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 157 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
1089.1.c.a	$1089$	$1$	1089.c	11.b	$2$	$2$	$2$	$0.543$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1089.1.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}-\beta q^{7}+\beta q^{13}+q^{16}-\beta q^{19}+\cdots$
1089.1.h.a	$1089$	$1$	1089.h	99.h	$6$	$4$	$2$	$0.543$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		✓	✓	✓	1089.1.h.a	$4$	$0$	$0$	$2$	$2$	$0$		$1$		$q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots$
1089.1.i.a	$1089$	$1$	1089.i	9.d	$6$	$2$	$1$	$0.543$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		✓	✓	✓	1089.1.i.a	$4$	$0$	$0$	$1$	$3$	$0$		$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+(1+\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots$
1089.1.k.a	$1089$	$1$	1089.k	11.d	$10$	$8$	$2$	$0.543$	8.0.64000000.1	$D_{4}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1089.1.c.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{2}q^{4}-\beta _{7}q^{7}-\beta _{1}q^{13}+\beta _{4}q^{16}+\cdots$
1089.1.r.a	$1089$	$1$	1089.r	99.n	$30$	$8$	$1$	$0.543$	$\Q(\zeta_{15})$	$D_{6}$	$\Q(\sqrt{-11}) $	None		✓	✓	✓	1089.1.i.a	$16$	$0$	$0$	$-1$	$-3$	$0$		$1$		$q+\zeta_{30}^{7}q^{3}-\zeta_{30}^{13}q^{4}+(\zeta_{30}^{6}+\zeta_{30}^{11}+\cdots)q^{5}+\cdots$
1089.1.s.a	$1089$	$1$	1089.s	99.o	$30$	$8$	$1$	$0.543$	$\Q(\zeta_{15})$	$D_{3}$	$\Q(\sqrt{-11}) $	None					99.1.h.a	$16$	$0$	$0$	$1$	$-1$	$0$		$1$		$q-\zeta_{30}^{7}q^{3}-\zeta_{30}^{13}q^{4}+\zeta_{30}q^{5}+\cdots$
1089.1.s.b	$1089$	$1$	1089.s	99.o	$30$	$16$	$2$	$0.543$	16.0.$\cdots$.1	$S_{4}$	None	None		✓	✓		1089.1.h.a	$16$	$0$	$0$	$-2$	$-2$	$0$		$1$		$q+\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+(\beta _{3}+\beta _{15})q^{5}+\cdots$
1089.2.a.a	$1089$	$2$	1089.a	1.a	$1$	$1$	$1$	$8.696$	$\Q$	$_{}$	None	None	✓				363.2.a.a	$1$	$1$	$-2$	$0$	$-4$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-4q^{5}-q^{7}+8q^{10}+\cdots$
1089.2.a.b	$1089$	$2$	1089.a	1.a	$1$	$1$	$1$	$8.696$	$\Q$	$_{}$	None	None	✓				11.2.a.a	$1$	$1$	$-2$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{5}+2q^{7}+2q^{10}+\cdots$
1089.2.a.c	$1089$	$2$	1089.a	1.a	$1$	$1$	$1$	$8.696$	$\Q$	$_{}$	None	None	✓				121.2.a.a	$1$	$1$	$-1$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}-2q^{7}+3q^{8}+q^{10}+\cdots$
1089.2.a.d	$1089$	$2$	1089.a	1.a	$1$	$1$	$1$	$8.696$	$\Q$	$_{}$	None	None	✓				99.2.a.a	$1$	$0$	$-1$	$0$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+4q^{5}+2q^{7}+3q^{8}-4q^{10}+\cdots$
1089.2.a.e	$1089$	$2$	1089.a	1.a	$1$	$1$	$1$	$8.696$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			1089.2.a.e	$2$	$0$	$0$	$0$	$0$	$-5$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-5q^{7}-2q^{13}+4q^{16}+7q^{19}+\cdots$
1089.2.a.f	$1089$	$2$	1089.a	1.a	$1$	$1$	$1$	$8.696$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			1089.2.a.e	$2$	$0$	$0$	$0$	$0$	$5$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+5q^{7}+2q^{13}+4q^{16}-7q^{19}+\cdots$
1089.2.a.g	$1089$	$2$	1089.a	1.a	$1$	$1$	$1$	$8.696$	$\Q$	$_{}$	$\Q(\sqrt{-11}) $	None	✓				121.2.a.b	$2$	$0$	$0$	$0$	$3$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+3q^{5}+4q^{16}-6q^{20}+9q^{23}+\cdots$
1089.2.a.h	$1089$	$2$	1089.a	1.a	$1$	$1$	$1$	$8.696$	$\Q$	$_{}$	None	None	✓				99.2.a.a	$1$	$0$	$1$	$0$	$-4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-4q^{5}+2q^{7}-3q^{8}-4q^{10}+\cdots$
1089.2.a.i	$1089$	$2$	1089.a	1.a	$1$	$1$	$1$	$8.696$	$\Q$	$_{}$	None	None	✓				121.2.a.a	$1$	$1$	$1$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}+2q^{7}-3q^{8}-q^{10}+\cdots$
1089.2.a.j	$1089$	$2$	1089.a	1.a	$1$	$1$	$1$	$8.696$	$\Q$	$_{}$	None	None	✓				33.2.a.a	$1$	$1$	$1$	$0$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{5}-4q^{7}-3q^{8}+2q^{10}+\cdots$
1089.2.a.k	$1089$	$2$	1089.a	1.a	$1$	$1$	$1$	$8.696$	$\Q$	$_{}$	None	None	✓				363.2.a.a	$1$	$1$	$2$	$0$	$-4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-4q^{5}+q^{7}-8q^{10}+\cdots$
1089.2.a.l	$1089$	$2$	1089.a	1.a	$1$	$2$	$2$	$8.696$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				33.2.e.b	$1$	$1$	$-3$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+3\beta q^{4}+(-1+\beta )q^{5}+\cdots$
1089.2.a.m	$1089$	$2$	1089.a	1.a	$1$	$2$	$2$	$8.696$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				33.2.e.a	$1$	$0$	$-1$	$0$	$3$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+(2-\beta )q^{5}+3q^{7}+\cdots$
1089.2.a.n	$1089$	$2$	1089.a	1.a	$1$	$2$	$2$	$8.696$	$\Q(\sqrt{3}) $	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			1089.2.a.n	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-\beta q^{7}+4\beta q^{13}+4q^{16}-3\beta q^{19}+\cdots$
1089.2.a.o	$1089$	$2$	1089.a	1.a	$1$	$2$	$2$	$8.696$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				363.2.a.f	$2$	$0$	$0$	$0$	$6$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}+3q^{5}+2\beta q^{7}-\beta q^{8}+\cdots$
1089.2.a.p	$1089$	$2$	1089.a	1.a	$1$	$2$	$2$	$8.696$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				363.2.a.g	$2$	$0$	$0$	$0$	$-4$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}+3q^{4}-2q^{5}-2\beta q^{7}-\beta q^{8}+\cdots$
1089.2.a.q	$1089$	$2$	1089.a	1.a	$1$	$2$	$2$	$8.696$	$\Q(\sqrt{7}) $	$_{}$	None	None	✓	✓			1089.2.a.q	$2$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+5q^{4}+\beta q^{5}-2q^{7}+3\beta q^{8}+\cdots$
1089.2.a.r	$1089$	$2$	1089.a	1.a	$1$	$2$	$2$	$8.696$	$\Q(\sqrt{7}) $	$_{}$	None	None	✓	✓			1089.2.a.q	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+5q^{4}-\beta q^{5}+2q^{7}+3\beta q^{8}+\cdots$
1089.2.a.s	$1089$	$2$	1089.a	1.a	$1$	$2$	$2$	$8.696$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				33.2.e.a	$1$	$1$	$1$	$0$	$3$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(2-\beta )q^{5}-3q^{7}+\cdots$
1089.2.a.t	$1089$	$2$	1089.a	1.a	$1$	$2$	$2$	$8.696$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				33.2.e.b	$1$	$0$	$3$	$0$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}+(-1+\beta )q^{5}+\cdots$
1089.2.a.u	$1089$	$2$	1089.a	1.a	$1$	$4$	$4$	$8.696$	$\Q(\sqrt{3}, \sqrt{11})$	$_{}$	None	None	✓		✓		363.2.a.j	$2$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{3})q^{4}+\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
1089.2.a.v	$1089$	$2$	1089.a	1.a	$1$	$4$	$4$	$8.696$	4.4.4400.1	$_{}$	None	None	✓		✓		99.2.f.c	$2$	$1$	$0$	$0$	$0$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{1}q^{5}+(-3+\cdots)q^{7}+\cdots$
1089.2.a.w	$1089$	$2$	1089.a	1.a	$1$	$4$	$4$	$8.696$	4.4.4400.1	$_{}$	None	None	✓		✓		99.2.f.c	$2$	$0$	$0$	$0$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{1}q^{5}+(3+2\beta _{2}+\cdots)q^{7}+\cdots$
1089.2.d.a	$1089$	$2$	1089.d	33.d	$2$	$2$	$2$	$8.696$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			1089.2.d.a	$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-q^{4}-\beta q^{5}-2\beta q^{7}+3q^{8}+\cdots$
1089.2.d.b	$1089$	$2$	1089.d	33.d	$2$	$2$	$2$	$8.696$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			1089.2.d.a	$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-q^{4}+\beta q^{5}-2\beta q^{7}-3q^{8}+\cdots$
1089.2.d.c	$1089$	$2$	1089.d	33.d	$2$	$4$	$4$	$8.696$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		✓			1089.2.d.c	$2$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{2})q^{2}+(2+2\beta _{2})q^{4}-2\beta _{1}q^{5}+\cdots$
1089.2.d.d	$1089$	$2$	1089.d	33.d	$2$	$4$	$4$	$8.696$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		✓			1089.2.d.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+q^{4}+(-2\beta _{1}+\beta _{3})q^{5}+2\beta _{3}q^{7}+\cdots$
1089.2.d.e	$1089$	$2$	1089.d	33.d	$2$	$4$	$4$	$8.696$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		✓			1089.2.d.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+q^{4}+(2\beta _{1}-\beta _{3})q^{5}+2\beta _{3}q^{7}+\cdots$
1089.2.d.f	$1089$	$2$	1089.d	33.d	$2$	$4$	$4$	$8.696$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		✓			1089.2.d.c	$2$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{2})q^{2}+(2+2\beta _{2})q^{4}-2\beta _{1}q^{5}+\cdots$
1089.2.d.g	$1089$	$2$	1089.d	33.d	$2$	$16$	$16$	$8.696$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None			✓		99.2.j.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{15}q^{2}+(1+\beta _{4})q^{4}+(-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots$
1089.2.e.a	$1089$	$2$	1089.e	9.c	$3$	$2$	$1$	$8.696$	$\Q(\sqrt{-3}) $	$_{}$	None	None					99.2.e.c	$2$	$0$	$-2$	$0$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$
1089.2.e.b	$1089$	$2$	1089.e	9.c	$3$	$2$	$1$	$8.696$	$\Q(\sqrt{-3}) $	$_{}$	None	None					99.2.e.b	$2$	$0$	$0$	$-3$	$3$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\zeta_{6})q^{3}+2\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots$
1089.2.e.c	$1089$	$2$	1089.e	9.c	$3$	$2$	$1$	$8.696$	$\Q(\sqrt{-3}) $	$_{}$	None	None					99.2.e.a	$2$	$0$	$1$	$-3$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
1089.2.e.d	$1089$	$2$	1089.e	9.c	$3$	$4$	$2$	$8.696$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None					99.2.m.a	$2$	$1$	$-3$	$-6$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{1}-\beta _{3})q^{2}+(-2-\beta _{3})q^{3}+\cdots$
1089.2.e.e	$1089$	$2$	1089.e	9.c	$3$	$4$	$2$	$8.696$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			1089.2.e.e	$4$	$0$	$0$	$-6$	$6$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta_{2} q^{2}+(-\beta_1-1)q^{3}+(\beta_1-1)q^{4}+\cdots$
1089.2.e.f	$1089$	$2$	1089.e	9.c	$3$	$4$	$2$	$8.696$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None		✓			1089.2.e.f	$4$	$0$	$0$	$1$	$-3$	$0$		$1$	$\mathrm{U}(1)[D_{3}]$	$q-\beta _{3}q^{3}+2\beta _{2}q^{4}+(1-2\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots$
1089.2.e.g	$1089$	$2$	1089.e	9.c	$3$	$4$	$2$	$8.696$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None					99.2.m.a	$2$	$0$	$3$	$-6$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}+\beta _{3})q^{2}+(-2-\beta _{3})q^{3}+\cdots$
1089.2.e.h	$1089$	$2$	1089.e	9.c	$3$	$6$	$3$	$8.696$	$\Q(\zeta_{18})$	$_{}$	None	None					99.2.e.d	$2$	$0$	$0$	$0$	$-3$	$-3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta_{5}+\beta_{4}+\cdots-\beta_{2})q^{2}+\cdots+(\beta_{4}+\beta_{2})q^{3}+\cdots$
1089.2.e.i	$1089$	$2$	1089.e	9.c	$3$	$8$	$4$	$8.696$	8.0.508277025.1	$_{}$	None	None					99.2.e.e	$2$	$0$	$1$	$5$	$-4$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{2}+\beta _{7})q^{2}+(1+\beta _{7})q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots$
1089.2.e.j	$1089$	$2$	1089.e	9.c	$3$	$12$	$6$	$8.696$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			1089.2.e.j	$4$	$0$	$0$	$4$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{7}q^{2}+(1+\beta _{2}-\beta _{6})q^{3}+(-1-2\beta _{4}+\cdots)q^{4}+\cdots$
1089.2.e.k	$1089$	$2$	1089.e	9.c	$3$	$16$	$8$	$8.696$	16.0.$\cdots$.1	$_{}$	None	None		✓			1089.2.e.k	$4$	$0$	$0$	$-2$	$4$	$0$		$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2}-\beta _{6})q^{2}-\beta _{13}q^{3}+(2\beta _{5}+\cdots)q^{4}+\cdots$
1089.2.e.l	$1089$	$2$	1089.e	9.c	$3$	$20$	$10$	$8.696$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			1089.2.e.l	$2$	$0$	$0$	$-1$	$-3$	$1$		$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{3}q^{2}-\beta _{16}q^{3}+(-\beta _{12}+\beta _{17}+\cdots)q^{4}+\cdots$
1089.2.e.m	$1089$	$2$	1089.e	9.c	$3$	$20$	$10$	$8.696$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			1089.2.e.l	$2$	$0$	$0$	$-1$	$-3$	$-1$		$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}-\beta _{16}q^{3}+(-\beta _{12}+\beta _{17}+\cdots)q^{4}+\cdots$

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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.