LMFDB - Newform search results

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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (1-50 of 51 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1587.1.b.a	$1587$	$1$	1587.b	3.b	$2$	$1$	$1$	$0.792$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-23}) $	$\Q(\sqrt{69}) $	✓	✓			1587.1.b.a	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q+q^{3}+q^{4}+q^{9}+q^{12}-2q^{13}+q^{16}+\cdots$
1587.1.b.b	$1587$	$1$	1587.b	3.b	$2$	$2$	$2$	$0.792$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None	✓	✓			1587.1.b.b	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-q^{3}+q^{4}-\beta q^{7}+q^{9}-q^{12}+q^{16}+\cdots$
1587.1.b.c	$1587$	$1$	1587.b	3.b	$2$	$2$	$2$	$0.792$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-23}) $	None		✓			1587.1.b.c	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{2}-\zeta_{6}q^{3}+(-1-\zeta_{6}+\cdots)q^{4}+\cdots$
1587.1.h.a	$1587$	$1$	1587.h	69.h	$22$	$10$	$1$	$0.792$	$\Q(\zeta_{22})$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-23}) $	$\Q(\sqrt{69}) $		✓			1587.1.b.a	$40$	$0$	$0$	$-1$	$0$	$0$		$1$		$q+\zeta_{22}^{4}q^{3}-\zeta_{22}q^{4}+\zeta_{22}^{8}q^{9}-\zeta_{22}^{5}q^{12}+\cdots$
1587.1.h.b	$1587$	$1$	1587.h	69.h	$22$	$20$	$2$	$0.792$	$\Q(\zeta_{33})$	$D_{6}$	$\Q(\sqrt{-23}) $	None		✓			1587.1.b.c	$40$	$0$	$0$	$1$	$0$	$0$		$1$		$q+(\zeta_{66}^{7}-\zeta_{66}^{29})q^{2}-\zeta_{66}q^{3}+(\zeta_{66}^{3}+\cdots)q^{4}+\cdots$
1587.1.h.c	$1587$	$1$	1587.h	69.h	$22$	$20$	$2$	$0.792$	20.0.$\cdots$.6	$D_{4}$	$\Q(\sqrt{-3}) $	None		✓			1587.1.b.b	$40$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\beta _{8}q^{3}+\beta _{2}q^{4}-\beta _{15}q^{7}+\beta _{16}q^{9}+\cdots$
1587.2.a.a	$1587$	$2$	1587.a	1.a	$1$	$1$	$1$	$12.672$	$\Q$	$_{}$	None	None	✓	✓			1587.2.a.a	$1$	$1$	$-2$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-2q^{6}-q^{7}+q^{9}+\cdots$
1587.2.a.b	$1587$	$2$	1587.a	1.a	$1$	$1$	$1$	$12.672$	$\Q$	$_{}$	None	None	✓	✓			1587.2.a.a	$1$	$1$	$-2$	$1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-2q^{6}+q^{7}+q^{9}+\cdots$
1587.2.a.c	$1587$	$2$	1587.a	1.a	$1$	$1$	$1$	$12.672$	$\Q$	$_{}$	None	None	✓	✓			1587.2.a.c	$1$	$0$	$1$	$-1$	$-4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-4q^{5}-q^{6}-4q^{7}+\cdots$
1587.2.a.d	$1587$	$2$	1587.a	1.a	$1$	$1$	$1$	$12.672$	$\Q$	$_{}$	None	None	✓	✓			1587.2.a.c	$1$	$0$	$1$	$-1$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+4q^{5}-q^{6}+4q^{7}+\cdots$
1587.2.a.e	$1587$	$2$	1587.a	1.a	$1$	$1$	$1$	$12.672$	$\Q$	$_{}$	None	None	✓				69.2.a.a	$1$	$1$	$1$	$1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}+2q^{7}-3q^{8}+\cdots$
1587.2.a.f	$1587$	$2$	1587.a	1.a	$1$	$2$	$2$	$12.672$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1587.2.a.f	$2$	$1$	$-2$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+2\beta q^{5}+q^{6}+3\beta q^{7}+\cdots$
1587.2.a.g	$1587$	$2$	1587.a	1.a	$1$	$2$	$2$	$12.672$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1587.2.a.g	$1$	$0$	$0$	$-2$	$-4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(-2+\beta )q^{5}-\beta q^{6}+\cdots$
1587.2.a.h	$1587$	$2$	1587.a	1.a	$1$	$2$	$2$	$12.672$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1587.2.a.g	$1$	$0$	$0$	$-2$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(2-\beta )q^{5}-\beta q^{6}+(1+\cdots)q^{7}+\cdots$
1587.2.a.i	$1587$	$2$	1587.a	1.a	$1$	$2$	$2$	$12.672$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				69.2.a.b	$1$	$0$	$0$	$-2$	$2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+3q^{4}+(1-\beta )q^{5}+\beta q^{6}+\cdots$
1587.2.a.j	$1587$	$2$	1587.a	1.a	$1$	$2$	$2$	$12.672$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			1587.2.a.j	$2$	$1$	$0$	$2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+2\beta q^{5}-\beta q^{7}+q^{9}+\cdots$
1587.2.a.k	$1587$	$2$	1587.a	1.a	$1$	$2$	$2$	$12.672$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			1587.2.a.k	$1$	$0$	$2$	$-2$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+(2+2\beta )q^{4}+(-1+\cdots)q^{5}+\cdots$
1587.2.a.l	$1587$	$2$	1587.a	1.a	$1$	$2$	$2$	$12.672$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			1587.2.a.k	$1$	$0$	$2$	$-2$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+(2+2\beta )q^{4}+(1+\beta )q^{5}+\cdots$
1587.2.a.m	$1587$	$2$	1587.a	1.a	$1$	$4$	$4$	$12.672$	$\Q(\zeta_{24})^+$	$_{}$	None	None	✓	✓			1587.2.a.m	$2$	$1$	$-4$	$-4$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{2}-q^{3}+(2-2\beta _{2})q^{4}+\cdots$
1587.2.a.n	$1587$	$2$	1587.a	1.a	$1$	$4$	$4$	$12.672$	$\Q(\zeta_{24})^+$	$_{}$	None	None	✓	✓			1587.2.a.n	$2$	$1$	$0$	$-4$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}-q^{3}+q^{4}+(-\beta _{1}-2\beta _{3})q^{5}+\cdots$
1587.2.a.o	$1587$	$2$	1587.a	1.a	$1$	$5$	$5$	$12.672$	$\Q(\zeta_{22})^+$	$_{}$	None	None	✓				69.2.e.a	$1$	$1$	$-2$	$-5$	$-3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{2}+\beta _{4})q^{2}-q^{3}+(2\beta _{1}+\beta _{3}-\beta _{4})q^{4}+\cdots$
1587.2.a.p	$1587$	$2$	1587.a	1.a	$1$	$5$	$5$	$12.672$	$\Q(\zeta_{22})^+$	$_{}$	None	None	✓				69.2.e.a	$1$	$0$	$-2$	$-5$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{2}+\beta _{4})q^{2}-q^{3}+(2\beta _{1}+\beta _{3}-\beta _{4})q^{4}+\cdots$
1587.2.a.q	$1587$	$2$	1587.a	1.a	$1$	$5$	$5$	$12.672$	$\Q(\zeta_{22})^+$	$_{}$	None	None	✓				69.2.e.b	$1$	$1$	$2$	$-5$	$-7$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{3}-\beta _{4})q^{2}-q^{3}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
1587.2.a.r	$1587$	$2$	1587.a	1.a	$1$	$5$	$5$	$12.672$	$\Q(\zeta_{22})^+$	$_{}$	None	None	✓				69.2.e.b	$1$	$0$	$2$	$-5$	$7$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{3}-\beta _{4})q^{2}-q^{3}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
1587.2.a.s	$1587$	$2$	1587.a	1.a	$1$	$6$	$6$	$12.672$	6.6.2803712.1	$_{}$	None	None	✓	✓			1587.2.a.s	$2$	$0$	$2$	$6$	$0$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+q^{3}+(1-\beta _{2}+\beta _{4})q^{4}+\beta _{5}q^{5}+\cdots$
1587.2.a.t	$1587$	$2$	1587.a	1.a	$1$	$10$	$10$	$12.672$	10.10.$\cdots$.1	$_{}$	None	None	✓		✓		69.2.e.c	$1$	$1$	$-2$	$10$	$-8$	$-19$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{4}-\beta _{6}-\beta _{7}+\cdots)q^{4}+\cdots$
1587.2.a.u	$1587$	$2$	1587.a	1.a	$1$	$10$	$10$	$12.672$	10.10.$\cdots$.1	$_{}$	None	None	✓				69.2.e.c	$1$	$0$	$-2$	$10$	$8$	$19$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{4}-\beta _{6}-\beta _{7}+\cdots)q^{4}+\cdots$
1587.2.a.v	$1587$	$2$	1587.a	1.a	$1$	$12$	$12$	$12.672$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	✓	✓		1587.2.a.v	$2$	$0$	$4$	$12$	$0$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+q^{3}+(2-\beta _{7}+\beta _{9})q^{4}-\beta _{6}q^{5}+\cdots$
1587.4.a.a	$1587$	$4$	1587.a	1.a	$1$	$2$	$2$	$93.636$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1587.4.a.a	$2$	$1$	$-6$	$6$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{2}+3q^{3}+q^{4}-3\beta q^{5}-9q^{6}+\cdots$
1587.4.a.b	$1587$	$4$	1587.a	1.a	$1$	$2$	$2$	$93.636$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				69.4.a.a	$1$	$0$	$-4$	$6$	$26$	$10$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-2-\beta )q^{2}+3q^{3}+(1+4\beta )q^{4}+\cdots$
1587.4.a.c	$1587$	$4$	1587.a	1.a	$1$	$2$	$2$	$93.636$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				69.4.a.b	$1$	$1$	$-2$	$-6$	$-8$	$28$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-3q^{3}+(1-2\beta )q^{4}+\cdots$
1587.4.a.d	$1587$	$4$	1587.a	1.a	$1$	$2$	$2$	$93.636$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1587.4.a.d	$2$	$1$	$0$	$6$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-8q^{4}-9\beta q^{5}+4\beta q^{7}+9q^{9}+\cdots$
1587.4.a.e	$1587$	$4$	1587.a	1.a	$1$	$4$	$4$	$93.636$	4.4.1140200.1	$_{}$	None	None	✓				69.4.a.c	$1$	$1$	$-2$	$-12$	$2$	$-32$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-3q^{3}+(6-\beta _{1}-2\beta _{2})q^{4}+\cdots$
1587.4.a.f	$1587$	$4$	1587.a	1.a	$1$	$4$	$4$	$93.636$	$\Q(\zeta_{24})^+$	$_{}$	None	None	✓	✓			1587.4.a.f	$2$	$1$	$0$	$-12$	$0$	$0$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-3q^{3}-2q^{4}+(-2\beta _{2}-2\beta _{3})q^{5}+\cdots$
1587.4.a.g	$1587$	$4$	1587.a	1.a	$1$	$4$	$4$	$93.636$	4.4.2009704.1	$_{}$	None	None	✓				69.4.a.d	$1$	$0$	$4$	$12$	$-4$	$14$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+3q^{3}+(7-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1587.4.a.h	$1587$	$4$	1587.a	1.a	$1$	$5$	$5$	$93.636$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	✓			1587.4.a.h	$1$	$1$	$-4$	$-15$	$-18$	$25$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-3q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1587.4.a.i	$1587$	$4$	1587.a	1.a	$1$	$5$	$5$	$93.636$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	✓			1587.4.a.h	$1$	$1$	$-4$	$-15$	$18$	$-25$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-3q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1587.4.a.j	$1587$	$4$	1587.a	1.a	$1$	$6$	$6$	$93.636$	6.6.$\cdots$.1	$_{}$	None	None	✓	✓			1587.4.a.j	$2$	$1$	$0$	$-18$	$0$	$0$	$-$	$3$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}-3q^{3}+(6-\beta _{2}+2\beta _{3})q^{4}+\cdots$
1587.4.a.k	$1587$	$4$	1587.a	1.a	$1$	$6$	$6$	$93.636$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	✓			1587.4.a.k	$2$	$1$	$0$	$-18$	$0$	$0$	$-$	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-3q^{3}+(6+\beta _{1}+\beta _{4})q^{4}+\cdots$
1587.4.a.l	$1587$	$4$	1587.a	1.a	$1$	$6$	$6$	$93.636$	6.6.52756992.1	$_{}$	None	None	✓	✓			1587.4.a.l	$2$	$1$	$2$	$18$	$0$	$0$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+3q^{3}+(10-2\beta _{4}-\beta _{5})q^{4}+\cdots$
1587.4.a.m	$1587$	$4$	1587.a	1.a	$1$	$6$	$6$	$93.636$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	✓			1587.4.a.m	$2$	$0$	$4$	$18$	$0$	$0$	$+$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	$q+(1+\beta _{5})q^{2}+3q^{3}+(4-\beta _{4}+\beta _{5})q^{4}+\cdots$
1587.4.a.n	$1587$	$4$	1587.a	1.a	$1$	$7$	$7$	$93.636$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓			1587.4.a.n	$1$	$0$	$0$	$21$	$-10$	$17$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+3q^{3}+(5+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
1587.4.a.o	$1587$	$4$	1587.a	1.a	$1$	$7$	$7$	$93.636$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓			1587.4.a.n	$1$	$0$	$0$	$21$	$10$	$-17$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+3q^{3}+(5+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
1587.4.a.p	$1587$	$4$	1587.a	1.a	$1$	$10$	$10$	$93.636$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	✓			1587.4.a.p	$2$	$0$	$4$	$-30$	$0$	$0$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-3q^{3}+(2+\beta _{7})q^{4}+(\beta _{2}+2\beta _{3}+\cdots)q^{5}+\cdots$
1587.4.a.q	$1587$	$4$	1587.a	1.a	$1$	$14$	$14$	$93.636$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	✓			1587.4.a.q	$2$	$0$	$8$	$42$	$0$	$0$	$+$	$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)$	$q+(1-\beta _{2})q^{2}+3q^{3}+(6-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
1587.4.a.r	$1587$	$4$	1587.a	1.a	$1$	$16$	$16$	$93.636$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	✓			1587.4.a.r	$2$	$1$	$-8$	$48$	$0$	$0$	$-$	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{8})q^{2}+3q^{3}+(1-\beta _{12})q^{4}+\cdots$
1587.4.a.s	$1587$	$4$	1587.a	1.a	$1$	$24$	$24$	$93.636$		$_{}$	None	None	✓	✓			1587.4.a.s	$2$	$0$	$8$	$-72$	$0$	$0$	$+$		$\mathrm{SU}(2)$
1587.4.a.t	$1587$	$4$	1587.a	1.a	$1$	$30$	$30$	$93.636$		$_{}$	None	None	✓		✓		69.4.e.a	$1$	$1$	$0$	$90$	$-44$	$-142$	$-$		$\mathrm{SU}(2)$
1587.4.a.u	$1587$	$4$	1587.a	1.a	$1$	$30$	$30$	$93.636$		$_{}$	None	None	✓		✓		69.4.e.a	$1$	$0$	$0$	$90$	$44$	$142$	$+$		$\mathrm{SU}(2)$
1587.4.a.v	$1587$	$4$	1587.a	1.a	$1$	$30$	$30$	$93.636$		$_{}$	None	None	✓		✓		69.4.e.b	$1$	$1$	$2$	$-90$	$-52$	$2$	$-$		$\mathrm{SU}(2)$

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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.