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 61 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
2775.1.b.a	$2775$	$1$	2775.b	555.b	$2$	$2$	$2$	$1.385$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-111}) $	$\Q(\sqrt{37}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{3}+q^{4}-iq^{7}-q^{9}-iq^{12}+\cdots$
2775.1.b.b	$2775$	$1$	2775.b	555.b	$2$	$4$	$4$	$1.385$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\cdots$
2775.1.h.a	$2775$	$1$	2775.h	111.d	$2$	$1$	$1$	$1.385$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-111}) $	$\Q(\sqrt{37}) $	✓	$4$	$0$	$0$	$-1$	$0$	$2$		$1$		$q-q^{3}-q^{4}+2q^{7}+q^{9}+q^{12}+q^{16}+\cdots$
2775.1.h.b	$2775$	$1$	2775.h	111.d	$2$	$2$	$2$	$1.385$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-111}) $	None	✓	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\beta q^{2}+q^{3}+q^{4}-\beta q^{6}+q^{9}+q^{12}+\cdots$
2775.1.h.c	$2775$	$1$	2775.h	111.d	$2$	$4$	$4$	$1.385$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-111}) $	None	✓	$4$	$0$	$0$	$-4$	$0$	$0$		$1$		$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
2775.1.h.d	$2775$	$1$	2775.h	111.d	$2$	$4$	$4$	$1.385$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-111}) $	None	✓	$4$	$0$	$0$	$4$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
2775.1.k.a	$2775$	$1$	2775.k	555.k	$4$	$4$	$2$	$1.385$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{3}+q^{4}+\zeta_{8}q^{7}+\zeta_{8}^{2}q^{9}-\zeta_{8}q^{12}+\cdots$
2775.1.u.a	$2775$	$1$	2775.u	555.u	$4$	$4$	$2$	$1.385$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{3}-q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}^{2}q^{9}+\cdots$
2775.1.w.a	$2775$	$1$	2775.w	111.h	$6$	$2$	$1$	$1.385$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$1$		$1$		$q+\zeta_{6}q^{3}+\zeta_{6}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
2775.1.x.a	$2775$	$1$	2775.x	555.w	$6$	$4$	$2$	$1.385$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{7}+\cdots$
2775.1.z.a	$2775$	$1$	2775.z	111.i	$6$	$2$	$1$	$1.385$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-1$		$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots$
2775.1.bb.a	$2775$	$1$	2775.bb	555.aa	$6$	$4$	$2$	$1.385$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{2}q^{4}-\zeta_{12}^{5}q^{7}+\cdots$
2775.1.bg.a	$2775$	$1$	2775.bg	2775.ag	$10$	$4$	$1$	$1.385$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-111}) $	None		$4$	$0$	$-2$	$-1$	$-1$	$8$		$1$		$q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}-\zeta_{10}q^{3}+(-\zeta_{10}+\cdots)q^{4}+\cdots$
2775.1.bg.b	$2775$	$1$	2775.bg	2775.ag	$10$	$4$	$1$	$1.385$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-111}) $	None		$4$	$0$	$2$	$-1$	$1$	$8$		$1$		$q+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{2}-\zeta_{10}q^{3}+(-\zeta_{10}+\cdots)q^{4}+\cdots$
2775.1.bg.c	$2775$	$1$	2775.bg	2775.ag	$10$	$8$	$2$	$1.385$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$-2$	$0$	$-16$		$1$		$q+(-\zeta_{20}^{3}-\zeta_{20}^{9})q^{2}-\zeta_{20}^{2}q^{3}+\cdots$
2775.1.bg.d	$2775$	$1$	2775.bg	2775.ag	$10$	$16$	$4$	$1.385$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$4$	$0$	$0$		$1$		$q+(\zeta_{40}+\zeta_{40}^{7})q^{2}-\zeta_{40}^{8}q^{3}+(\zeta_{40}^{2}+\cdots)q^{4}+\cdots$
2775.1.bi.a	$2775$	$1$	2775.bi	2775.ai	$10$	$32$	$8$	$1.385$	$\Q(\zeta_{80})$	$D_{40}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{80}^{17}-\zeta_{80}^{31})q^{2}+\zeta_{80}^{28}q^{3}+\cdots$
2775.1.bm.a	$2775$	$1$	2775.bm	555.ae	$12$	$8$	$2$	$1.385$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}q^{3}+\zeta_{24}^{4}q^{4}+\zeta_{24}q^{7}+\zeta_{24}^{2}q^{9}+\cdots$
2775.1.bw.a	$2775$	$1$	2775.bw	555.ao	$12$	$8$	$2$	$1.385$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{3}-\zeta_{24}^{4}q^{4}-\zeta_{24}^{7}q^{7}+\cdots$
2775.1.bz.a	$2775$	$1$	2775.bz	111.n	$18$	$6$	$1$	$1.385$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-3$		$1$		$q+\zeta_{18}^{5}q^{3}-\zeta_{18}^{8}q^{4}+(\zeta_{18}^{6}-\zeta_{18}^{7}+\cdots)q^{7}+\cdots$
2775.1.bz.b	$2775$	$1$	2775.bz	111.n	$18$	$6$	$1$	$1.385$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$3$		$1$		$q-\zeta_{18}^{5}q^{3}-\zeta_{18}^{8}q^{4}+(-\zeta_{18}^{6}+\zeta_{18}^{7}+\cdots)q^{7}+\cdots$
2775.1.ca.a	$2775$	$1$	2775.ca	555.ar	$18$	$12$	$2$	$1.385$	$\Q(\zeta_{36})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{36}^{7}q^{3}-\zeta_{36}^{4}q^{4}+(\zeta_{36}^{3}-\zeta_{36}^{17}+\cdots)q^{7}+\cdots$
2775.1.cd.a	$2775$	$1$	2775.cd	555.au	$18$	$12$	$2$	$1.385$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{36}^{7}q^{3}+\zeta_{36}^{4}q^{4}+(-\zeta_{36}^{3}+\zeta_{36}^{17}+\cdots)q^{7}+\cdots$
2775.1.ce.a	$2775$	$1$	2775.ce	111.p	$18$	$6$	$1$	$1.385$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-3$		$1$		$q-\zeta_{18}^{5}q^{3}+\zeta_{18}^{8}q^{4}+(\zeta_{18}^{6}-\zeta_{18}^{7}+\cdots)q^{7}+\cdots$
2775.1.ce.b	$2775$	$1$	2775.ce	111.p	$18$	$6$	$1$	$1.385$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$3$		$1$		$q+\zeta_{18}^{5}q^{3}+\zeta_{18}^{8}q^{4}+(-\zeta_{18}^{6}+\zeta_{18}^{7}+\cdots)q^{7}+\cdots$
2775.1.cy.a	$2775$	$1$	2775.cy	555.aw	$36$	$24$	$2$	$1.385$	$\Q(\zeta_{72})$	$D_{36}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{72}^{31}q^{3}+\zeta_{72}^{28}q^{4}+(-\zeta_{72}^{3}+\cdots)q^{7}+\cdots$
2775.1.di.a	$2775$	$1$	2775.di	555.bg	$36$	$24$	$2$	$1.385$	$\Q(\zeta_{72})$	$D_{36}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{72}^{35}q^{3}-\zeta_{72}^{20}q^{4}+(-\zeta_{72}^{15}+\cdots)q^{7}+\cdots$
2775.2.a.a	$2775$	$2$	2775.a	1.a	$1$	$1$	$1$	$22.158$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-2q^{6}+q^{9}-2q^{11}+\cdots$
2775.2.a.b	$2775$	$2$	2775.a	1.a	$1$	$1$	$1$	$22.158$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-2q^{6}+q^{7}+q^{9}+\cdots$
2775.2.a.c	$2775$	$2$	2775.a	1.a	$1$	$1$	$1$	$22.158$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-3q^{7}+q^{9}+4q^{11}+\cdots$
2775.2.a.d	$2775$	$2$	2775.a	1.a	$1$	$1$	$1$	$22.158$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-2q^{7}+q^{9}+2q^{12}+\cdots$
2775.2.a.e	$2775$	$2$	2775.a	1.a	$1$	$1$	$1$	$22.158$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-q^{7}+q^{9}-2q^{11}+2q^{12}+\cdots$
2775.2.a.f	$2775$	$2$	2775.a	1.a	$1$	$1$	$1$	$22.158$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+2q^{7}+q^{9}+4q^{11}+\cdots$
2775.2.a.g	$2775$	$2$	2775.a	1.a	$1$	$1$	$1$	$22.158$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{7}+q^{9}-2q^{11}-2q^{12}+\cdots$
2775.2.a.h	$2775$	$2$	2775.a	1.a	$1$	$1$	$1$	$22.158$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+3q^{7}+q^{9}+4q^{11}+\cdots$
2775.2.a.i	$2775$	$2$	2775.a	1.a	$1$	$1$	$1$	$22.158$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$-1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-2q^{6}-q^{7}+q^{9}+\cdots$
2775.2.a.j	$2775$	$2$	2775.a	1.a	$1$	$1$	$1$	$22.158$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$2$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-2q^{6}+q^{9}-2q^{11}+\cdots$
2775.2.a.k	$2775$	$2$	2775.a	1.a	$1$	$2$	$2$	$22.158$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$-2$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+(1+\cdots)q^{6}+\cdots$
2775.2.a.l	$2775$	$2$	2775.a	1.a	$1$	$2$	$2$	$22.158$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$0$	$-1$	$-2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(1+\beta )q^{4}+\beta q^{6}-q^{7}+\cdots$
2775.2.a.m	$2775$	$2$	2775.a	1.a	$1$	$2$	$2$	$22.158$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots$
2775.2.a.n	$2775$	$2$	2775.a	1.a	$1$	$2$	$2$	$22.158$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$1$	$-2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots$
2775.2.a.o	$2775$	$2$	2775.a	1.a	$1$	$2$	$2$	$22.158$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$2$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(1+\beta )q^{4}+\beta q^{6}+3q^{7}+\cdots$
2775.2.a.p	$2775$	$2$	2775.a	1.a	$1$	$2$	$2$	$22.158$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+(1+\beta )q^{6}+\cdots$
2775.2.a.q	$2775$	$2$	2775.a	1.a	$1$	$2$	$2$	$22.158$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$3$	$-2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+(-1-\beta )q^{6}+\cdots$
2775.2.a.r	$2775$	$2$	2775.a	1.a	$1$	$3$	$3$	$22.158$	3.3.148.1	$_{}$	None	None	✓	$1$	$0$	$-3$	$3$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
2775.2.a.s	$2775$	$2$	2775.a	1.a	$1$	$3$	$3$	$22.158$	3.3.229.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$-3$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}-q^{3}+(2+\beta _{1})q^{4}+\cdots$
2775.2.a.t	$2775$	$2$	2775.a	1.a	$1$	$3$	$3$	$22.158$	3.3.469.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$3$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
2775.2.a.u	$2775$	$2$	2775.a	1.a	$1$	$3$	$3$	$22.158$	3.3.257.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots$
2775.2.a.v	$2775$	$2$	2775.a	1.a	$1$	$3$	$3$	$22.158$	3.3.257.1	$_{}$	None	None	✓	$1$	$1$	$0$	$3$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots$
2775.2.a.w	$2775$	$2$	2775.a	1.a	$1$	$4$	$4$	$22.158$	4.4.4400.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$-4$	$0$	$8$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}-q^{3}+\beta _{2}q^{4}+(1+\beta _{2}+\cdots)q^{6}+\cdots$

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 61 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.