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 382 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
31.1.b.a	$31$	$1$	31.b	31.b	$2$	$1$	$1$	$0.015$	$\Q$	$D_{3}$	$\Q(\sqrt{-31}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$	$1$		$q-q^{2}-q^{5}-q^{7}+q^{8}+q^{9}+q^{10}+\cdots$
155.1.c.a	$155$	$1$	155.c	155.c	$2$	$1$	$1$	$0.077$	$\Q$	$D_{2}$	$\Q(\sqrt{-31}) $, $\Q(\sqrt{-155}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+q^{4}-q^{5}-q^{9}+q^{16}-2q^{19}-q^{20}+\cdots$
155.1.c.b	$155$	$1$	155.c	155.c	$2$	$2$	$2$	$0.077$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{2}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{4}+\cdots$
217.1.n.a	$217$	$1$	217.n	217.n	$6$	$6$	$3$	$0.108$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{5})q^{2}+(-\zeta_{18}+\zeta_{18}^{2}+\cdots)q^{4}+\cdots$
248.1.g.a	$248$	$1$	248.g	248.g	$2$	$1$	$1$	$0.124$	$\Q$	$D_{2}$	$\Q(\sqrt{-31}) $, $\Q(\sqrt{-62}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$1$	$0$	$0$	$-2$	$1$		$q+q^{2}+q^{4}-2q^{7}+q^{8}-q^{9}-2q^{14}+\cdots$
248.1.g.c	$248$	$1$	248.g	248.g	$2$	$2$	$2$	$0.124$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-1$	$0$	$0$	$2$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+(-\zeta_{6}-\zeta_{6}^{2})q^{5}+\cdots$
279.1.d.a	$279$	$1$	279.d	31.b	$2$	$1$	$1$	$0.139$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-31}) $	$\Q(\sqrt{93}) $	✓	$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q-q^{4}+2q^{7}+q^{16}-2q^{19}-q^{25}+\cdots$
279.1.d.b	$279$	$1$	279.d	31.b	$2$	$1$	$1$	$0.139$	$\Q$	$D_{3}$	$\Q(\sqrt{-31}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$-1$	$1$		$q+q^{2}+q^{5}-q^{7}-q^{8}+q^{10}-q^{14}+\cdots$
279.1.d.c	$279$	$1$	279.d	31.b	$2$	$2$	$2$	$0.139$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-31}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\beta q^{2}+2q^{4}+\beta q^{5}-q^{7}-\beta q^{8}+\cdots$
496.1.e.a	$496$	$1$	496.e	31.b	$2$	$1$	$1$	$0.248$	$\Q$	$D_{3}$	$\Q(\sqrt{-31}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$1$	$1$		$q-q^{5}+q^{7}+q^{9}+q^{19}-q^{31}-q^{35}+\cdots$
496.1.j.a	$496$	$1$	496.j	496.j	$4$	$2$	$1$	$0.248$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-2$	$0$	$2$	$0$	$1$		$q-q^{2}+q^{4}+(1+i)q^{5}-iq^{7}-q^{8}+\cdots$
496.1.j.b	$496$	$1$	496.j	496.j	$4$	$4$	$2$	$0.248$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$2$	$0$	$-2$	$0$	$1$		$q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+(\zeta_{12}^{4}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots$
589.1.m.a	$589$	$1$	589.m	589.m	$6$	$6$	$3$	$0.294$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{5})q^{2}+(-\zeta_{18}+\zeta_{18}^{2}+\cdots)q^{4}+\cdots$
589.1.bg.a	$589$	$1$	589.bg	589.ag	$18$	$18$	$3$	$0.294$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{54}^{17}-\zeta_{54}^{25})q^{2}+(-\zeta_{54}^{7}+\cdots)q^{4}+\cdots$
620.1.m.a	$620$	$1$	620.m	620.m	$4$	$2$	$1$	$0.309$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-2$	$0$	$0$	$2$	$1$		$q-q^{2}+q^{4}+iq^{5}+(1-i)q^{7}-q^{8}+\cdots$
620.1.m.b	$620$	$1$	620.m	620.m	$4$	$2$	$1$	$0.309$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-iq^{2}-q^{4}+iq^{5}+(-1+i)q^{7}+\cdots$
620.1.m.c	$620$	$1$	620.m	620.m	$4$	$4$	$2$	$0.309$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{5}q^{5}+\cdots$
620.1.m.d	$620$	$1$	620.m	620.m	$4$	$4$	$2$	$0.309$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$2$	$0$	$0$	$-2$	$1$		$q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-\zeta_{12}q^{5}+(\zeta_{12}^{4}+\cdots)q^{7}+\cdots$
775.1.c.a	$775$	$1$	775.c	155.c	$2$	$2$	$2$	$0.387$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-iq^{7}-iq^{8}-q^{9}-q^{14}+\cdots$
775.1.d.a	$775$	$1$	775.d	31.b	$2$	$1$	$1$	$0.387$	$\Q$	$D_{2}$	$\Q(\sqrt{-31}) $, $\Q(\sqrt{-155}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}+q^{9}+q^{16}+2q^{19}-q^{31}+\cdots$
775.1.d.b	$775$	$1$	775.d	31.b	$2$	$1$	$1$	$0.387$	$\Q$	$D_{3}$	$\Q(\sqrt{-31}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$1$	$1$		$q+q^{2}+q^{7}-q^{8}+q^{9}+q^{14}-q^{16}+\cdots$
775.1.d.c	$775$	$1$	775.d	31.b	$2$	$2$	$2$	$0.387$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-31}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{2}+2q^{4}+\beta q^{7}-\beta q^{8}+q^{9}+\cdots$
775.1.w.a	$775$	$1$	775.w	775.w	$10$	$4$	$1$	$0.387$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$3$	$0$	$-1$	$-2$	$1$		$q+(1-\zeta_{10})q^{2}+(1-\zeta_{10}+\zeta_{10}^{2})q^{4}+\cdots$
775.1.w.b	$775$	$1$	775.w	775.w	$10$	$8$	$2$	$0.387$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-3$	$0$	$1$	$2$	$1$		$q+(-\zeta_{30}^{5}-\zeta_{30}^{13})q^{2}+(-\zeta_{30}^{3}+\cdots)q^{4}+\cdots$
775.1.z.a	$775$	$1$	775.z	775.z	$10$	$4$	$1$	$0.387$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-5$	$0$	$1$	$0$	$1$		$q+(-1+\zeta_{10}^{4})q^{2}+(1-\zeta_{10}^{3}-\zeta_{10}^{4}+\cdots)q^{4}+\cdots$
775.1.z.b	$775$	$1$	775.z	775.z	$10$	$8$	$2$	$0.387$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$5$	$0$	$-1$	$0$	$1$		$q+(\zeta_{30}^{2}-\zeta_{30}^{10})q^{2}+(\zeta_{30}^{4}-\zeta_{30}^{5}+\cdots)q^{4}+\cdots$
868.1.c.a	$868$	$1$	868.c	868.c	$2$	$1$	$1$	$0.433$	$\Q$	$D_{2}$	$\Q(\sqrt{-31}) $, $\Q(\sqrt{-217}) $	$\Q(\sqrt{7}) $	✓	$4$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q-q^{2}+q^{4}-q^{7}-q^{8}+q^{9}+q^{14}+\cdots$
868.1.c.b	$868$	$1$	868.c	868.c	$2$	$1$	$1$	$0.433$	$\Q$	$D_{2}$	$\Q(\sqrt{-31}) $, $\Q(\sqrt{-217}) $	$\Q(\sqrt{7}) $	✓	$4$	$0$	$-1$	$0$	$0$	$1$	$1$		$q-q^{2}+q^{4}+q^{7}-q^{8}+q^{9}-q^{14}+\cdots$
868.1.c.c	$868$	$1$	868.c	868.c	$2$	$2$	$2$	$0.433$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$1$	$0$	$0$	$-1$	$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+(-\zeta_{6}-\zeta_{6}^{2})q^{5}+\cdots$
868.1.c.d	$868$	$1$	868.c	868.c	$2$	$2$	$2$	$0.433$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$1$	$0$	$0$	$1$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+(-\zeta_{6}-\zeta_{6}^{2})q^{5}+\cdots$
868.1.bj.a	$868$	$1$	868.bj	868.aj	$6$	$6$	$3$	$0.433$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{7}q^{2}-\zeta_{18}^{5}q^{4}+(\zeta_{18}^{2}-\zeta_{18}^{4}+\cdots)q^{5}+\cdots$
868.1.bj.b	$868$	$1$	868.bj	868.aj	$6$	$6$	$3$	$0.433$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}+(\zeta_{18}-\zeta_{18}^{5}+\cdots)q^{5}+\cdots$
961.1.e.a	$961$	$1$	961.e	31.e	$6$	$2$	$1$	$0.480$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-2$	$0$	$1$	$1$	$1$		$q-q^{2}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+q^{8}-\zeta_{6}q^{9}+\cdots$
961.1.f.a	$961$	$1$	961.f	31.f	$10$	$4$	$1$	$0.480$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-31}) $	None		$8$	$0$	$1$	$0$	$-4$	$1$	$1$		$q+\zeta_{10}^{3}q^{2}-q^{5}+\zeta_{10}q^{7}+\zeta_{10}^{4}q^{8}+\cdots$
961.1.h.a	$961$	$1$	961.h	31.h	$30$	$8$	$1$	$0.480$	$\Q(\zeta_{15})$	$D_{3}$	$\Q(\sqrt{-31}) $	None		$16$	$0$	$2$	$0$	$4$	$-1$	$1$		$q+\zeta_{30}^{3}q^{2}-\zeta_{30}^{10}q^{5}+\zeta_{30}^{11}q^{7}+\cdots$
992.1.g.a	$992$	$1$	992.g	248.g	$2$	$1$	$1$	$0.495$	$\Q$	$D_{2}$	$\Q(\sqrt{-31}) $, $\Q(\sqrt{-62}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+2q^{7}-q^{9}+q^{25}-q^{31}-2q^{41}+\cdots$
992.1.g.b	$992$	$1$	992.g	248.g	$2$	$2$	$2$	$0.495$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$2$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{5}-q^{7}-q^{9}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots$
992.1.y.a	$992$	$1$	992.y	992.y	$8$	$4$	$1$	$0.495$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$4$	$0$	$1$		$q-\zeta_{8}^{2}q^{2}-q^{4}+(1-\zeta_{8})q^{5}+\zeta_{8}^{2}q^{8}+\cdots$
992.1.y.b	$992$	$1$	992.y	992.y	$8$	$8$	$2$	$0.495$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$-4$	$0$	$1$		$q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}+(-\zeta_{24}+\zeta_{24}^{8}+\cdots)q^{5}+\cdots$
1085.1.o.a	$1085$	$1$	1085.o	1085.o	$4$	$2$	$1$	$0.541$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$2$	$0$	$0$	$-2$	$1$		$q+(1+i)q^{2}+iq^{4}+iq^{5}-q^{7}+q^{8}+\cdots$
1085.1.o.b	$1085$	$1$	1085.o	1085.o	$4$	$2$	$1$	$0.541$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+(1+i)q^{2}+iq^{4}-iq^{5}-iq^{7}+q^{8}+\cdots$
1085.1.o.c	$1085$	$1$	1085.o	1085.o	$4$	$4$	$2$	$0.541$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+(\zeta_{12}^{4}-\zeta_{12}^{5})q^{2}+(-\zeta_{12}^{2}+\zeta_{12}^{3}+\cdots)q^{4}+\cdots$
1085.1.o.d	$1085$	$1$	1085.o	1085.o	$4$	$4$	$2$	$0.541$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-2$	$0$	$0$	$2$	$1$		$q+(-\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}^{2}+\zeta_{12}^{3}+\cdots)q^{4}+\cdots$
1085.1.bh.a	$1085$	$1$	1085.bh	1085.ah	$6$	$6$	$3$	$0.541$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}+\zeta_{18}^{2})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{4}+\cdots$
1085.1.bh.b	$1085$	$1$	1085.bh	1085.ah	$6$	$6$	$3$	$0.541$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}-\zeta_{18}^{8})q^{2}+(\zeta_{18}^{3}-\zeta_{18}^{7}+\cdots)q^{4}+\cdots$
1085.1.cp.a	$1085$	$1$	1085.cp	1085.bp	$12$	$12$	$3$	$0.541$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{36}^{7}+\zeta_{36}^{8})q^{2}+(\zeta_{36}^{14}+\zeta_{36}^{15}+\cdots)q^{4}+\cdots$
1085.1.cp.b	$1085$	$1$	1085.cp	1085.bp	$12$	$12$	$3$	$0.541$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{36}^{5}-\zeta_{36}^{10})q^{2}+(-\zeta_{36}^{2}+\cdots)q^{4}+\cdots$
1116.1.b.a	$1116$	$1$	1116.b	372.b	$2$	$4$	$4$	$0.557$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-31}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
1116.1.b.b	$1116$	$1$	1116.b	372.b	$2$	$8$	$8$	$0.557$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-31}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+(\zeta_{24}^{5}+\zeta_{24}^{7}+\cdots)q^{5}+\cdots$
1240.1.e.a	$1240$	$1$	1240.e	1240.e	$2$	$1$	$1$	$0.619$	$\Q$	$D_{2}$	$\Q(\sqrt{-31}) $, $\Q(\sqrt{-310}) $	$\Q(\sqrt{10}) $	✓	$4$	$0$	$-1$	$0$	$1$	$0$	$1$		$q-q^{2}+q^{4}+q^{5}-q^{8}+q^{9}-q^{10}+\cdots$

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 382 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.