LMFDB - Newform search results

Refine search

Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

				Sort order	Select

Results (1-50 of 78 matches)

Next Download displayed columns for results to

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5328.2.a.a	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				888.2.a.d	$1$	$1$	$0$	$0$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+2q^{13}-6q^{23}+11q^{25}+\cdots$
5328.2.a.b	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				222.2.a.c	$1$	$1$	$0$	$0$	$-4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+q^{7}-q^{11}-3q^{13}-3q^{17}+\cdots$
5328.2.a.c	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				2664.2.a.b	$1$	$1$	$0$	$0$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}+5q^{11}+3q^{13}-q^{17}+\cdots$
5328.2.a.d	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				1332.2.a.a	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{11}-6q^{13}+6q^{17}+4q^{19}+\cdots$
5328.2.a.e	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				222.2.a.b	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{11}+6q^{13}-6q^{17}-8q^{19}+\cdots$
5328.2.a.f	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				666.2.a.c	$1$	$1$	$0$	$0$	$-2$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+3q^{7}+5q^{11}-3q^{13}-3q^{17}+\cdots$
5328.2.a.g	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				333.2.a.a	$1$	$0$	$0$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+4q^{7}-4q^{11}-2q^{13}-6q^{17}+\cdots$
5328.2.a.h	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				222.2.a.d	$1$	$1$	$0$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{7}+q^{11}+q^{13}+3q^{17}-3q^{19}+\cdots$
5328.2.a.i	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				888.2.a.b	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-6q^{13}+4q^{17}-4q^{19}+6q^{23}+\cdots$
5328.2.a.j	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				444.2.a.a	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{11}-2q^{13}-6q^{19}+8q^{23}+\cdots$
5328.2.a.k	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				37.2.a.b	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+3q^{11}-4q^{13}-6q^{17}-2q^{19}+\cdots$
5328.2.a.l	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				222.2.a.e	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+3q^{11}-q^{13}+3q^{17}+7q^{19}+\cdots$
5328.2.a.m	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				296.2.a.b	$1$	$1$	$0$	$0$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{7}-3q^{11}-2q^{17}+2q^{19}-6q^{23}+\cdots$
5328.2.a.n	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				2664.2.a.b	$1$	$1$	$0$	$0$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}-5q^{11}+3q^{13}+q^{17}+\cdots$
5328.2.a.o	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				296.2.a.a	$1$	$0$	$0$	$0$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}+q^{11}-6q^{13}+4q^{17}+\cdots$
5328.2.a.p	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				888.2.a.c	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{11}-2q^{13}+6q^{17}-4q^{23}+\cdots$
5328.2.a.q	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				1332.2.a.a	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+4q^{11}-6q^{13}-6q^{17}+4q^{19}+\cdots$
5328.2.a.r	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				37.2.a.a	$1$	$1$	$0$	$0$	$2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}-5q^{11}-2q^{13}+2q^{23}+\cdots$
5328.2.a.s	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				666.2.a.c	$1$	$1$	$0$	$0$	$2$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+3q^{7}-5q^{11}-3q^{13}+3q^{17}+\cdots$
5328.2.a.t	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				444.2.a.b	$1$	$1$	$0$	$0$	$2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+4q^{7}-4q^{11}-6q^{13}-6q^{17}+\cdots$
5328.2.a.u	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				333.2.a.a	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+4q^{7}+4q^{11}-2q^{13}+6q^{17}+\cdots$
5328.2.a.v	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				222.2.a.a	$1$	$0$	$0$	$0$	$4$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-3q^{7}+5q^{11}+3q^{13}-3q^{17}+\cdots$
5328.2.a.w	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				888.2.a.a	$1$	$1$	$0$	$0$	$4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+q^{7}-3q^{11}-5q^{13}-7q^{17}+\cdots$
5328.2.a.x	$5328$	$2$	5328.a	1.a	$1$	$1$	$1$	$42.544$	$\Q$	None	✓				148.2.a.a	$1$	$0$	$0$	$0$	$4$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+3q^{7}+5q^{11}+6q^{17}-2q^{19}+\cdots$
5328.2.a.y	$5328$	$2$	5328.a	1.a	$1$	$2$	$2$	$42.544$	$\Q(\sqrt{17}) $	None	✓				666.2.a.h	$1$	$0$	$0$	$0$	$-4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+(-1+\beta )q^{7}+(1-\beta )q^{11}+\cdots$
5328.2.a.z	$5328$	$2$	5328.a	1.a	$1$	$2$	$2$	$42.544$	$\Q(\sqrt{17}) $	None	✓				148.2.a.b	$1$	$1$	$0$	$0$	$-4$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+(-1+\beta )q^{7}+(1-\beta )q^{11}+\cdots$
5328.2.a.ba	$5328$	$2$	5328.a	1.a	$1$	$2$	$2$	$42.544$	$\Q(\sqrt{5}) $	None	✓				888.2.a.f	$1$	$1$	$0$	$0$	$-2$	$-8$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}-4q^{7}+(2+2\beta )q^{11}+\cdots$
5328.2.a.bb	$5328$	$2$	5328.a	1.a	$1$	$2$	$2$	$42.544$	$\Q(\sqrt{3}) $	None	✓				888.2.a.e	$1$	$0$	$0$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{5}+2q^{7}+(-2+2\beta )q^{11}+\cdots$
5328.2.a.bc	$5328$	$2$	5328.a	1.a	$1$	$2$	$2$	$42.544$	$\Q(\sqrt{5}) $	None	✓				74.2.a.b	$1$	$1$	$0$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-3\beta )q^{5}+2\beta q^{7}+(-3+\beta )q^{11}+\cdots$
5328.2.a.bd	$5328$	$2$	5328.a	1.a	$1$	$2$	$2$	$42.544$	$\Q(\sqrt{6}) $	None	✓				444.2.a.d	$1$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}-2q^{7}+(2+2\beta )q^{13}-\beta q^{17}+\cdots$
5328.2.a.be	$5328$	$2$	5328.a	1.a	$1$	$2$	$2$	$42.544$	$\Q(\sqrt{41}) $	None	✓				888.2.a.h	$1$	$1$	$0$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{7}+(1+\beta )q^{11}+(1-\beta )q^{13}+\cdots$
5328.2.a.bf	$5328$	$2$	5328.a	1.a	$1$	$2$	$2$	$42.544$	$\Q(\sqrt{13}) $	None	✓				74.2.a.a	$1$	$0$	$0$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-2+2\beta )q^{7}-\beta q^{11}+(-1+\cdots)q^{13}+\cdots$
5328.2.a.bg	$5328$	$2$	5328.a	1.a	$1$	$2$	$2$	$42.544$	$\Q(\sqrt{3}) $	None	✓				444.2.a.c	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}-2\beta q^{7}-4q^{11}-2\beta q^{13}+\cdots$
5328.2.a.bh	$5328$	$2$	5328.a	1.a	$1$	$2$	$2$	$42.544$	$\Q(\sqrt{17}) $	None	✓				666.2.a.h	$1$	$0$	$0$	$0$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+(-1+\beta )q^{7}+(-1+\beta )q^{11}+\cdots$
5328.2.a.bi	$5328$	$2$	5328.a	1.a	$1$	$2$	$2$	$42.544$	$\Q(\sqrt{2}) $	None	✓				888.2.a.g	$1$	$0$	$0$	$0$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{5}+(2-2\beta )q^{7}-2\beta q^{11}+\cdots$
5328.2.a.bj	$5328$	$2$	5328.a	1.a	$1$	$3$	$3$	$42.544$	3.3.148.1	None	✓		✓		111.2.a.a	$1$	$0$	$0$	$0$	$-4$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{5}+(2-\beta _{1}-\beta _{2})q^{7}+\cdots$
5328.2.a.bk	$5328$	$2$	5328.a	1.a	$1$	$3$	$3$	$42.544$	3.3.148.1	None	✓				2664.2.a.n	$1$	$1$	$0$	$0$	$-2$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{5}+(-2+\beta _{1}+\beta _{2})q^{7}+\cdots$
5328.2.a.bl	$5328$	$2$	5328.a	1.a	$1$	$3$	$3$	$42.544$	3.3.316.1	None	✓				888.2.a.i	$1$	$0$	$0$	$0$	$-2$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}+\beta _{2})q^{5}+(1+2\beta _{1}-\beta _{2})q^{7}+\cdots$
5328.2.a.bm	$5328$	$2$	5328.a	1.a	$1$	$3$	$3$	$42.544$	3.3.568.1	None	✓				888.2.a.j	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+(2-\beta _{2})q^{11}+\cdots$
5328.2.a.bn	$5328$	$2$	5328.a	1.a	$1$	$3$	$3$	$42.544$	3.3.229.1	None	✓				296.2.a.c	$1$	$0$	$0$	$0$	$1$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{5}+(-2-\beta _{1}+\beta _{2})q^{7}-3\beta _{1}q^{11}+\cdots$
5328.2.a.bo	$5328$	$2$	5328.a	1.a	$1$	$3$	$3$	$42.544$	3.3.148.1	None	✓				2664.2.a.n	$1$	$1$	$0$	$0$	$2$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{2})q^{5}+(-2+\beta _{1}+\beta _{2})q^{7}+\cdots$
5328.2.a.bp	$5328$	$2$	5328.a	1.a	$1$	$4$	$4$	$42.544$	4.4.48389.1	None	✓		✓		296.2.a.d	$1$	$1$	$0$	$0$	$-5$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{5}+(\beta _{2}-\beta _{3})q^{7}+(1+\beta _{2}+\cdots)q^{11}+\cdots$
5328.2.a.bq	$5328$	$2$	5328.a	1.a	$1$	$4$	$4$	$42.544$	4.4.27648.1	None	✓		✓		333.2.a.f	$2$	$1$	$0$	$0$	$0$	$-8$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{5}-2q^{7}+2q^{13}+\beta _{2}q^{17}+\cdots$
5328.2.a.br	$5328$	$2$	5328.a	1.a	$1$	$4$	$4$	$42.544$	4.4.7168.1	None	✓		✓		1332.2.a.i	$2$	$0$	$0$	$0$	$0$	$-8$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+(-2-\beta _{3})q^{7}-\beta _{2}q^{11}+\cdots$
5328.2.a.bs	$5328$	$2$	5328.a	1.a	$1$	$4$	$4$	$42.544$	4.4.6224.1	None	✓		✓		111.2.a.b	$1$	$1$	$0$	$0$	$2$	$-4$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{3})q^{5}+(-2+\beta _{2}+\beta _{3})q^{7}+\cdots$
5328.2.a.bt	$5328$	$2$	5328.a	1.a	$1$	$5$	$5$	$42.544$	5.5.935504.1	None	✓				2664.2.a.s	$1$	$0$	$0$	$0$	$-2$	$7$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{5}+(1-\beta _{4})q^{7}+(1+\beta _{2}-\beta _{3}+\cdots)q^{11}+\cdots$
5328.2.a.bu	$5328$	$2$	5328.a	1.a	$1$	$5$	$5$	$42.544$	5.5.935504.1	None	✓				2664.2.a.s	$1$	$0$	$0$	$0$	$2$	$7$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{5}+(1-\beta _{4})q^{7}+(-1-\beta _{2}+\beta _{3}+\cdots)q^{11}+\cdots$
5328.2.e.a	$5328$	$2$	5328.e	12.b	$2$	$2$	$2$	$42.544$	$\Q(\sqrt{-2}) $	None		✓			5328.2.e.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-4q^{11}-\beta q^{17}-2\beta q^{19}+\cdots$
5328.2.e.b	$5328$	$2$	5328.e	12.b	$2$	$2$	$2$	$42.544$	$\Q(\sqrt{-2}) $	None		✓			5328.2.e.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}+4q^{11}-\beta q^{17}+2\beta q^{19}+\cdots$
5328.2.e.c	$5328$	$2$	5328.e	12.b	$2$	$4$	$4$	$42.544$	$\Q(\sqrt{-2}, \sqrt{-5})$	None		✓			5328.2.e.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta _{1}q^{5}+2\beta _{2}q^{11}-6q^{13}-2\beta _{1}q^{17}+\cdots$

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 78 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.