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 56 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
2695.1.g.a	$2695$	$1$	2695.g	55.d	$2$	$1$	$1$	$1.345$	$\Q$	$D_{3}$	$\Q(\sqrt{-55}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$		$1$		$q-q^{2}-q^{5}+q^{8}+q^{9}+q^{10}+q^{11}+\cdots$
2695.1.g.b	$2695$	$1$	2695.g	55.d	$2$	$1$	$1$	$1.345$	$\Q$	$D_{3}$	$\Q(\sqrt{-55}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$0$		$1$		$q-q^{2}+q^{5}+q^{8}+q^{9}-q^{10}+q^{11}+\cdots$
2695.1.g.c	$2695$	$1$	2695.g	55.d	$2$	$1$	$1$	$1.345$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q-q^{4}+q^{5}+q^{9}-q^{11}+q^{16}-q^{20}+\cdots$
2695.1.g.d	$2695$	$1$	2695.g	55.d	$2$	$1$	$1$	$1.345$	$\Q$	$D_{3}$	$\Q(\sqrt{-55}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$0$		$1$		$q+q^{2}-q^{5}-q^{8}+q^{9}-q^{10}+q^{11}+\cdots$
2695.1.g.e	$2695$	$1$	2695.g	55.d	$2$	$1$	$1$	$1.345$	$\Q$	$D_{3}$	$\Q(\sqrt{-55}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$0$		$1$		$q+q^{2}+q^{5}-q^{8}+q^{9}+q^{10}+q^{11}+\cdots$
2695.1.g.f	$2695$	$1$	2695.g	55.d	$2$	$2$	$2$	$1.345$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{385}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{3}-q^{4}-iq^{5}-3q^{9}-q^{11}+\cdots$
2695.1.g.g	$2695$	$1$	2695.g	55.d	$2$	$2$	$2$	$1.345$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-55}) $	None	✓	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\beta q^{2}+2q^{4}-q^{5}-\beta q^{8}+q^{9}+\beta q^{10}+\cdots$
2695.1.g.h	$2695$	$1$	2695.g	55.d	$2$	$2$	$2$	$1.345$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-55}) $	None	✓	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\beta q^{2}+2q^{4}+q^{5}-\beta q^{8}+q^{9}-\beta q^{10}+\cdots$
2695.1.g.i	$2695$	$1$	2695.g	55.d	$2$	$4$	$4$	$1.345$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{8}+\zeta_{8}^{3})q^{3}-q^{4}-\zeta_{8}q^{5}-q^{9}+\cdots$
2695.1.l.a	$2695$	$1$	2695.l	385.l	$4$	$8$	$4$	$1.345$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{16}+\zeta_{16}^{3})q^{3}-\zeta_{16}^{4}q^{4}+\zeta_{16}^{5}q^{5}+\cdots$
2695.1.l.b	$2695$	$1$	2695.l	385.l	$4$	$8$	$4$	$1.345$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{16}^{5}-\zeta_{16}^{7})q^{3}-\zeta_{16}^{4}q^{4}+\cdots$
2695.1.q.a	$2695$	$1$	2695.q	385.q	$6$	$2$	$1$	$1.345$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}q^{5}-q^{8}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{10}+\cdots$
2695.1.q.b	$2695$	$1$	2695.q	385.q	$6$	$2$	$1$	$1.345$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $		$8$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\cdots$
2695.1.q.c	$2695$	$1$	2695.q	385.q	$6$	$2$	$1$	$1.345$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $		$8$	$0$	$0$	$0$	$1$	$0$		$1$		$q-\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\cdots$
2695.1.q.d	$2695$	$1$	2695.q	385.q	$6$	$2$	$1$	$1.345$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$1$	$0$	$1$	$0$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}q^{5}+q^{8}-\zeta_{6}q^{9}+\zeta_{6}^{2}q^{10}+\cdots$
2695.1.q.e	$2695$	$1$	2695.q	385.q	$6$	$4$	$2$	$1.345$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$-2$	$0$		$3$		$q+(\zeta_{12}^{3}+\zeta_{12}^{5})q^{2}+(-1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$
2695.1.q.f	$2695$	$1$	2695.q	385.q	$6$	$4$	$2$	$1.345$	$\Q(\zeta_{12})$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{385}) $		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}q^{5}-3\zeta_{12}^{4}q^{9}+\cdots$
2695.1.q.g	$2695$	$1$	2695.q	385.q	$6$	$8$	$4$	$1.345$	$\Q(\zeta_{24})$	$D_{4}$	$\Q(\sqrt{-11}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{24}+\zeta_{24}^{7})q^{3}+\zeta_{24}^{4}q^{4}-\zeta_{24}^{5}q^{5}+\cdots$
2695.1.x.a	$2695$	$1$	2695.x	55.h	$10$	$8$	$2$	$1.345$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{20}-\zeta_{20}^{5})q^{3}+\zeta_{20}^{2}q^{4}-\zeta_{20}^{9}q^{5}+\cdots$
2695.1.bg.a	$2695$	$1$	2695.bg	385.af	$12$	$16$	$4$	$1.345$	$\Q(\zeta_{48})$	$D_{8}$	$\Q(\sqrt{-11}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{48}-\zeta_{48}^{19})q^{3}+\zeta_{48}^{4}q^{4}+\cdots$
2695.1.bg.b	$2695$	$1$	2695.bg	385.af	$12$	$16$	$4$	$1.345$	$\Q(\zeta_{48})$	$D_{8}$	$\Q(\sqrt{-11}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{48}+\zeta_{48}^{19})q^{3}-\zeta_{48}^{4}q^{4}+\cdots$
2695.1.bi.a	$2695$	$1$	2695.bi	2695.ai	$14$	$6$	$1$	$1.345$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$-2$	$0$	$-1$	$-1$		$1$		$q+(-\zeta_{14}^{3}+\zeta_{14}^{6})q^{2}+(\zeta_{14}^{2}-\zeta_{14}^{5}+\cdots)q^{4}+\cdots$
2695.1.bi.b	$2695$	$1$	2695.bi	2695.ai	$14$	$6$	$1$	$1.345$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$2$	$0$	$-1$	$1$		$1$		$q+(\zeta_{14}^{3}-\zeta_{14}^{6})q^{2}+(\zeta_{14}^{2}-\zeta_{14}^{5}+\cdots)q^{4}+\cdots$
2695.1.bi.c	$2695$	$1$	2695.bi	2695.ai	$14$	$12$	$2$	$1.345$	$\Q(\zeta_{28})$	$D_{14}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$2$	$0$		$1$		$q+(\zeta_{28}^{5}-\zeta_{28}^{13})q^{2}+(\zeta_{28}^{4}+\zeta_{28}^{10}+\cdots)q^{4}+\cdots$
2695.1.ca.a	$2695$	$1$	2695.ca	385.an	$30$	$8$	$1$	$1.345$	$\Q(\zeta_{15})$	$D_{5}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$-3$	$1$	$0$		$1$		$q+(\zeta_{30}^{2}-\zeta_{30}^{5})q^{3}+\zeta_{30}^{14}q^{4}-\zeta_{30}^{13}q^{5}+\cdots$
2695.1.ca.b	$2695$	$1$	2695.ca	385.an	$30$	$8$	$1$	$1.345$	$\Q(\zeta_{15})$	$D_{5}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$3$	$-1$	$0$		$1$		$q+(-\zeta_{30}^{2}+\zeta_{30}^{5})q^{3}+\zeta_{30}^{14}q^{4}+\cdots$
2695.1.cc.a	$2695$	$1$	2695.cc	385.ap	$30$	$16$	$2$	$1.345$	$\Q(\zeta_{60})$	$D_{10}$	$\Q(\sqrt{-35}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{60}^{5}-\zeta_{60}^{23})q^{3}+\zeta_{60}^{26}q^{4}+\cdots$
2695.1.ck.a	$2695$	$1$	2695.ck	2695.bk	$42$	$12$	$1$	$1.345$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$-1$	$0$	$1$	$-2$		$1$		$q+(\zeta_{42}^{4}-\zeta_{42}^{9})q^{2}+(\zeta_{42}^{8}-\zeta_{42}^{13}+\cdots)q^{4}+\cdots$
2695.1.ck.b	$2695$	$1$	2695.ck	2695.bk	$42$	$12$	$1$	$1.345$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$1$	$0$	$1$	$2$		$1$		$q+(-\zeta_{42}^{4}+\zeta_{42}^{9})q^{2}+(\zeta_{42}^{8}-\zeta_{42}^{13}+\cdots)q^{4}+\cdots$
2695.1.ck.c	$2695$	$1$	2695.ck	2695.bk	$42$	$24$	$2$	$1.345$	$\Q(\zeta_{84})$	$D_{42}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+(\zeta_{84}^{15}-\zeta_{84}^{23})q^{2}+(-\zeta_{84}^{4}+\zeta_{84}^{30}+\cdots)q^{4}+\cdots$
2695.2.a.a	$2695$	$2$	2695.a	1.a	$1$	$1$	$1$	$21.520$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}+3q^{8}-3q^{9}+q^{10}+\cdots$
2695.2.a.b	$2695$	$2$	2695.a	1.a	$1$	$1$	$1$	$21.520$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$2$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}-q^{4}-q^{5}-2q^{6}+3q^{8}+\cdots$
2695.2.a.c	$2695$	$2$	2695.a	1.a	$1$	$1$	$1$	$21.520$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}-3q^{8}-3q^{9}-q^{10}+\cdots$
2695.2.a.d	$2695$	$2$	2695.a	1.a	$1$	$2$	$2$	$21.520$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1-\beta )q^{3}+q^{4}+q^{5}+(-3+\cdots)q^{6}+\cdots$
2695.2.a.e	$2695$	$2$	2695.a	1.a	$1$	$2$	$2$	$21.520$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-\beta q^{3}+(1+2\beta )q^{4}+q^{5}+\cdots$
2695.2.a.f	$2695$	$2$	2695.a	1.a	$1$	$2$	$2$	$21.520$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+2\beta q^{3}+(1+2\beta )q^{4}+q^{5}+\cdots$
2695.2.a.g	$2695$	$2$	2695.a	1.a	$1$	$3$	$3$	$21.520$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$2$	$3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(1-\beta _{1})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots$
2695.2.a.h	$2695$	$2$	2695.a	1.a	$1$	$3$	$3$	$21.520$	3.3.148.1	$_{}$	None	None	✓	$1$	$0$	$-3$	$4$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(1+\beta _{1})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots$
2695.2.a.i	$2695$	$2$	2695.a	1.a	$1$	$3$	$3$	$21.520$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots$
2695.2.a.j	$2695$	$2$	2695.a	1.a	$1$	$4$	$4$	$21.520$	4.4.1957.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$-3$	$4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1}-\beta _{2})q^{2}+(-1-\beta _{2})q^{3}+\cdots$
2695.2.a.k	$2695$	$2$	2695.a	1.a	$1$	$4$	$4$	$21.520$	4.4.1957.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$3$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1}-\beta _{2})q^{2}+(1+\beta _{2})q^{3}+\cdots$
2695.2.a.l	$2695$	$2$	2695.a	1.a	$1$	$4$	$4$	$21.520$	4.4.11348.1	$_{}$	None	None	✓	$1$	$0$	$2$	$-2$	$-4$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+(-1-\beta _{3})q^{3}+(2+\beta _{2}+\cdots)q^{4}+\cdots$
2695.2.a.m	$2695$	$2$	2695.a	1.a	$1$	$5$	$5$	$21.520$	5.5.303952.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$-5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+\cdots$
2695.2.a.n	$2695$	$2$	2695.a	1.a	$1$	$5$	$5$	$21.520$	5.5.303952.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$5$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+\cdots$
2695.2.a.o	$2695$	$2$	2695.a	1.a	$1$	$5$	$5$	$21.520$	5.5.394064.1	$_{}$	None	None	✓	$1$	$1$	$1$	$-4$	$-5$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
2695.2.a.p	$2695$	$2$	2695.a	1.a	$1$	$5$	$5$	$21.520$	5.5.394064.1	$_{}$	None	None	✓	$1$	$0$	$1$	$4$	$5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
2695.2.a.q	$2695$	$2$	2695.a	1.a	$1$	$6$	$6$	$21.520$	6.6.15751800.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$-1$	$6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-\beta _{1}q^{3}+(\beta _{2}+\beta _{5})q^{4}+q^{5}+\cdots$
2695.2.a.r	$2695$	$2$	2695.a	1.a	$1$	$6$	$6$	$21.520$	6.6.15751800.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$1$	$-6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}+(\beta _{2}+\beta _{5})q^{4}-q^{5}+\cdots$
2695.2.a.s	$2695$	$2$	2695.a	1.a	$1$	$8$	$8$	$21.520$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$-1$	$-8$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
2695.2.a.t	$2695$	$2$	2695.a	1.a	$1$	$8$	$8$	$21.520$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$1$	$8$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$

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 56 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.