LMFDB - Newform Search Results

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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:
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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

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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.