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.	Only for weight 1:	Projective image	Projective image type
		Only for weight 1:
					Sort order

Results (displaying all 25 matches)

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	Features
Universe	News

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 and more

L-functions

Modular Forms

Varieties

Fields

Representations

Groups

Knowledge

Learn more about

Refine search

Results (displaying all 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.