(-\zeta_{30}^{10}-\zeta_{30}^{14})q^{3}+\cdots$
2900.1.bb.c	$2900$	$1$	2900.bb	2900.ab	$10$	$8$	$2$	$1.447$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-29}) $	None		$8$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-\zeta_{20}^{3}q^{2}+(\zeta_{20}^{5}-\zeta_{20}^{7})q^{3}+\zeta_{20}^{6}q^{4}+\cdots$

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 105 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.