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 (38 matches)

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Label	Dim.	$A$	Field	CM	RM	Traces				Fricke sign	$q$-expansion
Label	Dim.	$A$	Field	CM	RM	$a_2$	$a_3$	$a_5$	$a_7$	Fricke sign	$q$-expansion
2009.1.i.a	$6$	$1.003$	6.0.64827.1	$\Q(\sqrt{-287}) $	None	$1$	$-1$	$0$	$0$		$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots$
2009.1.i.b	$6$	$1.003$	6.0.64827.1	$\Q(\sqrt{-287}) $	None	$1$	$1$	$0$	$0$		$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots$
2009.2.a.a	$2$	$16.042$	$\Q(\sqrt{5}) $	None	None	$-1$	$1$	$-1$	$0$	$+$	$q-\beta q^{2}+(1-\beta )q^{3}+(-1+\beta )q^{4}+(-1+\cdots)q^{5}+\cdots$
2009.2.a.b	$2$	$16.042$	$\Q(\sqrt{5}) $	None	None	$-1$	$3$	$1$	$0$	$-$	$q-\beta q^{2}+(1+\beta )q^{3}+(-1+\beta )q^{4}+(1+\cdots)q^{5}+\cdots$
2009.2.a.c	$2$	$16.042$	$\Q(\sqrt{13}) $	None	None	$0$	$-1$	$1$	$0$	$+$	$q-\beta q^{3}-2q^{4}+(1-\beta )q^{5}+\beta q^{9}+(-2+\cdots)q^{11}+\cdots$
2009.2.a.d	$2$	$16.042$	$\Q(\sqrt{13}) $	None	None	$0$	$1$	$-1$	$0$	$+$	$q+\beta q^{3}-2q^{4}+(-1+\beta )q^{5}+\beta q^{9}+\cdots$
2009.2.a.e	$2$	$16.042$	$\Q(\sqrt{5}) $	None	None	$1$	$-2$	$2$	$0$	$+$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots$
2009.2.a.f	$2$	$16.042$	$\Q(\sqrt{5}) $	None	None	$1$	$2$	$-2$	$0$	$+$	$q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}-q^{5}+\beta q^{6}+\cdots$
2009.2.a.g	$3$	$16.042$	3.3.148.1	None	None	$-1$	$0$	$2$	$0$	$-$	$q+(-\beta _{1}-\beta _{2})q^{2}-\beta _{2}q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots$
2009.2.a.h	$3$	$16.042$	3.3.257.1	None	None	$0$	$-3$	$0$	$0$	$-$	$q-\beta _{2}q^{2}+(-1-\beta _{2})q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots$
2009.2.a.i	$3$	$16.042$	3.3.257.1	None	None	$0$	$3$	$0$	$0$	$+$	$q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots$
2009.2.a.j	$3$	$16.042$	3.3.257.1	None	None	$1$	$1$	$-6$	$0$	$+$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$
2009.2.a.k	$3$	$16.042$	$\Q(\zeta_{14})^+$	None	None	$4$	$-5$	$-2$	$0$	$-$	$q+(1+\beta _{1})q^{2}+(-2+\beta _{1})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots$
2009.2.a.l	$5$	$16.042$	5.5.233489.1	None	None	$-2$	$-2$	$2$	$0$	$+$	$q-\beta _{2}q^{2}-\beta _{3}q^{3}+(1+\beta _{1})q^{4}+\beta _{3}q^{5}+\cdots$
2009.2.a.m	$5$	$16.042$	5.5.233489.1	None	None	$-2$	$2$	$-2$	$0$	$+$	$q-\beta _{2}q^{2}+\beta _{3}q^{3}+(1+\beta _{1})q^{4}-\beta _{3}q^{5}+\cdots$
2009.2.a.n	$5$	$16.042$	5.5.633117.1	None	None	$-1$	$-4$	$5$	$0$	$+$	$q-\beta _{1}q^{2}+(-1+\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots$
2009.2.a.o	$6$	$16.042$	6.6.185257757.1	None	None	$-1$	$4$	$1$	$0$	$-$	$q-\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
2009.2.a.p	$7$	$16.042$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	None	$-1$	$-7$	$-4$	$0$	$+$	$q+\beta _{2}q^{2}+(-1+\beta _{1})q^{3}+(1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
2009.2.a.q	$7$	$16.042$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	None	$-1$	$7$	$4$	$0$	$-$	$q+\beta _{2}q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
2009.2.a.r	$17$	$16.042$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	None	None	$3$	$-1$	$1$	$0$	$-$	$q+\beta _{1}q^{2}+\beta _{12}q^{3}+(1+\beta _{2})q^{4}+\beta _{13}q^{5}+\cdots$
2009.2.a.s	$17$	$16.042$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	None	None	$3$	$1$	$-1$	$0$	$-$	$q+\beta _{1}q^{2}-\beta _{12}q^{3}+(1+\beta _{2})q^{4}-\beta _{13}q^{5}+\cdots$
2009.2.a.t	$20$	$16.042$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	None	$-2$	$-8$	$-8$	$0$	$+$	$q-\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}-\beta _{18}q^{5}+\cdots$
2009.2.a.u	$20$	$16.042$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	None	$-2$	$8$	$8$	$0$	$-$	$q-\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}+\beta _{18}q^{5}+\cdots$
2009.4.a.a	$1$	$118.535$	$\Q$	None	None	$-1$	$2$	$12$	$0$	$+$	$q-q^{2}+2q^{3}-7q^{4}+12q^{5}-2q^{6}+\cdots$
2009.4.a.b	$3$	$118.535$	3.3.404.1	None	None	$-3$	$8$	$10$	$0$	$-$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+(3+\beta _{1}-2\beta _{2})q^{3}+\cdots$
2009.4.a.c	$7$	$118.535$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	None	$1$	$-4$	$-10$	$0$	$+$	$q+\beta _{1}q^{2}+(-1-\beta _{4}+\beta _{6})q^{3}+(6+\beta _{1}+\cdots)q^{4}+\cdots$
2009.4.a.d	$11$	$118.535$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	None	$-3$	$-3$	$14$	$0$	$-$	$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(3+\beta _{1}+\beta _{2})q^{4}+\cdots$
2009.4.a.e	$12$	$118.535$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	None	$-4$	$17$	$14$	$0$	$+$	$q-\beta _{1}q^{2}+(1-\beta _{5})q^{3}+(2+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
2009.4.a.f	$17$	$118.535$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	None	None	$6$	$-11$	$2$	$0$	$+$	$q+\beta _{1}q^{2}+(-1+\beta _{7})q^{3}+(6+\beta _{2})q^{4}+\cdots$
2009.4.a.g	$19$	$118.535$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	None	None	$4$	$-13$	$-26$	$0$	$-$	$q+\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(5+\beta _{2})q^{4}+\cdots$
2009.4.a.h	$30$	$118.535$		None	None	$1$	$-12$	$-20$	$0$	$-$
2009.4.a.i	$30$	$118.535$		None	None	$1$	$12$	$20$	$0$	$+$
2009.4.a.j	$36$	$118.535$		None	None	$-5$	$-6$	$4$	$0$	$-$
2009.4.a.k	$36$	$118.535$		None	None	$-5$	$6$	$-4$	$0$	$-$
2009.4.a.l	$44$	$118.535$		None	None	$3$	$-6$	$4$	$0$	$+$
2009.4.a.m	$44$	$118.535$		None	None	$3$	$6$	$-4$	$0$	$+$
2009.4.a.n	$60$	$118.535$		None	None	$2$	$-24$	$-40$	$0$	$-$
2009.4.a.o	$60$	$118.535$		None	None	$2$	$24$	$40$	$0$	$+$

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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	RM	Traces				Fricke sign	$q$-expansion
Label	Dim.	\(A\)	Field	CM	RM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	Fricke sign	$q$-expansion
2009.1.i.a	\(6\)	\(1.003\)	6.0.64827.1	\(\Q(\sqrt{-287}) \)	None	\(1\)	\(-1\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots\)
2009.1.i.b	\(6\)	\(1.003\)	6.0.64827.1	\(\Q(\sqrt{-287}) \)	None	\(1\)	\(1\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots\)
2009.2.a.a	\(2\)	\(16.042\)	\(\Q(\sqrt{5}) \)	None	None	\(-1\)	\(1\)	\(-1\)	\(0\)	\(+\)	\(q-\beta q^{2}+(1-\beta )q^{3}+(-1+\beta )q^{4}+(-1+\cdots)q^{5}+\cdots\)
2009.2.a.b	\(2\)	\(16.042\)	\(\Q(\sqrt{5}) \)	None	None	\(-1\)	\(3\)	\(1\)	\(0\)	\(-\)	\(q-\beta q^{2}+(1+\beta )q^{3}+(-1+\beta )q^{4}+(1+\cdots)q^{5}+\cdots\)
2009.2.a.c	\(2\)	\(16.042\)	\(\Q(\sqrt{13}) \)	None	None	\(0\)	\(-1\)	\(1\)	\(0\)	\(+\)	\(q-\beta q^{3}-2q^{4}+(1-\beta )q^{5}+\beta q^{9}+(-2+\cdots)q^{11}+\cdots\)
2009.2.a.d	\(2\)	\(16.042\)	\(\Q(\sqrt{13}) \)	None	None	\(0\)	\(1\)	\(-1\)	\(0\)	\(+\)	\(q+\beta q^{3}-2q^{4}+(-1+\beta )q^{5}+\beta q^{9}+\cdots\)
2009.2.a.e	\(2\)	\(16.042\)	\(\Q(\sqrt{5}) \)	None	None	\(1\)	\(-2\)	\(2\)	\(0\)	\(+\)	\(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots\)
2009.2.a.f	\(2\)	\(16.042\)	\(\Q(\sqrt{5}) \)	None	None	\(1\)	\(2\)	\(-2\)	\(0\)	\(+\)	\(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}-q^{5}+\beta q^{6}+\cdots\)
2009.2.a.g	\(3\)	\(16.042\)	3.3.148.1	None	None	\(-1\)	\(0\)	\(2\)	\(0\)	\(-\)	\(q+(-\beta _{1}-\beta _{2})q^{2}-\beta _{2}q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
2009.2.a.h	\(3\)	\(16.042\)	3.3.257.1	None	None	\(0\)	\(-3\)	\(0\)	\(0\)	\(-\)	\(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)
2009.2.a.i	\(3\)	\(16.042\)	3.3.257.1	None	None	\(0\)	\(3\)	\(0\)	\(0\)	\(+\)	\(q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)
2009.2.a.j	\(3\)	\(16.042\)	3.3.257.1	None	None	\(1\)	\(1\)	\(-6\)	\(0\)	\(+\)	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
2009.2.a.k	\(3\)	\(16.042\)	\(\Q(\zeta_{14})^+\)	None	None	\(4\)	\(-5\)	\(-2\)	\(0\)	\(-\)	\(q+(1+\beta _{1})q^{2}+(-2+\beta _{1})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
2009.2.a.l	\(5\)	\(16.042\)	5.5.233489.1	None	None	\(-2\)	\(-2\)	\(2\)	\(0\)	\(+\)	\(q-\beta _{2}q^{2}-\beta _{3}q^{3}+(1+\beta _{1})q^{4}+\beta _{3}q^{5}+\cdots\)
2009.2.a.m	\(5\)	\(16.042\)	5.5.233489.1	None	None	\(-2\)	\(2\)	\(-2\)	\(0\)	\(+\)	\(q-\beta _{2}q^{2}+\beta _{3}q^{3}+(1+\beta _{1})q^{4}-\beta _{3}q^{5}+\cdots\)
2009.2.a.n	\(5\)	\(16.042\)	5.5.633117.1	None	None	\(-1\)	\(-4\)	\(5\)	\(0\)	\(+\)	\(q-\beta _{1}q^{2}+(-1+\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
2009.2.a.o	\(6\)	\(16.042\)	6.6.185257757.1	None	None	\(-1\)	\(4\)	\(1\)	\(0\)	\(-\)	\(q-\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
2009.2.a.p	\(7\)	\(16.042\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	None	\(-1\)	\(-7\)	\(-4\)	\(0\)	\(+\)	\(q+\beta _{2}q^{2}+(-1+\beta _{1})q^{3}+(1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
2009.2.a.q	\(7\)	\(16.042\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	None	\(-1\)	\(7\)	\(4\)	\(0\)	\(-\)	\(q+\beta _{2}q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
2009.2.a.r	\(17\)	\(16.042\)	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	None	\(3\)	\(-1\)	\(1\)	\(0\)	\(-\)	\(q+\beta _{1}q^{2}+\beta _{12}q^{3}+(1+\beta _{2})q^{4}+\beta _{13}q^{5}+\cdots\)
2009.2.a.s	\(17\)	\(16.042\)	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	None	\(3\)	\(1\)	\(-1\)	\(0\)	\(-\)	\(q+\beta _{1}q^{2}-\beta _{12}q^{3}+(1+\beta _{2})q^{4}-\beta _{13}q^{5}+\cdots\)
2009.2.a.t	\(20\)	\(16.042\)	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	None	\(-2\)	\(-8\)	\(-8\)	\(0\)	\(+\)	\(q-\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}-\beta _{18}q^{5}+\cdots\)
2009.2.a.u	\(20\)	\(16.042\)	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	None	\(-2\)	\(8\)	\(8\)	\(0\)	\(-\)	\(q-\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}+\beta _{18}q^{5}+\cdots\)
2009.4.a.a	\(1\)	\(118.535\)	\(\Q\)	None	None	\(-1\)	\(2\)	\(12\)	\(0\)	\(+\)	\(q-q^{2}+2q^{3}-7q^{4}+12q^{5}-2q^{6}+\cdots\)
2009.4.a.b	\(3\)	\(118.535\)	3.3.404.1	None	None	\(-3\)	\(8\)	\(10\)	\(0\)	\(-\)	\(q+(-1+\beta _{1}-\beta _{2})q^{2}+(3+\beta _{1}-2\beta _{2})q^{3}+\cdots\)
2009.4.a.c	\(7\)	\(118.535\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	None	\(1\)	\(-4\)	\(-10\)	\(0\)	\(+\)	\(q+\beta _{1}q^{2}+(-1-\beta _{4}+\beta _{6})q^{3}+(6+\beta _{1}+\cdots)q^{4}+\cdots\)
2009.4.a.d	\(11\)	\(118.535\)	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	None	\(-3\)	\(-3\)	\(14\)	\(0\)	\(-\)	\(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(3+\beta _{1}+\beta _{2})q^{4}+\cdots\)
2009.4.a.e	\(12\)	\(118.535\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	None	\(-4\)	\(17\)	\(14\)	\(0\)	\(+\)	\(q-\beta _{1}q^{2}+(1-\beta _{5})q^{3}+(2+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2009.4.a.f	\(17\)	\(118.535\)	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	None	\(6\)	\(-11\)	\(2\)	\(0\)	\(+\)	\(q+\beta _{1}q^{2}+(-1+\beta _{7})q^{3}+(6+\beta _{2})q^{4}+\cdots\)
2009.4.a.g	\(19\)	\(118.535\)	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	None	\(4\)	\(-13\)	\(-26\)	\(0\)	\(-\)	\(q+\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(5+\beta _{2})q^{4}+\cdots\)
2009.4.a.h	\(30\)	\(118.535\)		None	None	\(1\)	\(-12\)	\(-20\)	\(0\)	\(-\)
2009.4.a.i	\(30\)	\(118.535\)		None	None	\(1\)	\(12\)	\(20\)	\(0\)	\(+\)
2009.4.a.j	\(36\)	\(118.535\)		None	None	\(-5\)	\(-6\)	\(4\)	\(0\)	\(-\)
2009.4.a.k	\(36\)	\(118.535\)		None	None	\(-5\)	\(6\)	\(-4\)	\(0\)	\(-\)
2009.4.a.l	\(44\)	\(118.535\)		None	None	\(3\)	\(-6\)	\(4\)	\(0\)	\(+\)
2009.4.a.m	\(44\)	\(118.535\)		None	None	\(3\)	\(6\)	\(-4\)	\(0\)	\(+\)
2009.4.a.n	\(60\)	\(118.535\)		None	None	\(2\)	\(-24\)	\(-40\)	\(0\)	\(-\)
2009.4.a.o	\(60\)	\(118.535\)		None	None	\(2\)	\(24\)	\(40\)	\(0\)	\(+\)

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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.