LMFDB - Newform search results

Refine search

Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twist	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

Results (25 matches)

Download to Pari/GP SageMath Magma

Label	Dim.	$A$	Field	CM	Traces				A-L signs		$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	2	503	$q$-expansion
8048.2.a.a	$1$	$64.264$	$\Q$	None	$0$	$-3$	$-2$	$-3$	$-$	$+$	$q-3q^{3}-2q^{5}-3q^{7}+6q^{9}-3q^{11}+\cdots$
8048.2.a.b	$1$	$64.264$	$\Q$	None	$0$	$-1$	$-4$	$-1$	$-$	$+$	$q-q^{3}-4q^{5}-q^{7}-2q^{9}+3q^{11}+\cdots$
8048.2.a.c	$1$	$64.264$	$\Q$	None	$0$	$-1$	$-4$	$3$	$-$	$+$	$q-q^{3}-4q^{5}+3q^{7}-2q^{9}-5q^{11}+\cdots$
8048.2.a.d	$1$	$64.264$	$\Q$	None	$0$	$-1$	$-2$	$-1$	$-$	$-$	$q-q^{3}-2q^{5}-q^{7}-2q^{9}-q^{11}-3q^{13}+\cdots$
8048.2.a.e	$1$	$64.264$	$\Q$	None	$0$	$-1$	$-2$	$3$	$-$	$-$	$q-q^{3}-2q^{5}+3q^{7}-2q^{9}-q^{11}+\cdots$
8048.2.a.f	$1$	$64.264$	$\Q$	None	$0$	$0$	$0$	$0$	$-$	$+$	$q-3q^{9}-4q^{11}+2q^{13}-2q^{17}+2q^{19}+\cdots$
8048.2.a.g	$1$	$64.264$	$\Q$	None	$0$	$1$	$0$	$-1$	$-$	$+$	$q+q^{3}-q^{7}-2q^{9}+5q^{11}-5q^{13}+\cdots$
8048.2.a.h	$1$	$64.264$	$\Q$	None	$0$	$1$	$0$	$-1$	$+$	$+$	$q+q^{3}-q^{7}-2q^{9}+5q^{11}+3q^{13}+\cdots$
8048.2.a.i	$1$	$64.264$	$\Q$	None	$0$	$1$	$0$	$5$	$+$	$-$	$q+q^{3}+5q^{7}-2q^{9}+5q^{11}+q^{13}+\cdots$
8048.2.a.j	$1$	$64.264$	$\Q$	None	$0$	$1$	$2$	$-1$	$+$	$+$	$q+q^{3}+2q^{5}-q^{7}-2q^{9}-3q^{11}+\cdots$
8048.2.a.k	$1$	$64.264$	$\Q$	None	$0$	$3$	$0$	$3$	$-$	$+$	$q+3q^{3}+3q^{7}+6q^{9}-q^{11}+5q^{13}+\cdots$
8048.2.a.l	$2$	$64.264$	$\Q(\sqrt{5}) $	None	$0$	$0$	$-2$	$4$	$-$	$-$	$q-\beta q^{3}+(-1+\beta )q^{5}+(2+\beta )q^{7}+2q^{9}+\cdots$
8048.2.a.m	$3$	$64.264$	3.3.257.1	None	$0$	$-1$	$0$	$-1$	$-$	$+$	$q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+\beta _{2}q^{9}+\cdots$
8048.2.a.n	$5$	$64.264$	5.5.36497.1	None	$0$	$0$	$-1$	$-3$	$-$	$-$	$q+(-\beta _{1}+\beta _{3}-\beta _{4})q^{3}+(\beta _{2}+\beta _{3})q^{5}+\cdots$
8048.2.a.o	$5$	$64.264$	5.5.205225.1	None	$0$	$4$	$-3$	$9$	$-$	$+$	$q+(1-\beta _{1})q^{3}+(-1-\beta _{1}-\beta _{3}-\beta _{4})q^{5}+\cdots$
8048.2.a.p	$10$	$64.264$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$0$	$8$	$-1$	$5$	$-$	$-$	$q+(1-\beta _{1})q^{3}-\beta _{2}q^{5}+(\beta _{1}-\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots$
8048.2.a.q	$12$	$64.264$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$0$	$-5$	$5$	$-8$	$-$	$-$	$q-\beta _{1}q^{3}-\beta _{9}q^{5}+(-1-\beta _{10})q^{7}+\cdots$
8048.2.a.r	$12$	$64.264$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$0$	$3$	$7$	$2$	$-$	$+$	$q+\beta _{4}q^{3}+(\beta _{7}-\beta _{10})q^{5}+(-\beta _{2}+\beta _{6}+\cdots)q^{7}+\cdots$
8048.2.a.s	$21$	$64.264$		None	$0$	$-10$	$3$	$-13$	$-$	$-$
8048.2.a.t	$21$	$64.264$		None	$0$	$10$	$-3$	$15$	$-$	$+$
8048.2.a.u	$26$	$64.264$		None	$0$	$-4$	$9$	$-11$	$-$	$+$
8048.2.a.v	$28$	$64.264$		None	$0$	$-2$	$-12$	$0$	$+$	$+$
8048.2.a.w	$29$	$64.264$		None	$0$	$7$	$-4$	$13$	$+$	$-$
8048.2.a.x	$33$	$64.264$		None	$0$	$-10$	$0$	$-12$	$+$	$+$
8048.2.a.y	$33$	$64.264$		None	$0$	$2$	$12$	$-4$	$+$	$-$

Download to Pari/GP SageMath Magma

Overview	Random
Universe	Knowledge

Degree 1	Degree 2
Degree 3	Degree 4
$\zeta$ zeros

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Label	Dim.	\(A\)	Field	CM	Traces				A-L signs		$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	2	503	$q$-expansion
8048.2.a.a	\(1\)	\(64.264\)	\(\Q\)	None	\(0\)	\(-3\)	\(-2\)	\(-3\)	\(-\)	\(+\)	\(q-3q^{3}-2q^{5}-3q^{7}+6q^{9}-3q^{11}+\cdots\)
8048.2.a.b	\(1\)	\(64.264\)	\(\Q\)	None	\(0\)	\(-1\)	\(-4\)	\(-1\)	\(-\)	\(+\)	\(q-q^{3}-4q^{5}-q^{7}-2q^{9}+3q^{11}+\cdots\)
8048.2.a.c	\(1\)	\(64.264\)	\(\Q\)	None	\(0\)	\(-1\)	\(-4\)	\(3\)	\(-\)	\(+\)	\(q-q^{3}-4q^{5}+3q^{7}-2q^{9}-5q^{11}+\cdots\)
8048.2.a.d	\(1\)	\(64.264\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(-1\)	\(-\)	\(-\)	\(q-q^{3}-2q^{5}-q^{7}-2q^{9}-q^{11}-3q^{13}+\cdots\)
8048.2.a.e	\(1\)	\(64.264\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(3\)	\(-\)	\(-\)	\(q-q^{3}-2q^{5}+3q^{7}-2q^{9}-q^{11}+\cdots\)
8048.2.a.f	\(1\)	\(64.264\)	\(\Q\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(+\)	\(q-3q^{9}-4q^{11}+2q^{13}-2q^{17}+2q^{19}+\cdots\)
8048.2.a.g	\(1\)	\(64.264\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(q+q^{3}-q^{7}-2q^{9}+5q^{11}-5q^{13}+\cdots\)
8048.2.a.h	\(1\)	\(64.264\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(q+q^{3}-q^{7}-2q^{9}+5q^{11}+3q^{13}+\cdots\)
8048.2.a.i	\(1\)	\(64.264\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(5\)	\(+\)	\(-\)	\(q+q^{3}+5q^{7}-2q^{9}+5q^{11}+q^{13}+\cdots\)
8048.2.a.j	\(1\)	\(64.264\)	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(-1\)	\(+\)	\(+\)	\(q+q^{3}+2q^{5}-q^{7}-2q^{9}-3q^{11}+\cdots\)
8048.2.a.k	\(1\)	\(64.264\)	\(\Q\)	None	\(0\)	\(3\)	\(0\)	\(3\)	\(-\)	\(+\)	\(q+3q^{3}+3q^{7}+6q^{9}-q^{11}+5q^{13}+\cdots\)
8048.2.a.l	\(2\)	\(64.264\)	\(\Q(\sqrt{5}) \)	None	\(0\)	\(0\)	\(-2\)	\(4\)	\(-\)	\(-\)	\(q-\beta q^{3}+(-1+\beta )q^{5}+(2+\beta )q^{7}+2q^{9}+\cdots\)
8048.2.a.m	\(3\)	\(64.264\)	3.3.257.1	None	\(0\)	\(-1\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+\beta _{2}q^{9}+\cdots\)
8048.2.a.n	\(5\)	\(64.264\)	5.5.36497.1	None	\(0\)	\(0\)	\(-1\)	\(-3\)	\(-\)	\(-\)	\(q+(-\beta _{1}+\beta _{3}-\beta _{4})q^{3}+(\beta _{2}+\beta _{3})q^{5}+\cdots\)
8048.2.a.o	\(5\)	\(64.264\)	5.5.205225.1	None	\(0\)	\(4\)	\(-3\)	\(9\)	\(-\)	\(+\)	\(q+(1-\beta _{1})q^{3}+(-1-\beta _{1}-\beta _{3}-\beta _{4})q^{5}+\cdots\)
8048.2.a.p	\(10\)	\(64.264\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(0\)	\(8\)	\(-1\)	\(5\)	\(-\)	\(-\)	\(q+(1-\beta _{1})q^{3}-\beta _{2}q^{5}+(\beta _{1}-\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
8048.2.a.q	\(12\)	\(64.264\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(0\)	\(-5\)	\(5\)	\(-8\)	\(-\)	\(-\)	\(q-\beta _{1}q^{3}-\beta _{9}q^{5}+(-1-\beta _{10})q^{7}+\cdots\)
8048.2.a.r	\(12\)	\(64.264\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(0\)	\(3\)	\(7\)	\(2\)	\(-\)	\(+\)	\(q+\beta _{4}q^{3}+(\beta _{7}-\beta _{10})q^{5}+(-\beta _{2}+\beta _{6}+\cdots)q^{7}+\cdots\)
8048.2.a.s	\(21\)	\(64.264\)		None	\(0\)	\(-10\)	\(3\)	\(-13\)	\(-\)	\(-\)
8048.2.a.t	\(21\)	\(64.264\)		None	\(0\)	\(10\)	\(-3\)	\(15\)	\(-\)	\(+\)
8048.2.a.u	\(26\)	\(64.264\)		None	\(0\)	\(-4\)	\(9\)	\(-11\)	\(-\)	\(+\)
8048.2.a.v	\(28\)	\(64.264\)		None	\(0\)	\(-2\)	\(-12\)	\(0\)	\(+\)	\(+\)
8048.2.a.w	\(29\)	\(64.264\)		None	\(0\)	\(7\)	\(-4\)	\(13\)	\(+\)	\(-\)
8048.2.a.x	\(33\)	\(64.264\)		None	\(0\)	\(-10\)	\(0\)	\(-12\)	\(+\)	\(+\)
8048.2.a.y	\(33\)	\(64.264\)		None	\(0\)	\(2\)	\(12\)	\(-4\)	\(+\)	\(-\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Learn more about

Refine search

Results (25 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.