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 89 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
2816.1.b.a	$2816$	$1$	2816.b	88.b	$2$	$2$	$2$	$1.405$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{3}-iq^{5}-iq^{11}-q^{15}-q^{23}+\cdots$
2816.1.b.b	$2816$	$1$	2816.b	88.b	$2$	$2$	$2$	$1.405$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+iq^{3}-iq^{5}+iq^{11}+q^{15}+q^{23}+\cdots$
2816.1.h.a	$2816$	$1$	2816.h	11.b	$2$	$1$	$1$	$1.405$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-11}) $	$\Q(\sqrt{22}) $	✓	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-2q^{3}+3q^{9}+q^{11}-q^{25}-4q^{27}+\cdots$
2816.1.h.b	$2816$	$1$	2816.h	11.b	$2$	$1$	$1$	$1.405$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-11}) $	$\Q(\sqrt{22}) $	✓	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+2q^{3}+3q^{9}-q^{11}-q^{25}+4q^{27}+\cdots$
2816.1.h.c	$2816$	$1$	2816.h	11.b	$2$	$2$	$2$	$1.405$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None	✓	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-q^{3}-\beta q^{5}-q^{11}+\beta q^{15}-\beta q^{23}+\cdots$
2816.1.h.d	$2816$	$1$	2816.h	11.b	$2$	$2$	$2$	$1.405$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-22}) $	$\Q(\sqrt{11}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{9}-iq^{11}-iq^{19}-q^{25}-iq^{43}+\cdots$
2816.1.h.e	$2816$	$1$	2816.h	11.b	$2$	$2$	$2$	$1.405$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None	✓	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+q^{3}-\beta q^{5}+q^{11}-\beta q^{15}+\beta q^{23}+\cdots$
2816.1.l.a	$2816$	$1$	2816.l	176.l	$4$	$4$	$2$	$1.405$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+(-1+\zeta_{8}^{2})q^{5}-\zeta_{8}^{2}q^{9}-\zeta_{8}^{3}q^{11}+\cdots$
2816.1.l.b	$2816$	$1$	2816.l	176.l	$4$	$4$	$2$	$1.405$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$0$	$4$	$0$		$1$		$q+(1-\zeta_{8}^{2})q^{5}-\zeta_{8}^{2}q^{9}-\zeta_{8}^{3}q^{11}+\cdots$
2816.1.l.c	$2816$	$1$	2816.l	176.l	$4$	$8$	$4$	$1.405$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$0$	$-4$	$0$		$2^{2}$		$q+(-\zeta_{24}^{7}-\zeta_{24}^{11})q^{3}+(\zeta_{24}^{8}-\zeta_{24}^{10}+\cdots)q^{5}+\cdots$
2816.1.l.d	$2816$	$1$	2816.l	176.l	$4$	$8$	$4$	$1.405$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$0$	$4$	$0$		$2^{2}$		$q+(\zeta_{24}^{7}+\zeta_{24}^{11})q^{3}+(-\zeta_{24}^{8}+\zeta_{24}^{10}+\cdots)q^{5}+\cdots$
2816.1.r.a	$2816$	$1$	2816.r	11.d	$10$	$4$	$1$	$1.405$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(-\zeta_{10}+\zeta_{10}^{2})q^{3}+(\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{9}+\cdots$
2816.1.r.b	$2816$	$1$	2816.r	11.d	$10$	$4$	$1$	$1.405$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(\zeta_{10}-\zeta_{10}^{2})q^{3}+(\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{9}+\cdots$
2816.1.r.c	$2816$	$1$	2816.r	11.d	$10$	$8$	$2$	$1.405$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{20}^{7}+\zeta_{20}^{9})q^{3}+(-\zeta_{20}^{4}-\zeta_{20}^{6}+\cdots)q^{9}+\cdots$
2816.1.v.a	$2816$	$1$	2816.v	44.h	$10$	$4$	$1$	$1.405$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{10}+\zeta_{10}^{3})q^{3}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{9}+\cdots$
2816.1.v.b	$2816$	$1$	2816.v	44.h	$10$	$4$	$1$	$1.405$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{10}-\zeta_{10}^{3})q^{3}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{9}+\cdots$
2816.1.v.c	$2816$	$1$	2816.v	44.h	$10$	$8$	$2$	$1.405$	$\Q(\zeta_{20})$	$D_{5}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{20}-\zeta_{20}^{7})q^{3}+(\zeta_{20}^{2}-\zeta_{20}^{4}+\cdots)q^{9}+\cdots$
2816.2.a.a	$2816$	$2$	2816.a	1.a	$1$	$2$	$2$	$22.486$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$-2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta q^{5}+2\beta q^{7}-2q^{9}-q^{11}+\cdots$
2816.2.a.b	$2816$	$2$	2816.a	1.a	$1$	$2$	$2$	$22.486$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}-2q^{9}+q^{11}-2\beta q^{13}+\cdots$
2816.2.a.c	$2816$	$2$	2816.a	1.a	$1$	$2$	$2$	$22.486$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-4$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-2+\beta )q^{5}+(-3+\beta )q^{7}+\cdots$
2816.2.a.d	$2816$	$2$	2816.a	1.a	$1$	$2$	$2$	$22.486$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-4$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-2-\beta )q^{5}+(3+\beta )q^{7}-q^{11}+\cdots$
2816.2.a.e	$2816$	$2$	2816.a	1.a	$1$	$2$	$2$	$22.486$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$4$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(2+\beta )q^{5}+(-3-\beta )q^{7}-q^{11}+\cdots$
2816.2.a.f	$2816$	$2$	2816.a	1.a	$1$	$2$	$2$	$22.486$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$4$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(2-\beta )q^{5}+(3-\beta )q^{7}+q^{11}+\cdots$
2816.2.a.g	$2816$	$2$	2816.a	1.a	$1$	$2$	$2$	$22.486$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}-2q^{9}-q^{11}-2\beta q^{13}+\cdots$
2816.2.a.h	$2816$	$2$	2816.a	1.a	$1$	$2$	$2$	$22.486$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta q^{5}-2\beta q^{7}-2q^{9}+q^{11}+\cdots$
2816.2.a.i	$2816$	$2$	2816.a	1.a	$1$	$3$	$3$	$22.486$	3.3.940.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{1}q^{5}+(-1-\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots$
2816.2.a.j	$2816$	$2$	2816.a	1.a	$1$	$3$	$3$	$22.486$	3.3.940.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{1}q^{5}+(-1-\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots$
2816.2.a.k	$2816$	$2$	2816.a	1.a	$1$	$3$	$3$	$22.486$	3.3.940.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{1}q^{5}+(1+\beta _{2})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots$
2816.2.a.l	$2816$	$2$	2816.a	1.a	$1$	$3$	$3$	$22.486$	3.3.940.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{1}q^{5}+(1+\beta _{2})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots$
2816.2.a.m	$2816$	$2$	2816.a	1.a	$1$	$4$	$4$	$22.486$	4.4.4352.1	$_{}$	None	None	✓	$2$	$1$	$0$	$-4$	$0$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}-\beta _{2}q^{5}+(\beta _{2}+\beta _{3})q^{7}+\cdots$
2816.2.a.n	$2816$	$2$	2816.a	1.a	$1$	$4$	$4$	$22.486$	4.4.4352.1	$_{}$	None	None	✓	$2$	$0$	$0$	$4$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+\beta _{2}q^{5}+(\beta _{2}+\beta _{3})q^{7}+\cdots$
2816.2.a.o	$2816$	$2$	2816.a	1.a	$1$	$5$	$5$	$22.486$	5.5.380224.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-4$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+(-1-\beta _{2})q^{5}+(-\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots$
2816.2.a.p	$2816$	$2$	2816.a	1.a	$1$	$5$	$5$	$22.486$	5.5.380224.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-4$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+(-1-\beta _{2})q^{5}+(\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$
2816.2.a.q	$2816$	$2$	2816.a	1.a	$1$	$5$	$5$	$22.486$	5.5.380224.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$4$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+(1+\beta _{2})q^{5}+(\beta _{1}+\beta _{3})q^{7}+\cdots$
2816.2.a.r	$2816$	$2$	2816.a	1.a	$1$	$5$	$5$	$22.486$	5.5.380224.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$4$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+(1+\beta _{2})q^{5}+(-\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots$
2816.2.a.s	$2816$	$2$	2816.a	1.a	$1$	$6$	$6$	$22.486$	6.6.33032192.1	$_{}$	None	None	✓	$2$	$1$	$0$	$-4$	$0$	$0$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1-\beta _{4})q^{3}-\beta _{3}q^{5}-\beta _{2}q^{7}+(2+\cdots)q^{9}+\cdots$
2816.2.a.t	$2816$	$2$	2816.a	1.a	$1$	$6$	$6$	$22.486$	6.6.74043072.1	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{5}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}+(3-\beta _{3}+\cdots)q^{9}+\cdots$
2816.2.a.u	$2816$	$2$	2816.a	1.a	$1$	$6$	$6$	$22.486$	6.6.74043072.1	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{5}q^{3}-\beta _{2}q^{5}+\beta _{1}q^{7}+(3-\beta _{3}+\cdots)q^{9}+\cdots$
2816.2.a.v	$2816$	$2$	2816.a	1.a	$1$	$6$	$6$	$22.486$	6.6.33032192.1	$_{}$	None	None	✓	$2$	$0$	$0$	$4$	$0$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1+\beta _{4})q^{3}+\beta _{3}q^{5}-\beta _{2}q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots$
2816.2.c.a	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-iq^{5}-4q^{7}+2q^{9}-iq^{11}+\cdots$
2816.2.c.b	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-3iq^{5}-4q^{7}+2q^{9}-iq^{11}+\cdots$
2816.2.c.c	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-2iq^{5}-4q^{7}+3q^{9}+iq^{11}+6q^{17}+\cdots$
2816.2.c.d	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$1$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{3}+3iq^{5}-2q^{7}-6q^{9}-iq^{11}+\cdots$
2816.2.c.e	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+3iq^{5}-2q^{7}+2q^{9}+iq^{11}+\cdots$
2816.2.c.f	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-iq^{5}-2q^{7}+2q^{9}+iq^{11}+\cdots$
2816.2.c.g	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{3}+iq^{5}-6q^{9}+iq^{11}+6iq^{13}+\cdots$
2816.2.c.h	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{3}-iq^{5}-6q^{9}+iq^{11}-6iq^{13}+\cdots$
2816.2.c.i	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$1$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{3}-3iq^{5}+2q^{7}-6q^{9}-iq^{11}+\cdots$
2816.2.c.j	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+iq^{5}+2q^{7}+2q^{9}+iq^{11}+\cdots$
2816.2.c.k	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-3iq^{5}+2q^{7}+2q^{9}+iq^{11}+\cdots$

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 89 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.