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 90 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
1140.1.p.a	$1140$	$1$	1140.p	1140.p	$2$	$1$	$1$	$0.569$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-285}) $	$\Q(\sqrt{19}) $	✓	✓			1140.1.p.a	$4$	$0$	$-1$	$1$	$-1$	$0$		$1$		$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
1140.1.p.b	$1140$	$1$	1140.p	1140.p	$2$	$1$	$1$	$0.569$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-285}) $	$\Q(\sqrt{19}) $	✓	✓			1140.1.p.a	$4$	$0$	$-1$	$1$	$1$	$0$		$1$		$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots$
1140.1.p.c	$1140$	$1$	1140.p	1140.p	$2$	$1$	$1$	$0.569$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-285}) $	$\Q(\sqrt{19}) $	✓	✓			1140.1.p.a	$4$	$0$	$1$	$-1$	$-1$	$0$		$1$		$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
1140.1.p.d	$1140$	$1$	1140.p	1140.p	$2$	$1$	$1$	$0.569$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-285}) $	$\Q(\sqrt{19}) $	✓	✓			1140.1.p.a	$4$	$0$	$1$	$-1$	$1$	$0$		$1$		$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
1140.1.p.e	$1140$	$1$	1140.p	1140.p	$2$	$8$	$8$	$0.569$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-95}) $	None		✓			1140.1.p.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{7}q^{3}-\zeta_{16}^{2}q^{4}+\cdots$
1140.1.p.f	$1140$	$1$	1140.p	1140.p	$2$	$8$	$8$	$0.569$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-95}) $	None		✓			1140.1.p.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}q^{2}-\zeta_{16}^{5}q^{3}+\zeta_{16}^{2}q^{4}+\zeta_{16}^{4}q^{5}+\cdots$
1140.1.bb.a	$1140$	$1$	1140.bb	285.n	$6$	$8$	$4$	$0.569$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	1140.1.bb.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{5}q^{3}+\zeta_{24}^{2}q^{5}+(-\zeta_{24}^{3}-\zeta_{24}^{9}+\cdots)q^{7}+\cdots$
1140.1.bl.a	$1140$	$1$	1140.bl	1140.al	$6$	$2$	$1$	$0.569$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-15}) $	None		✓			1140.1.bl.a	$4$	$0$	$-2$	$-1$	$1$	$0$		$1$		$q-q^{2}-\zeta_{6}q^{3}+q^{4}+\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots$
1140.1.bl.b	$1140$	$1$	1140.bl	1140.al	$6$	$2$	$1$	$0.569$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-15}) $	None		✓			1140.1.bl.a	$4$	$0$	$-1$	$1$	$1$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$
1140.1.bl.c	$1140$	$1$	1140.bl	1140.al	$6$	$2$	$1$	$0.569$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-15}) $	None		✓			1140.1.bl.a	$4$	$0$	$1$	$-1$	$-1$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$
1140.1.bl.d	$1140$	$1$	1140.bl	1140.al	$6$	$2$	$1$	$0.569$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-15}) $	None		✓			1140.1.bl.a	$4$	$0$	$2$	$1$	$-1$	$0$		$1$		$q+q^{2}+\zeta_{6}q^{3}+q^{4}-\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots$
1140.1.bx.a	$1140$	$1$	1140.bx	1140.ax	$18$	$6$	$1$	$0.569$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-15}) $	None		✓			1140.1.bx.a	$4$	$0$	$-3$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{3}q^{2}-\zeta_{18}^{4}q^{3}+\zeta_{18}^{6}q^{4}+\cdots$
1140.1.bx.b	$1140$	$1$	1140.bx	1140.ax	$18$	$6$	$1$	$0.569$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-15}) $	None		✓			1140.1.bx.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{8}q^{2}-\zeta_{18}^{4}q^{3}-\zeta_{18}^{7}q^{4}+\cdots$
1140.1.bx.c	$1140$	$1$	1140.bx	1140.ax	$18$	$6$	$1$	$0.569$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-15}) $	None		✓			1140.1.bx.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{8}q^{2}+\zeta_{18}^{4}q^{3}-\zeta_{18}^{7}q^{4}+\cdots$
1140.1.bx.d	$1140$	$1$	1140.bx	1140.ax	$18$	$6$	$1$	$0.569$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-15}) $	None		✓			1140.1.bx.a	$4$	$0$	$3$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{3}q^{2}+\zeta_{18}^{4}q^{3}+\zeta_{18}^{6}q^{4}+\cdots$
1140.2.a.a	$1140$	$2$	1140.a	1.a	$1$	$1$	$1$	$9.103$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1140.2.a.a	$1$	$1$	$0$	$-1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{7}+q^{9}+4q^{11}+q^{15}+\cdots$
1140.2.a.b	$1140$	$2$	1140.a	1.a	$1$	$1$	$1$	$9.103$	$\Q$	$_{}$	None	None	✓	✓			1140.2.a.b	$1$	$0$	$0$	$1$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-4q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots$
1140.2.a.c	$1140$	$2$	1140.a	1.a	$1$	$1$	$1$	$9.103$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1140.2.a.c	$1$	$1$	$0$	$1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{7}+q^{9}-4q^{13}-q^{15}+\cdots$
1140.2.a.d	$1140$	$2$	1140.a	1.a	$1$	$1$	$1$	$9.103$	$\Q$	$_{}$	None	None	✓	✓			1140.2.a.d	$1$	$0$	$0$	$1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+2q^{7}+q^{9}-4q^{13}-q^{15}+\cdots$
1140.2.a.e	$1140$	$2$	1140.a	1.a	$1$	$2$	$2$	$9.103$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓	✓	✓	1140.2.a.e	$1$	$0$	$0$	$-2$	$-2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
1140.2.a.f	$1140$	$2$	1140.a	1.a	$1$	$3$	$3$	$9.103$	3.3.1524.1	$_{}$	None	None	✓	✓	✓	✓	1140.2.a.f	$1$	$0$	$0$	$-3$	$3$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-\beta _{1}q^{7}+q^{9}+(-1-\beta _{2})q^{11}+\cdots$
1140.2.a.g	$1140$	$2$	1140.a	1.a	$1$	$3$	$3$	$9.103$	3.3.564.1	$_{}$	None	None	✓	✓	✓	✓	1140.2.a.g	$1$	$0$	$0$	$3$	$3$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+(1-\beta _{2})q^{7}+q^{9}+(2+\beta _{1}+\cdots)q^{11}+\cdots$
1140.2.b.a	$1140$	$2$	1140.b	76.d	$2$	$2$	$2$	$9.103$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			1140.2.b.a	$2$	$0$	$0$	$-2$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{2}-q^{3}-2q^{4}-q^{5}+\beta q^{6}+2\beta q^{8}+\cdots$
1140.2.b.b	$1140$	$2$	1140.b	76.d	$2$	$2$	$2$	$9.103$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			1140.2.b.a	$2$	$0$	$0$	$2$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{2}+q^{3}-2q^{4}-q^{5}-\beta q^{6}+2\beta q^{8}+\cdots$
1140.2.b.c	$1140$	$2$	1140.b	76.d	$2$	$18$	$18$	$9.103$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓			1140.2.b.c	$2$	$0$	$-1$	$-18$	$-18$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{2}-q^{3}+\beta _{6}q^{4}-q^{5}-\beta _{7}q^{6}+\cdots$
1140.2.b.d	$1140$	$2$	1140.b	76.d	$2$	$18$	$18$	$9.103$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓			1140.2.b.c	$2$	$0$	$1$	$18$	$-18$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{2}+q^{3}+\beta _{6}q^{4}-q^{5}-\beta _{7}q^{6}+\cdots$
1140.2.b.e	$1140$	$2$	1140.b	76.d	$2$	$20$	$20$	$9.103$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓			1140.2.b.e	$2$	$0$	$-1$	$-20$	$20$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
1140.2.b.f	$1140$	$2$	1140.b	76.d	$2$	$20$	$20$	$9.103$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓			1140.2.b.e	$2$	$0$	$1$	$20$	$20$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
1140.2.e.a	$1140$	$2$	1140.e	285.b	$2$	$16$	$16$	$9.103$	$\Q(i, \sqrt{2}, \sqrt{3}, \sqrt{5})$	$_{}$	None	None		✓			1140.2.e.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{18}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{3}+\beta _{5}q^{5}-\beta _{9}q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots$
1140.2.e.b	$1140$	$2$	1140.e	285.b	$2$	$24$	$24$	$9.103$		$_{}$	None	None		✓	✓		1140.2.e.b	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1140.2.f.a	$1140$	$2$	1140.f	5.b	$2$	$6$	$6$	$9.103$	6.0.350464.1	$_{}$	None	None		✓			1140.2.f.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+(-\beta _{1}+\beta _{4})q^{5}-\beta _{5}q^{7}+\cdots$
1140.2.f.b	$1140$	$2$	1140.f	5.b	$2$	$10$	$10$	$9.103$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		✓	✓		1140.2.f.b	$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}+\beta _{9}q^{5}+\beta _{6}q^{7}-q^{9}+(1+\cdots)q^{11}+\cdots$
1140.2.j.a	$1140$	$2$	1140.j	57.d	$2$	$28$	$28$	$9.103$		$_{}$	None	None		✓	✓	✓	1140.2.j.a	$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{2}]$
1140.2.q.a	$1140$	$2$	1140.q	19.c	$3$	$2$	$1$	$9.103$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1140.2.q.a	$2$	$0$	$0$	$-1$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-2q^{7}+\cdots$
1140.2.q.b	$1140$	$2$	1140.q	19.c	$3$	$2$	$1$	$9.103$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1140.2.q.b	$2$	$1$	$0$	$-1$	$-1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-q^{7}+\cdots$
1140.2.q.c	$1140$	$2$	1140.q	19.c	$3$	$2$	$1$	$9.103$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1140.2.q.c	$2$	$0$	$0$	$-1$	$-1$	$8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}+4q^{7}+\cdots$
1140.2.q.d	$1140$	$2$	1140.q	19.c	$3$	$2$	$1$	$9.103$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1140.2.q.d	$2$	$0$	$0$	$-1$	$1$	$-10$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-5q^{7}+\cdots$
1140.2.q.e	$1140$	$2$	1140.q	19.c	$3$	$2$	$1$	$9.103$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1140.2.q.e	$2$	$0$	$0$	$-1$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2q^{7}+\cdots$
1140.2.q.f	$1140$	$2$	1140.q	19.c	$3$	$2$	$1$	$9.103$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1140.2.q.f	$2$	$0$	$0$	$-1$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2q^{7}+\cdots$
1140.2.q.g	$1140$	$2$	1140.q	19.c	$3$	$2$	$1$	$9.103$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1140.2.q.g	$2$	$0$	$0$	$1$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-2q^{7}+\cdots$
1140.2.q.h	$1140$	$2$	1140.q	19.c	$3$	$2$	$1$	$9.103$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1140.2.q.h	$2$	$0$	$0$	$1$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-2q^{7}+\cdots$
1140.2.q.i	$1140$	$2$	1140.q	19.c	$3$	$2$	$1$	$9.103$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1140.2.q.i	$2$	$0$	$0$	$1$	$-1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}+q^{7}+\cdots$
1140.2.q.j	$1140$	$2$	1140.q	19.c	$3$	$2$	$1$	$9.103$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1140.2.q.j	$2$	$0$	$0$	$1$	$1$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-3q^{7}-\zeta_{6}q^{9}+\cdots$
1140.2.q.k	$1140$	$2$	1140.q	19.c	$3$	$2$	$1$	$9.103$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1140.2.q.k	$2$	$0$	$0$	$1$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2q^{7}-\zeta_{6}q^{9}+\cdots$
1140.2.q.l	$1140$	$2$	1140.q	19.c	$3$	$2$	$1$	$9.103$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1140.2.q.l	$2$	$0$	$0$	$1$	$1$	$8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+4q^{7}-\zeta_{6}q^{9}+\cdots$
1140.2.u.a	$1140$	$2$	1140.u	15.e	$4$	$36$	$18$	$9.103$		$_{}$	None	None		✓			1140.2.u.a	$4$	$0$	$0$	$-2$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
1140.2.u.b	$1140$	$2$	1140.u	15.e	$4$	$36$	$18$	$9.103$		$_{}$	None	None		✓			1140.2.u.b	$4$	$0$	$0$	$-2$	$0$	$12$			$\mathrm{SU}(2)[C_{4}]$
1140.2.y.a	$1140$	$2$	1140.y	95.g	$4$	$40$	$20$	$9.103$		$_{}$	None	None		✓	✓	✓	1140.2.y.a	$4$	$0$	$0$	$0$	$-4$	$4$			$\mathrm{SU}(2)[C_{4}]$
1140.2.z.a	$1140$	$2$	1140.z	285.q	$6$	$80$	$40$	$9.103$		$_{}$	None	None		✓	✓	✓	1140.2.z.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
1140.2.bg.a	$1140$	$2$	1140.bg	95.i	$6$	$4$	$2$	$9.103$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			1140.2.bg.a	$4$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+(-\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots$

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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.