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 113 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
357.2.a.a	$357$	$2$	357.a	1.a	$1$	$1$	$1$	$2.851$	$\Q$	None	✓	✓	✓	✓	357.2.a.a	$1$	$1$	$-2$	$1$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-3q^{5}-2q^{6}+\cdots$
357.2.a.b	$357$	$2$	357.a	1.a	$1$	$1$	$1$	$2.851$	$\Q$	None	✓	✓	✓	✓	357.2.a.b	$1$	$0$	$0$	$-1$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{5}-q^{7}+q^{9}+3q^{11}+\cdots$
357.2.a.c	$357$	$2$	357.a	1.a	$1$	$1$	$1$	$2.851$	$\Q$	None	✓	✓	✓	✓	357.2.a.c	$1$	$1$	$0$	$-1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{5}+q^{7}+q^{9}-5q^{11}+\cdots$
357.2.a.d	$357$	$2$	357.a	1.a	$1$	$1$	$1$	$2.851$	$\Q$	None	✓	✓	✓	✓	357.2.a.d	$1$	$0$	$2$	$1$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-q^{7}+\cdots$
357.2.a.e	$357$	$2$	357.a	1.a	$1$	$2$	$2$	$2.851$	$\Q(\sqrt{3}) $	None	✓	✓	✓	✓	357.2.a.e	$1$	$1$	$-2$	$2$	$-4$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+q^{3}+(2-2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots$
357.2.a.f	$357$	$2$	357.a	1.a	$1$	$2$	$2$	$2.851$	$\Q(\sqrt{2}) $	None	✓	✓	✓	✓	357.2.a.f	$1$	$1$	$0$	$-2$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(-1-\beta )q^{5}-\beta q^{6}+\cdots$
357.2.a.g	$357$	$2$	357.a	1.a	$1$	$3$	$3$	$2.851$	3.3.316.1	None	✓	✓	✓	✓	357.2.a.g	$1$	$0$	$1$	$3$	$2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
357.2.a.h	$357$	$2$	357.a	1.a	$1$	$4$	$4$	$2.851$	4.4.7232.1	None	✓	✓	✓	✓	357.2.a.h	$1$	$0$	$2$	$-4$	$-2$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+\beta _{1}q^{5}+\cdots$
357.2.c.a	$357$	$2$	357.c	357.c	$2$	$20$	$20$	$2.851$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$\Q(\sqrt{-119}) $		✓			357.2.c.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{8}q^{2}+\beta _{18}q^{3}+(-2-\beta _{10})q^{4}+\cdots$
357.2.c.b	$357$	$2$	357.c	357.c	$2$	$24$	$24$	$2.851$		None		✓	✓		357.2.c.b	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
357.2.d.a	$357$	$2$	357.d	21.c	$2$	$22$	$22$	$2.851$		None		✓			357.2.d.a	$2$	$0$	$0$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{2}]$
357.2.d.b	$357$	$2$	357.d	21.c	$2$	$22$	$22$	$2.851$		None		✓			357.2.d.a	$2$	$0$	$0$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{2}]$
357.2.f.a	$357$	$2$	357.f	17.b	$2$	$6$	$6$	$2.851$	6.0.350464.1	None		✓			357.2.f.a	$2$	$0$	$4$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{2})q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
357.2.f.b	$357$	$2$	357.f	17.b	$2$	$10$	$10$	$2.851$	10.0.$\cdots$.1	None		✓	✓		357.2.f.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{2}q^{3}+(2-\beta _{8})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$
357.2.i.a	$357$	$2$	357.i	7.c	$3$	$2$	$1$	$2.851$	$\Q(\sqrt{-3}) $	None		✓			357.2.i.a	$2$	$1$	$-1$	$-1$	$-3$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
357.2.i.b	$357$	$2$	357.i	7.c	$3$	$2$	$1$	$2.851$	$\Q(\sqrt{-3}) $	None		✓			357.2.i.b	$2$	$0$	$0$	$1$	$-4$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-4\zeta_{6}q^{5}+\cdots$
357.2.i.c	$357$	$2$	357.i	7.c	$3$	$2$	$1$	$2.851$	$\Q(\sqrt{-3}) $	None		✓			357.2.i.c	$2$	$0$	$1$	$-1$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
357.2.i.d	$357$	$2$	357.i	7.c	$3$	$8$	$4$	$2.851$	8.0.1767277521.3	None		✓			357.2.i.d	$2$	$0$	$1$	$-4$	$-4$	$7$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{3}+\beta _{7})q^{2}-\beta _{6}q^{3}+(\beta _{4}+\beta _{5}-2\beta _{6}+\cdots)q^{4}+\cdots$
357.2.i.e	$357$	$2$	357.i	7.c	$3$	$8$	$4$	$2.851$	8.0.7007196681.1	None		✓			357.2.i.e	$2$	$0$	$3$	$-4$	$6$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{1}+\beta _{4})q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots$
357.2.i.f	$357$	$2$	357.i	7.c	$3$	$10$	$5$	$2.851$	10.0.$\cdots$.1	None		✓			357.2.i.f	$2$	$0$	$2$	$5$	$-1$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{2}-\beta _{8})q^{2}+\beta _{4}q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots$
357.2.i.g	$357$	$2$	357.i	7.c	$3$	$12$	$6$	$2.851$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓		357.2.i.g	$2$	$0$	$-2$	$6$	$7$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}-\beta _{5}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}-\beta _{6}+\cdots)q^{4}+\cdots$
357.2.k.a	$357$	$2$	357.k	17.c	$4$	$12$	$6$	$2.851$	12.0.$\cdots$.1	None		✓			357.2.k.a	$2$	$0$	$0$	$0$	$8$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{10}q^{2}-\beta _{9}q^{3}+(1-\beta _{2}+\beta _{7}-\beta _{8}+\cdots)q^{4}+\cdots$
357.2.k.b	$357$	$2$	357.k	17.c	$4$	$20$	$10$	$2.851$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓	✓		357.2.k.b	$2$	$0$	$0$	$0$	$8$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{9}q^{3}+(-1-\beta _{7}+\beta _{8}+\cdots)q^{4}+\cdots$
357.2.l.a	$357$	$2$	357.l	357.l	$4$	$4$	$2$	$2.851$	$\Q(i, \sqrt{5})$	None		✓			357.2.l.a	$4$	$0$	$0$	$-2$	$4$	$-6$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{3})q^{3}+\cdots$
357.2.l.b	$357$	$2$	357.l	357.l	$4$	$4$	$2$	$2.851$	$\Q(i, \sqrt{5})$	None		✓			357.2.l.a	$4$	$0$	$0$	$2$	$-4$	$-6$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{1}-\beta _{3})q^{2}+(1-\beta _{3})q^{3}+3q^{4}+\cdots$
357.2.l.c	$357$	$2$	357.l	357.l	$4$	$80$	$40$	$2.851$		None		✓	✓		357.2.l.c	$8$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{4}]$
357.2.p.a	$357$	$2$	357.p	119.j	$6$	$48$	$24$	$2.851$		None		✓	✓	✓	357.2.p.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
357.2.r.a	$357$	$2$	357.r	21.g	$6$	$2$	$1$	$2.851$	$\Q(\sqrt{-3}) $	None		✓			357.2.r.a	$2$	$1$	$-3$	$-3$	$-3$	$4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2+\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}+(1+\cdots)q^{4}+\cdots$
357.2.r.b	$357$	$2$	357.r	21.g	$6$	$2$	$1$	$2.851$	$\Q(\sqrt{-3}) $	None		✓			357.2.r.b	$2$	$0$	$-3$	$3$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
357.2.r.c	$357$	$2$	357.r	21.g	$6$	$2$	$1$	$2.851$	$\Q(\sqrt{-3}) $	None		✓			357.2.r.a	$2$	$0$	$3$	$-3$	$3$	$4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(2-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
357.2.r.d	$357$	$2$	357.r	21.g	$6$	$2$	$1$	$2.851$	$\Q(\sqrt{-3}) $	None		✓			357.2.r.b	$2$	$0$	$3$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(2-\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
357.2.r.e	$357$	$2$	357.r	21.g	$6$	$4$	$2$	$2.851$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		✓			357.2.r.e	$2$	$1$	$-6$	$-2$	$-1$	$-8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2+\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(1+\cdots)q^{4}+\cdots$
357.2.r.f	$357$	$2$	357.r	21.g	$6$	$4$	$2$	$2.851$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		✓			357.2.r.e	$2$	$0$	$6$	$-1$	$1$	$-8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\beta _{2})q^{2}-\beta _{1}q^{3}+\beta _{2}q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
357.2.r.g	$357$	$2$	357.r	21.g	$6$	$34$	$17$	$2.851$		None		✓			357.2.r.g	$2$	$0$	$-6$	$4$	$2$	$-5$			$\mathrm{SU}(2)[C_{6}]$
357.2.r.h	$357$	$2$	357.r	21.g	$6$	$34$	$17$	$2.851$		None		✓			357.2.r.g	$2$	$0$	$6$	$2$	$-2$	$-5$			$\mathrm{SU}(2)[C_{6}]$
357.2.s.a	$357$	$2$	357.s	357.s	$6$	$88$	$44$	$2.851$		None		✓	✓	✓	357.2.s.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
357.2.u.a	$357$	$2$	357.u	17.d	$8$	$32$	$8$	$2.851$		None		✓			357.2.u.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
357.2.u.b	$357$	$2$	357.u	17.d	$8$	$48$	$12$	$2.851$		None		✓	✓		357.2.u.b	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
357.2.w.a	$357$	$2$	357.w	357.w	$8$	$176$	$44$	$2.851$		None		✓	✓	✓	357.2.w.a	$8$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{8}]$
357.2.y.a	$357$	$2$	357.y	357.y	$12$	$176$	$44$	$2.851$		None		✓	✓	✓	357.2.y.a	$8$	$0$	$0$	$-6$	$0$	$-8$			$\mathrm{SU}(2)[C_{12}]$
357.2.bb.a	$357$	$2$	357.bb	119.n	$12$	$96$	$24$	$2.851$		None		✓	✓	✓	357.2.bb.a	$4$	$0$	$0$	$0$	$4$	$4$			$\mathrm{SU}(2)[C_{12}]$
357.2.bc.a	$357$	$2$	357.bc	119.p	$16$	$192$	$24$	$2.851$		None		✓	✓	✓	357.2.bc.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
357.2.bf.a	$357$	$2$	357.bf	51.i	$16$	$288$	$36$	$2.851$		None		✓	✓	✓	357.2.bf.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
357.2.bh.a	$357$	$2$	357.bh	119.q	$24$	$192$	$24$	$2.851$		None		✓	✓	✓	357.2.bh.a	$4$	$0$	$0$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{24}]$
357.2.bj.a	$357$	$2$	357.bj	357.aj	$24$	$352$	$44$	$2.851$		None		✓	✓	✓	357.2.bj.a	$8$	$0$	$0$	$-12$	$0$	$-16$			$\mathrm{SU}(2)[C_{24}]$
357.2.bl.a	$357$	$2$	357.bl	119.s	$48$	$384$	$24$	$2.851$		None		✓	✓	✓	357.2.bl.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{48}]$
357.2.bm.a	$357$	$2$	357.bm	357.am	$48$	$704$	$44$	$2.851$		None		✓	✓	✓	357.2.bm.a	$8$	$0$	$0$	$-8$	$0$	$-32$			$\mathrm{SU}(2)[C_{48}]$
357.3.b.a	$357$	$3$	357.b	3.b	$2$	$64$	$64$	$9.728$		None		✓	✓	✓	357.3.b.a	$2$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
357.3.e.a	$357$	$3$	357.e	51.c	$2$	$72$	$72$	$9.728$		None		✓	✓	✓	357.3.e.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
357.3.g.a	$357$	$3$	357.g	7.b	$2$	$44$	$44$	$9.728$		None		✓	✓	✓	357.3.g.a	$2$	$0$	$-4$	$0$	$0$	$-16$			$\mathrm{SU}(2)[C_{2}]$

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 113 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.