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 348 matches)

Next Download displayed columns for results to

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
150.2.a.a	$150$	$2$	150.a	1.a	$1$	$1$	$1$	$1.198$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots$
150.2.a.b	$150$	$2$	150.a	1.a	$1$	$1$	$1$	$1.198$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+4q^{7}+q^{8}+\cdots$
150.2.a.c	$150$	$2$	150.a	1.a	$1$	$1$	$1$	$1.198$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots$
150.2.c.a	$150$	$2$	150.c	5.b	$2$	$2$	$2$	$1.198$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots$
150.2.e.a	$150$	$2$	150.e	15.e	$4$	$4$	$2$	$1.198$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$4$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+(1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
150.2.e.b	$150$	$2$	150.e	15.e	$4$	$8$	$4$	$1.198$	$\Q(\zeta_{24})$	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\zeta_{24}+\zeta_{24}^{5})q^{2}+(-2\zeta_{24}^{3}+\zeta_{24}^{7})q^{3}+\cdots$
150.2.g.a	$150$	$2$	150.g	25.d	$5$	$4$	$1$	$1.198$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$1$	$5$	$6$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
150.2.g.b	$150$	$2$	150.g	25.d	$5$	$4$	$1$	$1.198$	$\Q(\zeta_{10})$	None		$2$	$0$	$1$	$1$	$5$	$8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{3}+\cdots$
150.2.g.c	$150$	$2$	150.g	25.d	$5$	$8$	$2$	$1.198$	8.0.1064390625.3	None		$2$	$0$	$2$	$-2$	$-4$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{2}q^{2}+\beta _{5}q^{3}+\beta _{5}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
150.2.h.a	$150$	$2$	150.h	25.e	$10$	$8$	$2$	$1.198$	$\Q(\zeta_{20})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\zeta_{20}q^{2}-\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+(\zeta_{20}+\cdots)q^{5}+\cdots$
150.2.h.b	$150$	$2$	150.h	25.e	$10$	$16$	$4$	$1.198$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$0$	$4$	$0$		$5$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{8}q^{2}+\beta _{6}q^{3}-\beta _{10}q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots$
150.2.l.a	$150$	$2$	150.l	75.l	$20$	$80$	$10$	$1.198$		None		$4$	$0$	$0$	$4$	$0$	$4$			$\mathrm{SU}(2)[C_{20}]$
150.3.b.a	$150$	$3$	150.b	15.d	$2$	$4$	$4$	$4.087$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{8}^{3}q^{2}+(-\zeta_{8}-2\zeta_{8}^{3})q^{3}+2q^{4}+\cdots$
150.3.b.b	$150$	$3$	150.b	15.d	$2$	$8$	$8$	$4.087$	8.0.40960000.1	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-\beta _{3}q^{3}+2q^{4}+(-1-\beta _{4}+\cdots)q^{6}+\cdots$
150.3.d.a	$150$	$3$	150.d	3.b	$2$	$2$	$2$	$4.087$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$-2$	$0$	$-14$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+(-1-2\beta )q^{3}-2q^{4}+(4-\beta )q^{6}+\cdots$
150.3.d.b	$150$	$3$	150.d	3.b	$2$	$2$	$2$	$4.087$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$2$	$0$	$14$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+(1-2\beta )q^{3}-2q^{4}+(4+\beta )q^{6}+\cdots$
150.3.d.c	$150$	$3$	150.d	3.b	$2$	$4$	$4$	$4.087$	$\Q(\sqrt{-2}, \sqrt{-5})$	None		$2$	$0$	$0$	$-4$	$0$	$-8$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}-2q^{4}+\cdots$
150.3.d.d	$150$	$3$	150.d	3.b	$2$	$4$	$4$	$4.087$	$\Q(\sqrt{-2}, \sqrt{-17})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-\beta _{1}q^{3}-2q^{4}+(-1+\beta _{3})q^{6}+\cdots$
150.3.f.a	$150$	$3$	150.f	5.c	$4$	$4$	$2$	$4.087$	$\Q(i, \sqrt{6})$	None		$2$	$0$	$-4$	$0$	$0$	$-24$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+\cdots$
150.3.f.b	$150$	$3$	150.f	5.c	$4$	$4$	$2$	$4.087$	$\Q(i, \sqrt{6})$	None		$2$	$0$	$-4$	$0$	$0$	$16$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+\cdots$
150.3.f.c	$150$	$3$	150.f	5.c	$4$	$4$	$2$	$4.087$	$\Q(i, \sqrt{6})$	None		$2$	$0$	$4$	$0$	$0$	$24$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots$
150.3.i.a	$150$	$3$	150.i	75.h	$10$	$80$	$20$	$4.087$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
150.3.j.a	$150$	$3$	150.j	75.j	$10$	$80$	$20$	$4.087$		None		$4$	$0$	$0$	$-4$	$0$	$-8$			$\mathrm{SU}(2)[C_{10}]$
150.3.k.a	$150$	$3$	150.k	25.f	$20$	$32$	$4$	$4.087$		None		$2$	$0$	$8$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{20}]$
150.3.k.b	$150$	$3$	150.k	25.f	$20$	$48$	$6$	$4.087$		None		$2$	$0$	$-12$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{20}]$
150.4.a.a	$150$	$4$	150.a	1.a	$1$	$1$	$1$	$8.850$	$\Q$	None	✓	$1$	$1$	$-2$	$-3$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+6q^{6}-q^{7}+\cdots$
150.4.a.b	$150$	$4$	150.a	1.a	$1$	$1$	$1$	$8.850$	$\Q$	None	✓	$1$	$0$	$-2$	$-3$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+4q^{7}+\cdots$
150.4.a.c	$150$	$4$	150.a	1.a	$1$	$1$	$1$	$8.850$	$\Q$	None	✓	$1$	$1$	$-2$	$3$	$0$	$-23$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}-6q^{6}-23q^{7}+\cdots$
150.4.a.d	$150$	$4$	150.a	1.a	$1$	$1$	$1$	$8.850$	$\Q$	None	✓	$1$	$0$	$-2$	$3$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+2q^{7}+\cdots$
150.4.a.e	$150$	$4$	150.a	1.a	$1$	$1$	$1$	$8.850$	$\Q$	None	✓	$1$	$1$	$2$	$-3$	$0$	$-32$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}-6q^{6}-2^{5}q^{7}+\cdots$
150.4.a.f	$150$	$4$	150.a	1.a	$1$	$1$	$1$	$8.850$	$\Q$	None	✓	$1$	$0$	$2$	$-3$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}-6q^{6}-2q^{7}+\cdots$
150.4.a.g	$150$	$4$	150.a	1.a	$1$	$1$	$1$	$8.850$	$\Q$	None	✓	$1$	$0$	$2$	$-3$	$0$	$23$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+23q^{7}+\cdots$
150.4.a.h	$150$	$4$	150.a	1.a	$1$	$1$	$1$	$8.850$	$\Q$	None	✓	$1$	$0$	$2$	$3$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+q^{7}+\cdots$
150.4.a.i	$150$	$4$	150.a	1.a	$1$	$1$	$1$	$8.850$	$\Q$	None	✓	$1$	$0$	$2$	$3$	$0$	$16$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+2^{4}q^{7}+\cdots$
150.4.c.a	$150$	$4$	150.c	5.b	$2$	$2$	$2$	$8.850$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}+3iq^{3}-4q^{4}-6q^{6}-2^{5}iq^{7}+\cdots$
150.4.c.b	$150$	$4$	150.c	5.b	$2$	$2$	$2$	$8.850$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}+3iq^{3}-4q^{4}-6q^{6}+23iq^{7}+\cdots$
150.4.c.c	$150$	$4$	150.c	5.b	$2$	$2$	$2$	$8.850$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}-3iq^{3}-4q^{4}+6q^{6}-4iq^{7}+\cdots$
150.4.c.d	$150$	$4$	150.c	5.b	$2$	$2$	$2$	$8.850$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}-3iq^{3}-4q^{4}+6q^{6}+2^{4}iq^{7}+\cdots$
150.4.c.e	$150$	$4$	150.c	5.b	$2$	$2$	$2$	$8.850$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}-3iq^{3}-4q^{4}+6q^{6}+iq^{7}+\cdots$
150.4.e.a	$150$	$4$	150.e	15.e	$4$	$4$	$2$	$8.850$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$-12$	$0$	$72$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+2\zeta_{8}q^{2}+(-3-3\zeta_{8}^{2}+3\zeta_{8}^{3})q^{3}+\cdots$
150.4.e.b	$150$	$4$	150.e	15.e	$4$	$4$	$2$	$8.850$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$12$	$0$	$-72$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+2\zeta_{8}q^{2}+(3+3\zeta_{8}^{2}+3\zeta_{8}^{3})q^{3}+\cdots$
150.4.e.c	$150$	$4$	150.e	15.e	$4$	$12$	$6$	$8.850$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$4$	$0$	$0$	$-8$	$0$	$-12$		$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{2}+(-1-\beta _{4}+\beta _{9})q^{3}+4\beta _{4}q^{4}+\cdots$
150.4.e.d	$150$	$4$	150.e	15.e	$4$	$16$	$8$	$8.850$	16.0.$\cdots$.10	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{13}q^{2}-\beta _{5}q^{3}+4\beta _{7}q^{4}+(2-2\beta _{2}+\cdots)q^{6}+\cdots$
150.4.g.a	$150$	$4$	150.g	25.d	$5$	$12$	$3$	$8.850$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$-6$	$9$	$-10$	$-44$		$5^{3}$	$\mathrm{SU}(2)[C_{5}]$	$q-2\beta _{1}q^{2}+(3-3\beta _{1}+3\beta _{3}+3\beta _{5}+\cdots)q^{3}+\cdots$
150.4.g.b	$150$	$4$	150.g	25.d	$5$	$16$	$4$	$8.850$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-8$	$-12$	$15$	$46$		$5^{4}$	$\mathrm{SU}(2)[C_{5}]$	$q-2\beta _{6}q^{2}+(-3+3\beta _{4}+3\beta _{5}+3\beta _{6}+\cdots)q^{3}+\cdots$
150.4.g.c	$150$	$4$	150.g	25.d	$5$	$16$	$4$	$8.850$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$8$	$-12$	$5$	$12$		$2^{4}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{5}]$	$q+(2-2\beta _{1}+2\beta _{2}-2\beta _{3})q^{2}-3\beta _{1}q^{3}+\cdots$
150.4.g.d	$150$	$4$	150.g	25.d	$5$	$20$	$5$	$8.850$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$10$	$15$	$-16$	$-10$		$2^{4}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{5}]$	$q-2\beta _{3}q^{2}+3\beta _{5}q^{3}-4\beta _{5}q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$
150.4.h.a	$150$	$4$	150.h	25.e	$10$	$24$	$6$	$8.850$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
150.4.h.b	$150$	$4$	150.h	25.e	$10$	$32$	$8$	$8.850$		None		$2$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{10}]$
150.4.l.a	$150$	$4$	150.l	75.l	$20$	$240$	$30$	$8.850$		None		$4$	$0$	$0$	$-8$	$0$	$-12$			$\mathrm{SU}(2)[C_{20}]$

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 348 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.