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-twist	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (displaying all 33 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	3	167	$q$-expansion
8016.2.a.a	$1$	$64.008$	$\Q$	None	$0$	$-1$	$-3$	$3$	$-$	$+$	$-$	$q-q^{3}-3q^{5}+3q^{7}+q^{9}-6q^{13}+\cdots$
8016.2.a.b	$1$	$64.008$	$\Q$	None	$0$	$-1$	$-1$	$1$	$-$	$+$	$+$	$q-q^{3}-q^{5}+q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots$
8016.2.a.c	$1$	$64.008$	$\Q$	None	$0$	$-1$	$-1$	$1$	$+$	$+$	$+$	$q-q^{3}-q^{5}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
8016.2.a.d	$1$	$64.008$	$\Q$	None	$0$	$-1$	$0$	$-4$	$+$	$+$	$-$	$q-q^{3}-4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
8016.2.a.e	$1$	$64.008$	$\Q$	None	$0$	$-1$	$0$	$0$	$+$	$+$	$+$	$q-q^{3}+q^{9}+2q^{17}+8q^{19}+4q^{23}+\cdots$
8016.2.a.f	$1$	$64.008$	$\Q$	None	$0$	$-1$	$2$	$4$	$-$	$+$	$+$	$q-q^{3}+2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots$
8016.2.a.g	$1$	$64.008$	$\Q$	None	$0$	$1$	$-4$	$-4$	$-$	$-$	$+$	$q+q^{3}-4q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots$
8016.2.a.h	$1$	$64.008$	$\Q$	None	$0$	$1$	$0$	$0$	$-$	$-$	$+$	$q+q^{3}+q^{9}-4q^{13}+6q^{17}-4q^{23}+\cdots$
8016.2.a.i	$1$	$64.008$	$\Q$	None	$0$	$1$	$1$	$3$	$+$	$-$	$-$	$q+q^{3}+q^{5}+3q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
8016.2.a.j	$1$	$64.008$	$\Q$	None	$0$	$1$	$3$	$-3$	$-$	$-$	$+$	$q+q^{3}+3q^{5}-3q^{7}+q^{9}-6q^{11}+\cdots$
8016.2.a.k	$2$	$64.008$	$\Q(\sqrt{2}) $	None	$0$	$2$	$-4$	$0$	$-$	$-$	$-$	$q+q^{3}+(-2+\beta )q^{5}+2\beta q^{7}+q^{9}+\cdots$
8016.2.a.l	$3$	$64.008$	3.3.148.1	None	$0$	$3$	$-3$	$5$	$-$	$-$	$+$	$q+q^{3}+(-1+\beta _{2})q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+\cdots$
8016.2.a.m	$3$	$64.008$	3.3.1300.1	None	$0$	$3$	$3$	$-1$	$-$	$-$	$-$	$q+q^{3}+(1-\beta _{1})q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots$
8016.2.a.n	$3$	$64.008$	3.3.148.1	None	$0$	$3$	$6$	$4$	$+$	$-$	$+$	$q+q^{3}+(2-\beta _{2})q^{5}+(2-2\beta _{1})q^{7}+q^{9}+\cdots$
8016.2.a.o	$4$	$64.008$	4.4.2777.1	None	$0$	$4$	$5$	$-1$	$-$	$-$	$-$	$q+q^{3}+(1-\beta _{1})q^{5}+(-\beta _{2}+\beta _{3})q^{7}+\cdots$
8016.2.a.p	$5$	$64.008$	5.5.36497.1	None	$0$	$-5$	$-9$	$4$	$-$	$+$	$+$	$q-q^{3}+(-2-\beta _{1}-\beta _{2}-\beta _{4})q^{5}+(1+\cdots)q^{7}+\cdots$
8016.2.a.q	$5$	$64.008$	5.5.161121.1	None	$0$	$-5$	$-7$	$2$	$-$	$+$	$-$	$q-q^{3}+(-1-\beta _{3}-\beta _{4})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
8016.2.a.r	$5$	$64.008$	5.5.11256624.1	None	$0$	$-5$	$-1$	$-9$	$-$	$+$	$-$	$q-q^{3}+\beta _{2}q^{5}+(-2+\beta _{4})q^{7}+q^{9}+\cdots$
8016.2.a.s	$5$	$64.008$	5.5.284897.1	None	$0$	$-5$	$1$	$4$	$+$	$+$	$+$	$q-q^{3}+(-\beta _{3}+\beta _{4})q^{5}+(1+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$
8016.2.a.t	$5$	$64.008$	5.5.149169.1	None	$0$	$5$	$-3$	$2$	$-$	$-$	$+$	$q+q^{3}+(-\beta _{1}+\beta _{3}-\beta _{4})q^{5}+(\beta _{1}+\beta _{4})q^{7}+\cdots$
8016.2.a.u	$5$	$64.008$	5.5.38569.1	None	$0$	$5$	$-1$	$4$	$-$	$-$	$-$	$q+q^{3}+(\beta _{1}+\beta _{4})q^{5}+(1+\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
8016.2.a.v	$7$	$64.008$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$0$	$-7$	$5$	$-7$	$-$	$+$	$+$	$q-q^{3}+(1-\beta _{1})q^{5}+(-1+\beta _{3})q^{7}+\cdots$
8016.2.a.w	$7$	$64.008$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$0$	$7$	$-3$	$-8$	$+$	$-$	$-$	$q+q^{3}-\beta _{1}q^{5}+(-1-\beta _{2})q^{7}+q^{9}+\cdots$
8016.2.a.x	$8$	$64.008$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$0$	$-8$	$7$	$4$	$-$	$+$	$-$	$q-q^{3}+(1+\beta _{2})q^{5}+(1-\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots$
8016.2.a.y	$8$	$64.008$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$0$	$8$	$0$	$1$	$+$	$-$	$+$	$q+q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots$
8016.2.a.z	$8$	$64.008$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$0$	$8$	$1$	$0$	$-$	$-$	$+$	$q+q^{3}+(\beta _{1}+\beta _{2}-\beta _{5})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
8016.2.a.ba	$9$	$64.008$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	$0$	$-9$	$-6$	$11$	$+$	$+$	$-$	$q-q^{3}+(-1+\beta _{1})q^{5}+(2-\beta _{5}-\beta _{7}+\cdots)q^{7}+\cdots$
8016.2.a.bb	$9$	$64.008$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	$0$	$-9$	$9$	$-2$	$-$	$+$	$+$	$q-q^{3}+(1-\beta _{1})q^{5}+\beta _{6}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
8016.2.a.bc	$9$	$64.008$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	$0$	$9$	$1$	$-2$	$-$	$-$	$-$	$q+q^{3}+\beta _{1}q^{5}+(\beta _{3}+\beta _{6})q^{7}+q^{9}+\cdots$
8016.2.a.bd	$10$	$64.008$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$0$	$10$	$-10$	$-1$	$+$	$-$	$-$	$q+q^{3}+(-1-\beta _{1})q^{5}+(-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots$
8016.2.a.be	$11$	$64.008$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	$0$	$11$	$10$	$1$	$+$	$-$	$+$	$q+q^{3}+(1-\beta _{1})q^{5}-\beta _{3}q^{7}+q^{9}+\beta _{10}q^{11}+\cdots$
8016.2.a.bf	$12$	$64.008$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$0$	$-12$	$4$	$-11$	$+$	$+$	$+$	$q-q^{3}+\beta _{1}q^{5}+(-1+\beta _{9})q^{7}+q^{9}+\cdots$
8016.2.a.bg	$13$	$64.008$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	$0$	$-13$	$2$	$-1$	$+$	$+$	$-$	$q-q^{3}+\beta _{1}q^{5}+\beta _{9}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$

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	3	167	$q$-expansion
8016.2.a.a	\(1\)	\(64.008\)	\(\Q\)	None	\(0\)	\(-1\)	\(-3\)	\(3\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}-3q^{5}+3q^{7}+q^{9}-6q^{13}+\cdots\)
8016.2.a.b	\(1\)	\(64.008\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(1\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}-q^{5}+q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots\)
8016.2.a.c	\(1\)	\(64.008\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(1\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-q^{5}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
8016.2.a.d	\(1\)	\(64.008\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(-4\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
8016.2.a.e	\(1\)	\(64.008\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+q^{9}+2q^{17}+8q^{19}+4q^{23}+\cdots\)
8016.2.a.f	\(1\)	\(64.008\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(4\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}+2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
8016.2.a.g	\(1\)	\(64.008\)	\(\Q\)	None	\(0\)	\(1\)	\(-4\)	\(-4\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}-4q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
8016.2.a.h	\(1\)	\(64.008\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+q^{9}-4q^{13}+6q^{17}-4q^{23}+\cdots\)
8016.2.a.i	\(1\)	\(64.008\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(3\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+q^{5}+3q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
8016.2.a.j	\(1\)	\(64.008\)	\(\Q\)	None	\(0\)	\(1\)	\(3\)	\(-3\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+3q^{5}-3q^{7}+q^{9}-6q^{11}+\cdots\)
8016.2.a.k	\(2\)	\(64.008\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(-4\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+(-2+\beta )q^{5}+2\beta q^{7}+q^{9}+\cdots\)
8016.2.a.l	\(3\)	\(64.008\)	3.3.148.1	None	\(0\)	\(3\)	\(-3\)	\(5\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+(-1+\beta _{2})q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+\cdots\)
8016.2.a.m	\(3\)	\(64.008\)	3.3.1300.1	None	\(0\)	\(3\)	\(3\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+(1-\beta _{1})q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
8016.2.a.n	\(3\)	\(64.008\)	3.3.148.1	None	\(0\)	\(3\)	\(6\)	\(4\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}+(2-\beta _{2})q^{5}+(2-2\beta _{1})q^{7}+q^{9}+\cdots\)
8016.2.a.o	\(4\)	\(64.008\)	4.4.2777.1	None	\(0\)	\(4\)	\(5\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+(1-\beta _{1})q^{5}+(-\beta _{2}+\beta _{3})q^{7}+\cdots\)
8016.2.a.p	\(5\)	\(64.008\)	5.5.36497.1	None	\(0\)	\(-5\)	\(-9\)	\(4\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}+(-2-\beta _{1}-\beta _{2}-\beta _{4})q^{5}+(1+\cdots)q^{7}+\cdots\)
8016.2.a.q	\(5\)	\(64.008\)	5.5.161121.1	None	\(0\)	\(-5\)	\(-7\)	\(2\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+(-1-\beta _{3}-\beta _{4})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
8016.2.a.r	\(5\)	\(64.008\)	5.5.11256624.1	None	\(0\)	\(-5\)	\(-1\)	\(-9\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+\beta _{2}q^{5}+(-2+\beta _{4})q^{7}+q^{9}+\cdots\)
8016.2.a.s	\(5\)	\(64.008\)	5.5.284897.1	None	\(0\)	\(-5\)	\(1\)	\(4\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+(-\beta _{3}+\beta _{4})q^{5}+(1+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
8016.2.a.t	\(5\)	\(64.008\)	5.5.149169.1	None	\(0\)	\(5\)	\(-3\)	\(2\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+(-\beta _{1}+\beta _{3}-\beta _{4})q^{5}+(\beta _{1}+\beta _{4})q^{7}+\cdots\)
8016.2.a.u	\(5\)	\(64.008\)	5.5.38569.1	None	\(0\)	\(5\)	\(-1\)	\(4\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+(\beta _{1}+\beta _{4})q^{5}+(1+\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
8016.2.a.v	\(7\)	\(64.008\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(0\)	\(-7\)	\(5\)	\(-7\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}+(1-\beta _{1})q^{5}+(-1+\beta _{3})q^{7}+\cdots\)
8016.2.a.w	\(7\)	\(64.008\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(0\)	\(7\)	\(-3\)	\(-8\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}-\beta _{1}q^{5}+(-1-\beta _{2})q^{7}+q^{9}+\cdots\)
8016.2.a.x	\(8\)	\(64.008\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(0\)	\(-8\)	\(7\)	\(4\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+(1+\beta _{2})q^{5}+(1-\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots\)
8016.2.a.y	\(8\)	\(64.008\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(0\)	\(8\)	\(0\)	\(1\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
8016.2.a.z	\(8\)	\(64.008\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(0\)	\(8\)	\(1\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+(\beta _{1}+\beta _{2}-\beta _{5})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
8016.2.a.ba	\(9\)	\(64.008\)	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	\(0\)	\(-9\)	\(-6\)	\(11\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+(-1+\beta _{1})q^{5}+(2-\beta _{5}-\beta _{7}+\cdots)q^{7}+\cdots\)
8016.2.a.bb	\(9\)	\(64.008\)	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	\(0\)	\(-9\)	\(9\)	\(-2\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}+(1-\beta _{1})q^{5}+\beta _{6}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
8016.2.a.bc	\(9\)	\(64.008\)	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	\(0\)	\(9\)	\(1\)	\(-2\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+\beta _{1}q^{5}+(\beta _{3}+\beta _{6})q^{7}+q^{9}+\cdots\)
8016.2.a.bd	\(10\)	\(64.008\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(0\)	\(10\)	\(-10\)	\(-1\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+(-1-\beta _{1})q^{5}+(-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
8016.2.a.be	\(11\)	\(64.008\)	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	\(0\)	\(11\)	\(10\)	\(1\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}+(1-\beta _{1})q^{5}-\beta _{3}q^{7}+q^{9}+\beta _{10}q^{11}+\cdots\)
8016.2.a.bf	\(12\)	\(64.008\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(0\)	\(-12\)	\(4\)	\(-11\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+\beta _{1}q^{5}+(-1+\beta _{9})q^{7}+q^{9}+\cdots\)
8016.2.a.bg	\(13\)	\(64.008\)	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	\(0\)	\(-13\)	\(2\)	\(-1\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+\beta _{1}q^{5}+\beta _{9}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)

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