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 183 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
741.1.p.a	$741$	$1$	741.p	741.p	$4$	$2$	$1$	$0.370$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		✓			741.1.p.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-i q^{3}-i q^{4}+(-i+1)q^{7}-q^{9}+\cdots$
741.1.p.b	$741$	$1$	741.p	741.p	$4$	$2$	$1$	$0.370$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		✓			741.1.p.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+i q^{3}-i q^{4}+(-i+1)q^{7}-q^{9}+\cdots$
741.1.w.a	$741$	$1$	741.w	741.w	$6$	$2$	$1$	$0.370$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			741.1.w.a	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{7}+\cdots$
741.1.w.b	$741$	$1$	741.w	741.w	$6$	$2$	$1$	$0.370$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			741.1.w.a	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{4}+(-\zeta_{6}-\zeta_{6}^{2})q^{7}+\cdots$
741.1.cc.a	$741$	$1$	741.cc	741.bc	$12$	$4$	$1$	$0.370$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓			741.1.cc.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\zeta_{12}q^{3}-\zeta_{12}^{5}q^{4}+(\zeta_{12}^{4}-\zeta_{12}^{5}+\cdots)q^{7}+\cdots$
741.1.cc.b	$741$	$1$	741.cc	741.bc	$12$	$4$	$1$	$0.370$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓			741.1.cc.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+\zeta_{12}q^{3}-\zeta_{12}^{5}q^{4}+(-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{7}+\cdots$
741.1.cm.a	$741$	$1$	741.cm	741.bm	$18$	$6$	$1$	$0.370$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	741.1.cm.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{8}q^{3}-\zeta_{18}^{4}q^{4}+(\zeta_{18}^{2}+\zeta_{18}^{7}+\cdots)q^{7}+\cdots$
741.1.cu.a	$741$	$1$	741.cu	741.bu	$18$	$6$	$1$	$0.370$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	741.1.cu.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{7}q^{3}+\zeta_{18}^{8}q^{4}+(-\zeta_{18}-\zeta_{18}^{5}+\cdots)q^{7}+\cdots$
741.1.cv.a	$741$	$1$	741.cv	741.bv	$18$	$6$	$1$	$0.370$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	741.1.cm.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}q^{3}+\zeta_{18}^{5}q^{4}+(\zeta_{18}^{2}-\zeta_{18}^{4}+\cdots)q^{7}+\cdots$
741.1.de.a	$741$	$1$	741.de	741.ce	$18$	$6$	$1$	$0.370$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	741.1.cu.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{8}q^{3}+\zeta_{18}^{4}q^{4}+(\zeta_{18}^{2}-\zeta_{18}^{7}+\cdots)q^{7}+\cdots$
741.1.di.a	$741$	$1$	741.di	741.ci	$36$	$12$	$1$	$0.370$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	741.1.di.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{36}^{5}q^{3}+\zeta_{36}^{7}q^{4}+(-\zeta_{36}+\zeta_{36}^{8}+\cdots)q^{7}+\cdots$
741.1.dp.a	$741$	$1$	741.dp	741.cp	$36$	$12$	$1$	$0.370$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	741.1.di.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{36}q^{3}+\zeta_{36}^{5}q^{4}+(-\zeta_{36}^{2}+\zeta_{36}^{13}+\cdots)q^{7}+\cdots$
741.2.a.a	$741$	$2$	741.a	1.a	$1$	$1$	$1$	$5.917$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	741.2.a.a	$1$	$1$	$0$	$1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots$
741.2.a.b	$741$	$2$	741.a	1.a	$1$	$1$	$1$	$5.917$	$\Q$	$_{}$	None	None	✓	✓			741.2.a.b	$1$	$0$	$1$	$-1$	$-3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-3q^{5}-q^{6}+q^{7}+\cdots$
741.2.a.c	$741$	$2$	741.a	1.a	$1$	$1$	$1$	$5.917$	$\Q$	$_{}$	None	None	✓	✓			741.2.a.c	$1$	$0$	$1$	$-1$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}+3q^{7}+\cdots$
741.2.a.d	$741$	$2$	741.a	1.a	$1$	$1$	$1$	$5.917$	$\Q$	$_{}$	None	None	✓	✓			741.2.a.d	$1$	$0$	$1$	$1$	$3$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+3q^{5}+q^{6}+5q^{7}+\cdots$
741.2.a.e	$741$	$2$	741.a	1.a	$1$	$1$	$1$	$5.917$	$\Q$	$_{}$	None	None	✓	✓			741.2.a.e	$1$	$0$	$2$	$1$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-q^{7}+\cdots$
741.2.a.f	$741$	$2$	741.a	1.a	$1$	$2$	$2$	$5.917$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓	✓	741.2.a.f	$1$	$1$	$0$	$2$	$-2$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}-q^{5}+\beta q^{6}+(-3-\beta )q^{7}+\cdots$
741.2.a.g	$741$	$2$	741.a	1.a	$1$	$2$	$2$	$5.917$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓		741.2.a.g	$1$	$0$	$1$	$-2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(2+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots$
741.2.a.h	$741$	$2$	741.a	1.a	$1$	$3$	$3$	$5.917$	3.3.621.1	$_{}$	None	None	✓	✓	✓		741.2.a.h	$1$	$0$	$0$	$3$	$-3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
741.2.a.i	$741$	$2$	741.a	1.a	$1$	$4$	$4$	$5.917$	4.4.11324.1	$_{}$	None	None	✓	✓	✓	✓	741.2.a.i	$1$	$1$	$-1$	$-4$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{3})q^{5}+\cdots$
741.2.a.j	$741$	$2$	741.a	1.a	$1$	$5$	$5$	$5.917$	5.5.504568.1	$_{}$	None	None	✓	✓	✓	✓	741.2.a.j	$1$	$1$	$-1$	$-5$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
741.2.a.k	$741$	$2$	741.a	1.a	$1$	$5$	$5$	$5.917$	5.5.2762272.1	$_{}$	None	None	✓	✓	✓		741.2.a.k	$1$	$0$	$1$	$-5$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{3}+\cdots)q^{5}+\cdots$
741.2.a.l	$741$	$2$	741.a	1.a	$1$	$9$	$9$	$5.917$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	741.2.a.l	$1$	$0$	$0$	$9$	$0$	$4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots$
741.2.b.a	$741$	$2$	741.b	13.b	$2$	$22$	$22$	$5.917$		$_{}$	None	None		✓			741.2.b.a	$2$	$0$	$0$	$-22$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
741.2.b.b	$741$	$2$	741.b	13.b	$2$	$22$	$22$	$5.917$		$_{}$	None	None		✓			741.2.b.b	$2$	$0$	$0$	$22$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
741.2.d.a	$741$	$2$	741.d	741.d	$2$	$88$	$88$	$5.917$		$_{}$	None	None		✓	✓	✓	741.2.d.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
741.2.g.a	$741$	$2$	741.g	57.d	$2$	$80$	$80$	$5.917$		$_{}$	None	None		✓	✓	✓	741.2.g.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
741.2.i.a	$741$	$2$	741.i	247.e	$3$	$2$	$1$	$5.917$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			741.2.i.a	$2$	$0$	$-1$	$-1$	$3$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+(1-\zeta_{6})q^{4}+(3-3\zeta_{6})q^{5}+\cdots$
741.2.i.b	$741$	$2$	741.i	247.e	$3$	$2$	$1$	$5.917$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			741.2.i.b	$2$	$0$	$-1$	$1$	$-1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+(1-\zeta_{6})q^{4}+(-1+\cdots)q^{5}+\cdots$
741.2.i.c	$741$	$2$	741.i	247.e	$3$	$2$	$1$	$5.917$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			741.2.i.c	$2$	$0$	$0$	$-1$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{3}+(2-2\zeta_{6})q^{4}+(-4+4\zeta_{6})q^{5}+\cdots$
741.2.i.d	$741$	$2$	741.i	247.e	$3$	$2$	$1$	$5.917$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			741.2.i.d	$2$	$0$	$1$	$-1$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}-\zeta_{6}q^{3}+(1-\zeta_{6})q^{4}+(-1+\cdots)q^{5}+\cdots$
741.2.i.e	$741$	$2$	741.i	247.e	$3$	$4$	$2$	$5.917$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			741.2.i.e	$2$	$0$	$0$	$-2$	$2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+(-1-\beta _{1})q^{3}+3\beta _{1}q^{4}+\cdots$
741.2.i.f	$741$	$2$	741.i	247.e	$3$	$38$	$19$	$5.917$		$_{}$	None	None		✓			741.2.i.f	$2$	$0$	$0$	$-19$	$-1$	$-5$			$\mathrm{SU}(2)[C_{3}]$
741.2.i.g	$741$	$2$	741.i	247.e	$3$	$42$	$21$	$5.917$		$_{}$	None	None		✓	✓		741.2.i.g	$2$	$0$	$1$	$21$	$2$	$-1$			$\mathrm{SU}(2)[C_{3}]$
741.2.j.a	$741$	$2$	741.j	19.c	$3$	$6$	$3$	$5.917$	6.0.2958147.4	$_{}$	None	None		✓			741.2.j.a	$2$	$0$	$-1$	$-3$	$3$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+(-1-\beta _{3})q^{3}+(2\beta _{3}+\beta _{5})q^{4}+\cdots$
741.2.j.b	$741$	$2$	741.j	19.c	$3$	$16$	$8$	$5.917$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			741.2.j.b	$2$	$0$	$-1$	$-8$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{3})q^{2}+\beta _{6}q^{3}+(-1-\beta _{6}+\cdots)q^{4}+\cdots$
741.2.j.c	$741$	$2$	741.j	19.c	$3$	$18$	$9$	$5.917$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		✓			741.2.j.c	$2$	$0$	$0$	$-9$	$2$	$-14$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}-\beta _{8}q^{3}+(-1-\beta _{3}+\beta _{8}+\cdots)q^{4}+\cdots$
741.2.j.d	$741$	$2$	741.j	19.c	$3$	$18$	$9$	$5.917$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		✓			741.2.j.d	$2$	$0$	$0$	$9$	$-2$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(1+\beta _{8})q^{3}+(-1-\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots$
741.2.j.e	$741$	$2$	741.j	19.c	$3$	$22$	$11$	$5.917$		$_{}$	None	None		✓	✓		741.2.j.e	$2$	$0$	$2$	$11$	$0$	$10$			$\mathrm{SU}(2)[C_{3}]$
741.2.k.a	$741$	$2$	741.k	13.c	$3$	$2$	$1$	$5.917$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			741.2.k.a	$2$	$0$	$-2$	$-1$	$8$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$
741.2.k.b	$741$	$2$	741.k	13.c	$3$	$2$	$1$	$5.917$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			741.2.k.b	$2$	$0$	$0$	$-1$	$-4$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{4}-2q^{5}-3\zeta_{6}q^{7}+\cdots$
741.2.k.c	$741$	$2$	741.k	13.c	$3$	$2$	$1$	$5.917$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			741.2.k.c	$2$	$0$	$0$	$-1$	$0$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{4}-3\zeta_{6}q^{7}+\cdots$
741.2.k.d	$741$	$2$	741.k	13.c	$3$	$2$	$1$	$5.917$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			741.2.k.d	$2$	$0$	$2$	$-1$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$
741.2.k.e	$741$	$2$	741.k	13.c	$3$	$2$	$1$	$5.917$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			741.2.k.e	$2$	$0$	$2$	$1$	$-4$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$
741.2.k.f	$741$	$2$	741.k	13.c	$3$	$12$	$6$	$5.917$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			741.2.k.f	$2$	$0$	$-1$	$-6$	$8$	$-6$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{4})q^{2}-\beta _{5}q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
741.2.k.g	$741$	$2$	741.k	13.c	$3$	$18$	$9$	$5.917$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓			741.2.k.g	$2$	$0$	$-3$	$9$	$16$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+\beta _{7}q^{3}+(-1-\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots$
741.2.k.h	$741$	$2$	741.k	13.c	$3$	$20$	$10$	$5.917$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓			741.2.k.h	$2$	$0$	$3$	$-10$	$-4$	$10$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+\beta _{6}q^{3}+(\beta _{1}-\beta _{3}-\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots$
741.2.k.i	$741$	$2$	741.k	13.c	$3$	$20$	$10$	$5.917$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓			741.2.k.i	$2$	$0$	$3$	$10$	$-4$	$6$		$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{2})q^{2}+\beta _{5}q^{3}+(-1+\beta _{5}+\cdots)q^{4}+\cdots$
741.2.l.a	$741$	$2$	741.l	247.h	$3$	$2$	$1$	$5.917$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			741.2.i.d	$2$	$0$	$-2$	$2$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+q^{3}-q^{4}+(-1+\zeta_{6})q^{5}-q^{6}+\cdots$

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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.