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 matches 1-50 of at least 1000) Next

Label	Dim.	$A$	Field	CM	Traces				Fricke sign	$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	Fricke sign	$q$-expansion
4001.2.a.a	$149$	$31.948$		None	$-6$	$-28$	$-19$	$-47$	$+$
4001.2.a.b	$184$	$31.948$		None	$3$	$28$	$15$	$49$	$-$
4002.2.a.a	$1$	$31.956$	$\Q$	None	$-1$	$-1$	$-2$	$-2$	$-$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-2q^{7}+\cdots$
4002.2.a.b	$1$	$31.956$	$\Q$	None	$-1$	$-1$	$0$	$-4$	$+$	$q-q^{2}-q^{3}+q^{4}+q^{6}-4q^{7}-q^{8}+\cdots$
4002.2.a.c	$1$	$31.956$	$\Q$	None	$-1$	$-1$	$1$	$4$	$-$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots$
4002.2.a.d	$1$	$31.956$	$\Q$	None	$-1$	$1$	$-3$	$-3$	$+$	$q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-3q^{7}+\cdots$
4002.2.a.e	$1$	$31.956$	$\Q$	None	$-1$	$1$	$-1$	$0$	$-$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
4002.2.a.f	$1$	$31.956$	$\Q$	None	$-1$	$1$	$2$	$0$	$+$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots$
4002.2.a.g	$1$	$31.956$	$\Q$	None	$-1$	$1$	$4$	$0$	$-$	$q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{8}+\cdots$
4002.2.a.h	$1$	$31.956$	$\Q$	None	$1$	$-1$	$-2$	$-2$	$+$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots$
4002.2.a.i	$1$	$31.956$	$\Q$	None	$1$	$-1$	$-2$	$2$	$+$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+2q^{7}+\cdots$
4002.2.a.j	$1$	$31.956$	$\Q$	None	$1$	$-1$	$1$	$-4$	$+$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots$
4002.2.a.k	$1$	$31.956$	$\Q$	None	$1$	$-1$	$1$	$1$	$+$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
4002.2.a.l	$1$	$31.956$	$\Q$	None	$1$	$-1$	$2$	$4$	$-$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+4q^{7}+\cdots$
4002.2.a.m	$1$	$31.956$	$\Q$	None	$1$	$1$	$-3$	$-4$	$+$	$q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-4q^{7}+\cdots$
4002.2.a.n	$1$	$31.956$	$\Q$	None	$1$	$1$	$-2$	$-4$	$-$	$q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-4q^{7}+\cdots$
4002.2.a.o	$1$	$31.956$	$\Q$	None	$1$	$1$	$-1$	$-3$	$+$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-3q^{7}+\cdots$
4002.2.a.p	$1$	$31.956$	$\Q$	None	$1$	$1$	$-1$	$0$	$+$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
4002.2.a.q	$1$	$31.956$	$\Q$	None	$1$	$1$	$0$	$4$	$-$	$q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots$
4002.2.a.r	$1$	$31.956$	$\Q$	None	$1$	$1$	$3$	$1$	$-$	$q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{7}+\cdots$
4002.2.a.s	$2$	$31.956$	$\Q(\sqrt{17}) $	None	$-2$	$-2$	$-3$	$3$	$-$	$q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots$
4002.2.a.t	$2$	$31.956$	$\Q(\sqrt{2}) $	None	$-2$	$-2$	$0$	$0$	$-$	$q-q^{2}-q^{3}+q^{4}+2\beta q^{5}+q^{6}+\beta q^{7}+\cdots$
4002.2.a.u	$2$	$31.956$	$\Q(\sqrt{17}) $	None	$-2$	$2$	$1$	$1$	$-$	$q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+\beta q^{7}+\cdots$
4002.2.a.v	$2$	$31.956$	$\Q(\sqrt{17}) $	None	$2$	$-2$	$-3$	$0$	$+$	$q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots$
4002.2.a.w	$2$	$31.956$	$\Q(\sqrt{3}) $	None	$2$	$2$	$6$	$6$	$-$	$q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+3q^{7}+\cdots$
4002.2.a.x	$2$	$31.956$	$\Q(\sqrt{6}) $	None	$2$	$2$	$8$	$4$	$-$	$q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+(2-\beta )q^{7}+\cdots$
4002.2.a.y	$3$	$31.956$	3.3.1772.1	None	$-3$	$-3$	$-1$	$6$	$-$	$q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+(2+\cdots)q^{7}+\cdots$
4002.2.a.z	$3$	$31.956$	3.3.316.1	None	$3$	$-3$	$0$	$-2$	$+$	$q+q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots$
4002.2.a.ba	$4$	$31.956$	4.4.16448.2	None	$-4$	$-4$	$2$	$6$	$-$	$q-q^{2}-q^{3}+q^{4}+\beta _{3}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots$
4002.2.a.bb	$4$	$31.956$	4.4.23252.1	None	$-4$	$4$	$-3$	$-2$	$+$	$q-q^{2}+q^{3}+q^{4}+(-1+\beta _{3})q^{5}-q^{6}+\cdots$
4002.2.a.bc	$4$	$31.956$	4.4.11324.1	None	$4$	$4$	$-4$	$-4$	$+$	$q+q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots$
4002.2.a.bd	$4$	$31.956$	4.4.19796.1	None	$4$	$4$	$-1$	$2$	$-$	$q+q^{2}+q^{3}+q^{4}-\beta _{3}q^{5}+q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots$
4002.2.a.be	$5$	$31.956$	5.5.2389280.1	None	$-5$	$-5$	$1$	$-4$	$+$	$q-q^{2}-q^{3}+q^{4}+\beta _{2}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
4002.2.a.bf	$6$	$31.956$	6.6.61157024.1	None	$-6$	$6$	$3$	$2$	$-$	$q-q^{2}+q^{3}+q^{4}+\beta _{4}q^{5}-q^{6}+(\beta _{4}+\cdots)q^{7}+\cdots$
4002.2.a.bg	$7$	$31.956$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$-7$	$-7$	$2$	$-5$	$+$	$q-q^{2}-q^{3}+q^{4}-\beta _{5}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
4002.2.a.bh	$7$	$31.956$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$7$	$7$	$1$	$-2$	$-$	$q+q^{2}+q^{3}+q^{4}+\beta _{3}q^{5}+q^{6}-\beta _{6}q^{7}+\cdots$
4002.2.a.bi	$8$	$31.956$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$-8$	$8$	$-3$	$-6$	$+$	$q-q^{2}+q^{3}+q^{4}-\beta _{4}q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
4002.2.a.bj	$8$	$31.956$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$8$	$-8$	$1$	$0$	$-$	$q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}-\beta _{4}q^{7}+\cdots$
4002.2.a.bk	$8$	$31.956$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$8$	$-8$	$2$	$5$	$-$	$q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+(1+\cdots)q^{7}+\cdots$
4003.2.a.a	$2$	$31.964$	$\Q(\sqrt{2}) $	None	$0$	$0$	$0$	$-2$	$+$	$q+\beta q^{2}+\beta q^{3}+\beta q^{5}+2q^{6}-q^{7}+\cdots$
4003.2.a.b	$152$	$31.964$		None	$-22$	$-18$	$-59$	$-19$	$+$
4003.2.a.c	$179$	$31.964$		None	$22$	$16$	$61$	$21$	$-$
4004.2.a.a	$1$	$31.972$	$\Q$	None	$0$	$-2$	$0$	$1$	$-$	$q-2q^{3}+q^{7}+q^{9}-q^{11}+q^{13}+6q^{17}+\cdots$
4004.2.a.b	$1$	$31.972$	$\Q$	None	$0$	$-1$	$-3$	$-1$	$+$	$q-q^{3}-3q^{5}-q^{7}-2q^{9}-q^{11}+q^{13}+\cdots$
4004.2.a.c	$1$	$31.972$	$\Q$	None	$0$	$2$	$4$	$1$	$-$	$q+2q^{3}+4q^{5}+q^{7}+q^{9}+q^{11}-q^{13}+\cdots$
4004.2.a.d	$4$	$31.972$	4.4.3981.1	None	$0$	$-3$	$-1$	$4$	$+$	$q+(-1-\beta _{3})q^{3}+(\beta _{2}+\beta _{3})q^{5}+q^{7}+\cdots$
4004.2.a.e	$4$	$31.972$	$\Q(\zeta_{15})^+$	None	$0$	$1$	$1$	$-4$	$+$	$q+(-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+\cdots$
4004.2.a.f	$5$	$31.972$	5.5.463341.1	None	$0$	$3$	$0$	$-5$	$+$	$q+(1-\beta _{1})q^{3}-\beta _{2}q^{5}-q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
4004.2.a.g	$6$	$31.972$	6.6.246302029.1	None	$0$	$-2$	$-3$	$6$	$+$	$q-\beta _{1}q^{3}+(-1-\beta _{4})q^{5}+q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots$
4004.2.a.h	$9$	$31.972$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	$0$	$3$	$0$	$9$	$-$	$q+\beta _{1}q^{3}-\beta _{4}q^{5}+q^{7}+(2+\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots$

In order to download results, determine the number of results.

Introduction	Features
Universe	News

Label	Dim.	\(A\)	Field	CM	Traces				Fricke sign	$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	Fricke sign	$q$-expansion
4001.2.a.a	\(149\)	\(31.948\)		None	\(-6\)	\(-28\)	\(-19\)	\(-47\)	\(+\)
4001.2.a.b	\(184\)	\(31.948\)		None	\(3\)	\(28\)	\(15\)	\(49\)	\(-\)
4002.2.a.a	\(1\)	\(31.956\)	\(\Q\)	None	\(-1\)	\(-1\)	\(-2\)	\(-2\)	\(-\)	\(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-2q^{7}+\cdots\)
4002.2.a.b	\(1\)	\(31.956\)	\(\Q\)	None	\(-1\)	\(-1\)	\(0\)	\(-4\)	\(+\)	\(q-q^{2}-q^{3}+q^{4}+q^{6}-4q^{7}-q^{8}+\cdots\)
4002.2.a.c	\(1\)	\(31.956\)	\(\Q\)	None	\(-1\)	\(-1\)	\(1\)	\(4\)	\(-\)	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots\)
4002.2.a.d	\(1\)	\(31.956\)	\(\Q\)	None	\(-1\)	\(1\)	\(-3\)	\(-3\)	\(+\)	\(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-3q^{7}+\cdots\)
4002.2.a.e	\(1\)	\(31.956\)	\(\Q\)	None	\(-1\)	\(1\)	\(-1\)	\(0\)	\(-\)	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
4002.2.a.f	\(1\)	\(31.956\)	\(\Q\)	None	\(-1\)	\(1\)	\(2\)	\(0\)	\(+\)	\(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
4002.2.a.g	\(1\)	\(31.956\)	\(\Q\)	None	\(-1\)	\(1\)	\(4\)	\(0\)	\(-\)	\(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{8}+\cdots\)
4002.2.a.h	\(1\)	\(31.956\)	\(\Q\)	None	\(1\)	\(-1\)	\(-2\)	\(-2\)	\(+\)	\(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\)
4002.2.a.i	\(1\)	\(31.956\)	\(\Q\)	None	\(1\)	\(-1\)	\(-2\)	\(2\)	\(+\)	\(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+2q^{7}+\cdots\)
4002.2.a.j	\(1\)	\(31.956\)	\(\Q\)	None	\(1\)	\(-1\)	\(1\)	\(-4\)	\(+\)	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
4002.2.a.k	\(1\)	\(31.956\)	\(\Q\)	None	\(1\)	\(-1\)	\(1\)	\(1\)	\(+\)	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
4002.2.a.l	\(1\)	\(31.956\)	\(\Q\)	None	\(1\)	\(-1\)	\(2\)	\(4\)	\(-\)	\(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+4q^{7}+\cdots\)
4002.2.a.m	\(1\)	\(31.956\)	\(\Q\)	None	\(1\)	\(1\)	\(-3\)	\(-4\)	\(+\)	\(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-4q^{7}+\cdots\)
4002.2.a.n	\(1\)	\(31.956\)	\(\Q\)	None	\(1\)	\(1\)	\(-2\)	\(-4\)	\(-\)	\(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-4q^{7}+\cdots\)
4002.2.a.o	\(1\)	\(31.956\)	\(\Q\)	None	\(1\)	\(1\)	\(-1\)	\(-3\)	\(+\)	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-3q^{7}+\cdots\)
4002.2.a.p	\(1\)	\(31.956\)	\(\Q\)	None	\(1\)	\(1\)	\(-1\)	\(0\)	\(+\)	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
4002.2.a.q	\(1\)	\(31.956\)	\(\Q\)	None	\(1\)	\(1\)	\(0\)	\(4\)	\(-\)	\(q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots\)
4002.2.a.r	\(1\)	\(31.956\)	\(\Q\)	None	\(1\)	\(1\)	\(3\)	\(1\)	\(-\)	\(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{7}+\cdots\)
4002.2.a.s	\(2\)	\(31.956\)	\(\Q(\sqrt{17}) \)	None	\(-2\)	\(-2\)	\(-3\)	\(3\)	\(-\)	\(q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
4002.2.a.t	\(2\)	\(31.956\)	\(\Q(\sqrt{2}) \)	None	\(-2\)	\(-2\)	\(0\)	\(0\)	\(-\)	\(q-q^{2}-q^{3}+q^{4}+2\beta q^{5}+q^{6}+\beta q^{7}+\cdots\)
4002.2.a.u	\(2\)	\(31.956\)	\(\Q(\sqrt{17}) \)	None	\(-2\)	\(2\)	\(1\)	\(1\)	\(-\)	\(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+\beta q^{7}+\cdots\)
4002.2.a.v	\(2\)	\(31.956\)	\(\Q(\sqrt{17}) \)	None	\(2\)	\(-2\)	\(-3\)	\(0\)	\(+\)	\(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
4002.2.a.w	\(2\)	\(31.956\)	\(\Q(\sqrt{3}) \)	None	\(2\)	\(2\)	\(6\)	\(6\)	\(-\)	\(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+3q^{7}+\cdots\)
4002.2.a.x	\(2\)	\(31.956\)	\(\Q(\sqrt{6}) \)	None	\(2\)	\(2\)	\(8\)	\(4\)	\(-\)	\(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+(2-\beta )q^{7}+\cdots\)
4002.2.a.y	\(3\)	\(31.956\)	3.3.1772.1	None	\(-3\)	\(-3\)	\(-1\)	\(6\)	\(-\)	\(q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+(2+\cdots)q^{7}+\cdots\)
4002.2.a.z	\(3\)	\(31.956\)	3.3.316.1	None	\(3\)	\(-3\)	\(0\)	\(-2\)	\(+\)	\(q+q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
4002.2.a.ba	\(4\)	\(31.956\)	4.4.16448.2	None	\(-4\)	\(-4\)	\(2\)	\(6\)	\(-\)	\(q-q^{2}-q^{3}+q^{4}+\beta _{3}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots\)
4002.2.a.bb	\(4\)	\(31.956\)	4.4.23252.1	None	\(-4\)	\(4\)	\(-3\)	\(-2\)	\(+\)	\(q-q^{2}+q^{3}+q^{4}+(-1+\beta _{3})q^{5}-q^{6}+\cdots\)
4002.2.a.bc	\(4\)	\(31.956\)	4.4.11324.1	None	\(4\)	\(4\)	\(-4\)	\(-4\)	\(+\)	\(q+q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots\)
4002.2.a.bd	\(4\)	\(31.956\)	4.4.19796.1	None	\(4\)	\(4\)	\(-1\)	\(2\)	\(-\)	\(q+q^{2}+q^{3}+q^{4}-\beta _{3}q^{5}+q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
4002.2.a.be	\(5\)	\(31.956\)	5.5.2389280.1	None	\(-5\)	\(-5\)	\(1\)	\(-4\)	\(+\)	\(q-q^{2}-q^{3}+q^{4}+\beta _{2}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
4002.2.a.bf	\(6\)	\(31.956\)	6.6.61157024.1	None	\(-6\)	\(6\)	\(3\)	\(2\)	\(-\)	\(q-q^{2}+q^{3}+q^{4}+\beta _{4}q^{5}-q^{6}+(\beta _{4}+\cdots)q^{7}+\cdots\)
4002.2.a.bg	\(7\)	\(31.956\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(-7\)	\(-7\)	\(2\)	\(-5\)	\(+\)	\(q-q^{2}-q^{3}+q^{4}-\beta _{5}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
4002.2.a.bh	\(7\)	\(31.956\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(7\)	\(7\)	\(1\)	\(-2\)	\(-\)	\(q+q^{2}+q^{3}+q^{4}+\beta _{3}q^{5}+q^{6}-\beta _{6}q^{7}+\cdots\)
4002.2.a.bi	\(8\)	\(31.956\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(-8\)	\(8\)	\(-3\)	\(-6\)	\(+\)	\(q-q^{2}+q^{3}+q^{4}-\beta _{4}q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
4002.2.a.bj	\(8\)	\(31.956\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(8\)	\(-8\)	\(1\)	\(0\)	\(-\)	\(q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}-\beta _{4}q^{7}+\cdots\)
4002.2.a.bk	\(8\)	\(31.956\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(8\)	\(-8\)	\(2\)	\(5\)	\(-\)	\(q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+(1+\cdots)q^{7}+\cdots\)
4003.2.a.a	\(2\)	\(31.964\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(q+\beta q^{2}+\beta q^{3}+\beta q^{5}+2q^{6}-q^{7}+\cdots\)
4003.2.a.b	\(152\)	\(31.964\)		None	\(-22\)	\(-18\)	\(-59\)	\(-19\)	\(+\)
4003.2.a.c	\(179\)	\(31.964\)		None	\(22\)	\(16\)	\(61\)	\(21\)	\(-\)
4004.2.a.a	\(1\)	\(31.972\)	\(\Q\)	None	\(0\)	\(-2\)	\(0\)	\(1\)	\(-\)	\(q-2q^{3}+q^{7}+q^{9}-q^{11}+q^{13}+6q^{17}+\cdots\)
4004.2.a.b	\(1\)	\(31.972\)	\(\Q\)	None	\(0\)	\(-1\)	\(-3\)	\(-1\)	\(+\)	\(q-q^{3}-3q^{5}-q^{7}-2q^{9}-q^{11}+q^{13}+\cdots\)
4004.2.a.c	\(1\)	\(31.972\)	\(\Q\)	None	\(0\)	\(2\)	\(4\)	\(1\)	\(-\)	\(q+2q^{3}+4q^{5}+q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
4004.2.a.d	\(4\)	\(31.972\)	4.4.3981.1	None	\(0\)	\(-3\)	\(-1\)	\(4\)	\(+\)	\(q+(-1-\beta _{3})q^{3}+(\beta _{2}+\beta _{3})q^{5}+q^{7}+\cdots\)
4004.2.a.e	\(4\)	\(31.972\)	\(\Q(\zeta_{15})^+\)	None	\(0\)	\(1\)	\(1\)	\(-4\)	\(+\)	\(q+(-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+\cdots\)
4004.2.a.f	\(5\)	\(31.972\)	5.5.463341.1	None	\(0\)	\(3\)	\(0\)	\(-5\)	\(+\)	\(q+(1-\beta _{1})q^{3}-\beta _{2}q^{5}-q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
4004.2.a.g	\(6\)	\(31.972\)	6.6.246302029.1	None	\(0\)	\(-2\)	\(-3\)	\(6\)	\(+\)	\(q-\beta _{1}q^{3}+(-1-\beta _{4})q^{5}+q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots\)
4004.2.a.h	\(9\)	\(31.972\)	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	\(0\)	\(3\)	\(0\)	\(9\)	\(-\)	\(q+\beta _{1}q^{3}-\beta _{4}q^{5}+q^{7}+(2+\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)

Introduction and more

L-functions

Modular Forms

Varieties

Fields

Representations

Groups

Knowledge

Learn more about

Refine search

Results (displaying matches 1-50 of at least 1000) Next

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.