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 60 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
2223.1.f.a	$2223$	$1$	2223.f	247.d	$2$	$1$	$1$	$1.109$	$\Q$	$D_{3}$	$\Q(\sqrt{-247}) $	None	✓				247.1.d.a	$2$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{8}-q^{13}-q^{16}+q^{17}-q^{19}+\cdots$
2223.1.f.b	$2223$	$1$	2223.f	247.d	$2$	$1$	$1$	$1.109$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-247}) $	$\Q(\sqrt{741}) $	✓	✓			2223.1.f.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{4}-q^{13}+q^{16}+q^{19}+q^{25}+\cdots$
2223.1.f.c	$2223$	$1$	2223.f	247.d	$2$	$1$	$1$	$1.109$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-247}) $	$\Q(\sqrt{741}) $	✓	✓			2223.1.f.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{4}+q^{13}+q^{16}-q^{19}+q^{25}+\cdots$
2223.1.f.d	$2223$	$1$	2223.f	247.d	$2$	$1$	$1$	$1.109$	$\Q$	$D_{3}$	$\Q(\sqrt{-247}) $	None	✓				247.1.d.a	$2$	$0$	$1$	$0$	$0$	$0$		$1$		$q+q^{2}-q^{8}+q^{13}-q^{16}+q^{17}+q^{19}+\cdots$
2223.1.f.e	$2223$	$1$	2223.f	247.d	$2$	$2$	$2$	$1.109$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-247}) $	None	✓	✓			2223.1.f.e	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{2}+2q^{4}-\beta q^{8}-q^{13}+q^{16}+\cdots$
2223.1.f.f	$2223$	$1$	2223.f	247.d	$2$	$2$	$2$	$1.109$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-247}) $	None	✓	✓			2223.1.f.e	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{2}+2q^{4}-\beta q^{8}+q^{13}+q^{16}+\cdots$
2223.1.cb.a	$2223$	$1$	2223.cb	247.n	$6$	$2$	$1$	$1.109$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			2223.1.cb.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{6}q^{4}+(-\zeta_{6}-\zeta_{6}^{2})q^{7}-\zeta_{6}^{2}q^{13}+\cdots$
2223.1.cb.b	$2223$	$1$	2223.cb	247.n	$6$	$2$	$1$	$1.109$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			2223.1.cb.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{6}q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{7}+q^{13}+\zeta_{6}^{2}q^{16}+\cdots$
2223.1.gh.a	$2223$	$1$	2223.gh	247.ab	$12$	$4$	$1$	$1.109$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓			2223.1.gh.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-\zeta_{12}q^{4}+(-\zeta_{12}^{4}+\zeta_{12}^{5})q^{7}-\zeta_{12}^{3}q^{13}+\cdots$
2223.1.gh.b	$2223$	$1$	2223.gh	247.ab	$12$	$4$	$1$	$1.109$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓			2223.1.gh.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-\zeta_{12}q^{4}+(\zeta_{12}+\zeta_{12}^{2})q^{7}+\zeta_{12}^{5}q^{13}+\cdots$
2223.1.gv.a	$2223$	$1$	2223.gv	247.ah	$18$	$6$	$1$	$1.109$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	2223.1.gv.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{4}q^{4}+(-\zeta_{18}^{2}-\zeta_{18}^{7})q^{7}+\cdots$
2223.1.hp.a	$2223$	$1$	2223.hp	247.aj	$18$	$6$	$1$	$1.109$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	2223.1.hp.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{8}q^{4}+(\zeta_{18}+\zeta_{18}^{5})q^{7}-q^{13}+\cdots$
2223.1.ii.a	$2223$	$1$	2223.ii	247.am	$18$	$6$	$1$	$1.109$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	2223.1.gv.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{7}q^{4}+(\zeta_{18}+\zeta_{18}^{2})q^{7}+q^{13}+\cdots$
2223.1.jf.a	$2223$	$1$	2223.jf	247.ap	$18$	$6$	$1$	$1.109$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	2223.1.hp.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{4}q^{4}+(-\zeta_{18}^{2}+\zeta_{18}^{7})q^{7}+\cdots$
2223.1.jp.a	$2223$	$1$	2223.jp	247.au	$36$	$12$	$1$	$1.109$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	2223.1.jp.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{36}^{11}q^{4}+(\zeta_{36}^{10}-\zeta_{36}^{17})q^{7}+\cdots$
2223.1.ke.a	$2223$	$1$	2223.ke	247.at	$36$	$12$	$1$	$1.109$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	2223.1.jp.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{36}^{13}q^{4}+(-\zeta_{36}^{5}-\zeta_{36}^{16})q^{7}+\cdots$
2223.2.a.a	$2223$	$2$	2223.a	1.a	$1$	$1$	$1$	$17.751$	$\Q$	$_{}$	None	None	✓				741.2.a.e	$1$	$0$	$-2$	$0$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{5}-q^{7}+2q^{10}+\cdots$
2223.2.a.b	$2223$	$2$	2223.a	1.a	$1$	$1$	$1$	$17.751$	$\Q$	$_{}$	None	None	✓				741.2.a.d	$1$	$0$	$-1$	$0$	$-3$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-3q^{5}+5q^{7}+3q^{8}+3q^{10}+\cdots$
2223.2.a.c	$2223$	$2$	2223.a	1.a	$1$	$1$	$1$	$17.751$	$\Q$	$_{}$	None	None	✓				741.2.a.c	$1$	$1$	$-1$	$0$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}+3q^{7}+3q^{8}+q^{10}+\cdots$
2223.2.a.d	$2223$	$2$	2223.a	1.a	$1$	$1$	$1$	$17.751$	$\Q$	$_{}$	None	None	✓				741.2.a.b	$1$	$1$	$-1$	$0$	$3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{5}+q^{7}+3q^{8}-3q^{10}+\cdots$
2223.2.a.e	$2223$	$2$	2223.a	1.a	$1$	$1$	$1$	$17.751$	$\Q$	$_{}$	None	None	✓				741.2.a.a	$1$	$1$	$0$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{5}-3q^{7}+3q^{11}+q^{13}+\cdots$
2223.2.a.f	$2223$	$2$	2223.a	1.a	$1$	$2$	$2$	$17.751$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				247.2.a.a	$1$	$1$	$-1$	$0$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}-2\beta q^{5}-2q^{7}+\cdots$
2223.2.a.g	$2223$	$2$	2223.a	1.a	$1$	$2$	$2$	$17.751$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				741.2.a.g	$1$	$1$	$-1$	$0$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(2+\beta )q^{4}-q^{5}+q^{7}+(-4+\cdots)q^{8}+\cdots$
2223.2.a.h	$2223$	$2$	2223.a	1.a	$1$	$2$	$2$	$17.751$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			2223.2.a.h	$2$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+\beta q^{5}-q^{7}-\beta q^{11}+q^{13}+\cdots$
2223.2.a.i	$2223$	$2$	2223.a	1.a	$1$	$2$	$2$	$17.751$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				741.2.a.f	$1$	$1$	$0$	$0$	$2$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{5}+(-3+\beta )q^{7}-2\beta q^{8}+\cdots$
2223.2.a.j	$2223$	$2$	2223.a	1.a	$1$	$2$	$2$	$17.751$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			2223.2.a.j	$2$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-\beta q^{5}-q^{7}-\beta q^{8}-3q^{10}+\cdots$
2223.2.a.k	$2223$	$2$	2223.a	1.a	$1$	$3$	$3$	$17.751$	3.3.621.1	$_{}$	None	None	✓				741.2.a.h	$1$	$0$	$0$	$0$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots$
2223.2.a.l	$2223$	$2$	2223.a	1.a	$1$	$3$	$3$	$17.751$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓				247.2.a.b	$1$	$0$	$3$	$0$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
2223.2.a.m	$2223$	$2$	2223.a	1.a	$1$	$4$	$4$	$17.751$	4.4.11324.1	$_{}$	None	None	✓				741.2.a.i	$1$	$0$	$1$	$0$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots$
2223.2.a.n	$2223$	$2$	2223.a	1.a	$1$	$4$	$4$	$17.751$	4.4.6809.1	$_{}$	None	None	✓				247.2.a.c	$1$	$0$	$3$	$0$	$8$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{3})q^{2}+(1-\beta _{2}+\beta _{3})q^{4}+(2+\cdots)q^{5}+\cdots$
2223.2.a.o	$2223$	$2$	2223.a	1.a	$1$	$5$	$5$	$17.751$	5.5.288565.1	$_{}$	None	None	✓				247.2.a.e	$1$	$1$	$-4$	$0$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
2223.2.a.p	$2223$	$2$	2223.a	1.a	$1$	$5$	$5$	$17.751$	5.5.2762272.1	$_{}$	None	None	✓				741.2.a.k	$1$	$1$	$-1$	$0$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1+\beta _{3})q^{5}+\cdots$
2223.2.a.q	$2223$	$2$	2223.a	1.a	$1$	$5$	$5$	$17.751$	5.5.2655049.1	$_{}$	None	None	✓		✓		247.2.a.d	$1$	$1$	$0$	$0$	$-2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots$
2223.2.a.r	$2223$	$2$	2223.a	1.a	$1$	$5$	$5$	$17.751$	5.5.504568.1	$_{}$	None	None	✓		✓		741.2.a.j	$1$	$0$	$1$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{2}+\beta _{4})q^{5}+\cdots$
2223.2.a.s	$2223$	$2$	2223.a	1.a	$1$	$8$	$8$	$17.751$	8.8.$\cdots$.1	$_{}$	None	None	✓	✓	✓	✓	2223.2.a.s	$2$	$1$	$0$	$0$	$0$	$-10$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-\beta _{2}-\beta _{7})q^{4}-\beta _{3}q^{5}+\cdots$
2223.2.a.t	$2223$	$2$	2223.a	1.a	$1$	$9$	$9$	$17.751$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓		✓		741.2.a.l	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{6}q^{5}-\beta _{5}q^{7}+\cdots$
2223.2.a.u	$2223$	$2$	2223.a	1.a	$1$	$10$	$10$	$17.751$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	2223.2.a.u	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+\beta _{7}q^{7}+\cdots$
2223.2.a.v	$2223$	$2$	2223.a	1.a	$1$	$14$	$14$	$17.751$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	2223.2.a.v	$2$	$0$	$0$	$0$	$0$	$6$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{9}q^{5}+\beta _{7}q^{7}+\cdots$
2223.2.d.a	$2223$	$2$	2223.d	741.d	$2$	$16$	$16$	$17.751$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			2223.2.d.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{11}q^{2}-\beta _{1}q^{4}-\beta _{8}q^{5}-\beta _{12}q^{7}+\cdots$
2223.2.d.b	$2223$	$2$	2223.d	741.d	$2$	$24$	$24$	$17.751$		$_{}$	$\Q(\sqrt{-247}) $	None		✓			2223.2.d.b	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{U}(1)[D_{2}]$
2223.2.d.c	$2223$	$2$	2223.d	741.d	$2$	$56$	$56$	$17.751$		$_{}$	None	None		✓	✓		2223.2.d.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2223.2.g.a	$2223$	$2$	2223.g	57.d	$2$	$80$	$80$	$17.751$		$_{}$	None	None		✓	✓	✓	2223.2.g.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2223.4.a.a	$2223$	$4$	2223.a	1.a	$1$	$1$	$1$	$131.161$	$\Q$	$_{}$	None	None	✓				741.4.a.a	$1$	$0$	$-5$	$0$	$-20$	$-9$	$+$	$1$	$\mathrm{SU}(2)$	$q-5q^{2}+17q^{4}-20q^{5}-9q^{7}-45q^{8}+\cdots$
2223.4.a.b	$2223$	$4$	2223.a	1.a	$1$	$1$	$1$	$131.161$	$\Q$	$_{}$	None	None	✓				247.4.a.a	$1$	$2$	$3$	$0$	$-7$	$-27$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}+q^{4}-7q^{5}-3^{3}q^{7}-21q^{8}+\cdots$
2223.4.a.c	$2223$	$4$	2223.a	1.a	$1$	$8$	$8$	$131.161$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓				741.4.a.b	$1$	$1$	$5$	$0$	$8$	$-53$	$-$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
2223.4.a.d	$2223$	$4$	2223.a	1.a	$1$	$10$	$10$	$131.161$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓				247.4.a.b	$1$	$0$	$0$	$0$	$27$	$36$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(3-\beta _{1}+\cdots)q^{5}+\cdots$
2223.4.a.e	$2223$	$4$	2223.a	1.a	$1$	$12$	$12$	$131.161$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓				741.4.a.c	$1$	$0$	$3$	$0$	$22$	$-23$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+(2-\beta _{9})q^{5}+\cdots$
2223.4.a.f	$2223$	$4$	2223.a	1.a	$1$	$13$	$13$	$131.161$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓				741.4.a.e	$1$	$1$	$-3$	$0$	$16$	$-21$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(4+\beta _{2})q^{4}+(1+\beta _{4})q^{5}+\cdots$
2223.4.a.g	$2223$	$4$	2223.a	1.a	$1$	$13$	$13$	$131.161$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓				741.4.a.d	$1$	$1$	$5$	$0$	$2$	$-63$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(3+\beta _{1}+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
2223.4.a.h	$2223$	$4$	2223.a	1.a	$1$	$13$	$13$	$131.161$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓				247.4.a.c	$1$	$0$	$9$	$0$	$34$	$-27$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(5-\beta _{1}+\beta _{2})q^{4}+(3+\cdots)q^{5}+\cdots$

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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.