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.		Projective image	Projective image type
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Results (1-50 of 78 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2000.1.b.a	$2000$	$1$	2000.b	4.b	$2$	$4$	$4$	$0.998$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q+(\zeta_{10}+\zeta_{10}^{4})q^{3}+(-\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{7}+\cdots$
2000.1.h.a	$2000$	$1$	2000.h	20.d	$2$	$4$	$4$	$0.998$	$\Q(\zeta_{20})^+$	$D_{10}$	$\Q(\sqrt{-5}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{3}+\beta _{3}q^{7}+(2+\beta _{2})q^{9}+(-1+\cdots)q^{21}+\cdots$
2000.1.x.a	$2000$	$1$	2000.x	100.h	$10$	$4$	$1$	$0.998$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{10}^{2}q^{9}+(\zeta_{10}-\zeta_{10}^{3})q^{13}+(-\zeta_{10}+\cdots)q^{17}+\cdots$
2000.1.z.a	$2000$	$1$	2000.z	100.j	$10$	$8$	$2$	$0.998$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$5$		$q+\zeta_{20}^{8}q^{9}+(\zeta_{20}^{7}+\zeta_{20}^{9})q^{13}+(\zeta_{20}^{3}+\cdots)q^{17}+\cdots$
2000.1.bp.a	$2000$	$1$	2000.bp	500.n	$50$	$20$	$1$	$0.998$	$\Q(\zeta_{50})$	$D_{50}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{50}^{9}q^{5}+\zeta_{50}^{7}q^{9}+(\zeta_{50}^{3}-\zeta_{50}^{11}+\cdots)q^{13}+\cdots$
2000.2.a.a	$2000$	$2$	2000.a	1.a	$1$	$2$	$2$	$15.970$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}-3q^{7}+(-1+3\beta )q^{9}+\cdots$
2000.2.a.b	$2000$	$2$	2000.a	1.a	$1$	$2$	$2$	$15.970$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(-2+3\beta )q^{7}+(-1+\cdots)q^{9}+\cdots$
2000.2.a.c	$2000$	$2$	2000.a	1.a	$1$	$2$	$2$	$15.970$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2\beta q^{3}+\beta q^{7}+(1+4\beta )q^{9}+(-5+\cdots)q^{11}+\cdots$
2000.2.a.d	$2000$	$2$	2000.a	1.a	$1$	$2$	$2$	$15.970$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-3+2\beta )q^{7}+(-2+\beta )q^{9}+\cdots$
2000.2.a.e	$2000$	$2$	2000.a	1.a	$1$	$2$	$2$	$15.970$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-1+\beta )q^{7}+(-2+\beta )q^{9}+\cdots$
2000.2.a.f	$2000$	$2$	2000.a	1.a	$1$	$2$	$2$	$15.970$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1+2\beta )q^{7}+(-2+\beta )q^{9}+\cdots$
2000.2.a.g	$2000$	$2$	2000.a	1.a	$1$	$2$	$2$	$15.970$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1-2\beta )q^{7}+(-2+\beta )q^{9}+\cdots$
2000.2.a.h	$2000$	$2$	2000.a	1.a	$1$	$2$	$2$	$15.970$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1-\beta )q^{7}+(-2+\beta )q^{9}-2\beta q^{11}+\cdots$
2000.2.a.i	$2000$	$2$	2000.a	1.a	$1$	$2$	$2$	$15.970$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(3-2\beta )q^{7}+(-2+\beta )q^{9}+\cdots$
2000.2.a.j	$2000$	$2$	2000.a	1.a	$1$	$2$	$2$	$15.970$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{3}-\beta q^{7}+(1+4\beta )q^{9}+(-5+\cdots)q^{11}+\cdots$
2000.2.a.k	$2000$	$2$	2000.a	1.a	$1$	$2$	$2$	$15.970$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(2-3\beta )q^{7}+(-1+3\beta )q^{9}+\cdots$
2000.2.a.l	$2000$	$2$	2000.a	1.a	$1$	$2$	$2$	$15.970$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+3q^{7}+(-1+3\beta )q^{9}+\cdots$
2000.2.a.m	$2000$	$2$	2000.a	1.a	$1$	$4$	$4$	$15.970$	4.4.4400.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-4$	$0$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-2-\beta _{2}-\beta _{3})q^{7}+\cdots$
2000.2.a.n	$2000$	$2$	2000.a	1.a	$1$	$4$	$4$	$15.970$	4.4.10025.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$-9$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}-\beta _{2})q^{3}+(-2+\beta _{2}+\beta _{3})q^{7}+\cdots$
2000.2.a.o	$2000$	$2$	2000.a	1.a	$1$	$4$	$4$	$15.970$	4.4.4400.1	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots$
2000.2.a.p	$2000$	$2$	2000.a	1.a	$1$	$4$	$4$	$15.970$	4.4.12400.1	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+(2-3\beta _{2}+\cdots)q^{9}+\cdots$
2000.2.a.q	$2000$	$2$	2000.a	1.a	$1$	$4$	$4$	$15.970$	4.4.10025.1	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(2+\beta _{3})q^{7}+(2-\beta _{2}+\beta _{3})q^{9}+\cdots$
2000.2.a.r	$2000$	$2$	2000.a	1.a	$1$	$4$	$4$	$15.970$	4.4.4400.1	$_{}$	None	None	✓	$1$	$0$	$0$	$4$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}+(2+\beta _{2}-\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots$
2000.2.c.a	$2000$	$2$	2000.c	5.b	$2$	$4$	$4$	$15.970$	4.0.12400.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+(-\beta _{1}+\beta _{3})q^{7}+(-2-3\beta _{2}+\cdots)q^{9}+\cdots$
2000.2.c.b	$2000$	$2$	2000.c	5.b	$2$	$4$	$4$	$15.970$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta _{1}q^{3}+\beta _{1}q^{7}+(-1+4\beta _{2})q^{9}+\cdots$
2000.2.c.c	$2000$	$2$	2000.c	5.b	$2$	$4$	$4$	$15.970$	4.0.4400.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$
2000.2.c.d	$2000$	$2$	2000.c	5.b	$2$	$4$	$4$	$15.970$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{3})q^{3}+(3\beta _{1}+2\beta _{3})q^{7}+(1+\cdots)q^{9}+\cdots$
2000.2.c.e	$2000$	$2$	2000.c	5.b	$2$	$4$	$4$	$15.970$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{3})q^{3}+3\beta _{3}q^{7}+(1+3\beta _{2}+\cdots)q^{9}+\cdots$
2000.2.c.f	$2000$	$2$	2000.c	5.b	$2$	$4$	$4$	$15.970$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{7}+(2+\beta _{2})q^{9}+\cdots$
2000.2.c.g	$2000$	$2$	2000.c	5.b	$2$	$4$	$4$	$15.970$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(2\beta _{1}+3\beta _{3})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
2000.2.c.h	$2000$	$2$	2000.c	5.b	$2$	$4$	$4$	$15.970$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(2\beta _{1}-\beta _{3})q^{7}+(2+\beta _{2})q^{9}+\cdots$
2000.2.c.i	$2000$	$2$	2000.c	5.b	$2$	$8$	$8$	$15.970$	8.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(3\beta _{2}+\beta _{3}-\beta _{7})q^{7}+(-3+\cdots)q^{9}+\cdots$
2000.2.c.j	$2000$	$2$	2000.c	5.b	$2$	$8$	$8$	$15.970$	8.0.309760000.3	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{5}+\beta _{7})q^{3}+(\beta _{4}-\beta _{7})q^{7}+(-2+\cdots)q^{9}+\cdots$
2000.2.n.a	$2000$	$2$	2000.n	20.e	$4$	$8$	$4$	$15.970$	$\Q(\zeta_{20})$	$_{}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$-10$	$0$	$10$		$2^{2}$	$\mathrm{U}(1)[D_{4}]$	$q+(-1+\zeta_{20}^{3}-\zeta_{20}^{5})q^{3}+(3-3\zeta_{20}+\cdots)q^{7}+\cdots$
2000.2.n.b	$2000$	$2$	2000.n	20.e	$4$	$8$	$4$	$15.970$	8.0.1024000000.2	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{5}q^{3}+(\beta _{3}+\beta _{7})q^{7}+(-\beta _{2}-\beta _{6}+\cdots)q^{9}+\cdots$
2000.2.n.c	$2000$	$2$	2000.n	20.e	$4$	$8$	$4$	$15.970$	8.0.1024000000.2	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{5}q^{3}+(\beta _{3}+\beta _{7})q^{7}+(-\beta _{2}-\beta _{6}+\cdots)q^{9}+\cdots$
2000.2.n.d	$2000$	$2$	2000.n	20.e	$4$	$8$	$4$	$15.970$	$\Q(\zeta_{20})$	$_{}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$10$	$0$	$-10$		$2^{2}$	$\mathrm{U}(1)[D_{4}]$	$q+(1+\zeta_{20}^{2}-\zeta_{20}^{3}-\zeta_{20}^{6})q^{3}+(-3+\cdots)q^{7}+\cdots$
2000.2.n.e	$2000$	$2$	2000.n	20.e	$4$	$32$	$16$	$15.970$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
2000.2.n.f	$2000$	$2$	2000.n	20.e	$4$	$32$	$16$	$15.970$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
2000.3.b.a	$2000$	$3$	2000.b	4.b	$2$	$8$	$8$	$54.496$	$\Q(\zeta_{20})$	$_{}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{12}\cdot 5^{5}$	$\mathrm{U}(1)[D_{2}]$	$q-\zeta_{20}q^{3}+(\zeta_{20}-\zeta_{20}^{5})q^{7}+(-9+\cdots)q^{9}+\cdots$
2000.3.b.b	$2000$	$3$	2000.b	4.b	$2$	$8$	$8$	$54.496$	8.0.$\cdots$.7	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}-\beta _{6}q^{7}+(-2-\beta _{1}-\beta _{5}+\cdots)q^{9}+\cdots$
2000.3.b.c	$2000$	$3$	2000.b	4.b	$2$	$8$	$8$	$54.496$	8.0.$\cdots$.7	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}-\beta _{6}q^{7}+(-2-\beta _{1}-\beta _{5}+\cdots)q^{9}+\cdots$
2000.3.b.d	$2000$	$3$	2000.b	4.b	$2$	$8$	$8$	$54.496$	8.0.484000000.9	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
2000.3.b.e	$2000$	$3$	2000.b	4.b	$2$	$16$	$16$	$54.496$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{24}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{3}+(\beta _{6}-\beta _{13})q^{7}+(-5+2\beta _{2}+\cdots)q^{9}+\cdots$
2000.3.b.f	$2000$	$3$	2000.b	4.b	$2$	$16$	$16$	$54.496$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{3}-\beta _{14}q^{7}+(-3+\beta _{1})q^{9}+\cdots$
2000.3.b.g	$2000$	$3$	2000.b	4.b	$2$	$16$	$16$	$54.496$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{3}-\beta _{14}q^{7}+(-3+\beta _{1})q^{9}+\cdots$
2000.3.b.h	$2000$	$3$	2000.b	4.b	$2$	$16$	$16$	$54.496$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{32}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{9}q^{3}+\beta _{7}q^{7}+(-2-\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots$
2000.3.h.a	$2000$	$3$	2000.h	20.d	$2$	$4$	$4$	$54.496$	$\Q(\zeta_{20})^+$	$_{}$	$\Q(\sqrt{-5}) $	None	✓	$2$	$0$	$0$	$-10$	$0$	$-30$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+(-2-\beta _{1}+\beta _{2})q^{3}+(-9-3\beta _{2}+\cdots)q^{7}+\cdots$
2000.3.h.b	$2000$	$3$	2000.h	20.d	$2$	$4$	$4$	$54.496$	$\Q(\zeta_{20})^+$	$_{}$	$\Q(\sqrt{-5}) $	None	✓	$2$	$0$	$0$	$10$	$0$	$30$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+(2+\beta _{1}-\beta _{2})q^{3}+(9+3\beta _{2}+\beta _{3})q^{7}+\cdots$
2000.3.h.c	$2000$	$3$	2000.h	20.d	$2$	$8$	$8$	$54.496$	8.0.484000000.6	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3}+\cdots)q^{9}+\cdots$

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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.