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 64 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
1860.1.l.a	$1860$	$1$	1860.l	1860.l	$2$	$1$	$1$	$0.928$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-465}) $	$\Q(\sqrt{31}) $	✓	✓			1860.1.l.a	$4$	$0$	$-1$	$-1$	$1$	$0$		$1$		$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots$
1860.1.l.b	$1860$	$1$	1860.l	1860.l	$2$	$1$	$1$	$0.928$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-465}) $	$\Q(\sqrt{31}) $	✓	✓			1860.1.l.a	$4$	$0$	$-1$	$1$	$1$	$0$		$1$		$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots$
1860.1.l.c	$1860$	$1$	1860.l	1860.l	$2$	$1$	$1$	$0.928$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-465}) $	$\Q(\sqrt{31}) $	✓	✓			1860.1.l.a	$4$	$0$	$1$	$-1$	$-1$	$0$		$1$		$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
1860.1.l.d	$1860$	$1$	1860.l	1860.l	$2$	$1$	$1$	$0.928$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-465}) $	$\Q(\sqrt{31}) $	✓	✓			1860.1.l.a	$4$	$0$	$1$	$1$	$-1$	$0$		$1$		$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
1860.1.be.a	$1860$	$1$	1860.be	1860.ae	$6$	$2$	$1$	$0.928$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-15}) $	None		✓			1860.1.be.a	$4$	$0$	$-1$	$-1$	$1$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$
1860.1.be.b	$1860$	$1$	1860.be	1860.ae	$6$	$2$	$1$	$0.928$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-15}) $	None		✓			1860.1.be.a	$4$	$0$	$-1$	$1$	$1$	$0$		$1$		$q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\cdots$
1860.1.be.c	$1860$	$1$	1860.be	1860.ae	$6$	$2$	$1$	$0.928$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-15}) $	None		✓			1860.1.be.a	$4$	$0$	$1$	$-1$	$-1$	$0$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots$
1860.1.be.d	$1860$	$1$	1860.be	1860.ae	$6$	$2$	$1$	$0.928$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-15}) $	None		✓			1860.1.be.a	$4$	$0$	$1$	$1$	$-1$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$
1860.1.bt.a	$1860$	$1$	1860.bt	1860.at	$10$	$4$	$1$	$0.928$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-15}) $	None		✓			1860.1.bt.a	$4$	$0$	$-1$	$-1$	$-4$	$0$		$1$		$q+\zeta_{10}^{2}q^{2}-\zeta_{10}q^{3}+\zeta_{10}^{4}q^{4}-q^{5}+\cdots$
1860.1.bt.b	$1860$	$1$	1860.bt	1860.at	$10$	$4$	$1$	$0.928$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-15}) $	None		✓			1860.1.bt.a	$4$	$0$	$-1$	$1$	$-4$	$0$		$1$		$q-\zeta_{10}q^{2}+\zeta_{10}q^{3}+\zeta_{10}^{2}q^{4}-q^{5}+\cdots$
1860.1.bt.c	$1860$	$1$	1860.bt	1860.at	$10$	$4$	$1$	$0.928$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-15}) $	None		✓			1860.1.bt.a	$4$	$0$	$1$	$-1$	$4$	$0$		$1$		$q+\zeta_{10}q^{2}-\zeta_{10}q^{3}+\zeta_{10}^{2}q^{4}+q^{5}+\cdots$
1860.1.bt.d	$1860$	$1$	1860.bt	1860.at	$10$	$4$	$1$	$0.928$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-15}) $	None		✓			1860.1.bt.a	$4$	$0$	$1$	$1$	$4$	$0$		$1$		$q-\zeta_{10}^{2}q^{2}+\zeta_{10}q^{3}+\zeta_{10}^{4}q^{4}+q^{5}+\cdots$
1860.1.df.a	$1860$	$1$	1860.df	1860.cf	$30$	$8$	$1$	$0.928$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-15}) $	None		✓			1860.1.df.a	$4$	$0$	$-1$	$-1$	$-4$	$0$		$1$		$q-\zeta_{30}^{8}q^{2}-\zeta_{30}^{14}q^{3}-\zeta_{30}q^{4}+\cdots$
1860.1.df.b	$1860$	$1$	1860.df	1860.cf	$30$	$8$	$1$	$0.928$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-15}) $	None		✓			1860.1.df.a	$4$	$0$	$-1$	$1$	$-4$	$0$		$1$		$q-\zeta_{30}^{4}q^{2}+\zeta_{30}^{14}q^{3}+\zeta_{30}^{8}q^{4}+\cdots$
1860.1.df.c	$1860$	$1$	1860.df	1860.cf	$30$	$8$	$1$	$0.928$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-15}) $	None		✓			1860.1.df.a	$4$	$0$	$1$	$-1$	$4$	$0$		$1$		$q+\zeta_{30}^{4}q^{2}-\zeta_{30}^{14}q^{3}+\zeta_{30}^{8}q^{4}+\cdots$
1860.1.df.d	$1860$	$1$	1860.df	1860.cf	$30$	$8$	$1$	$0.928$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-15}) $	None		✓			1860.1.df.a	$4$	$0$	$1$	$1$	$4$	$0$		$1$		$q+\zeta_{30}^{8}q^{2}+\zeta_{30}^{14}q^{3}-\zeta_{30}q^{4}+\cdots$
1860.2.a.a	$1860$	$2$	1860.a	1.a	$1$	$1$	$1$	$14.852$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1860.2.a.a	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}-2q^{13}-q^{15}-4q^{17}+\cdots$
1860.2.a.b	$1860$	$2$	1860.a	1.a	$1$	$1$	$1$	$14.852$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1860.2.a.b	$1$	$1$	$0$	$1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{7}+q^{9}-4q^{11}-4q^{13}+\cdots$
1860.2.a.c	$1860$	$2$	1860.a	1.a	$1$	$1$	$1$	$14.852$	$\Q$	$_{}$	None	None	✓	✓			1860.2.a.c	$1$	$0$	$0$	$1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+2q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots$
1860.2.a.d	$1860$	$2$	1860.a	1.a	$1$	$2$	$2$	$14.852$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	✓	✓	✓	1860.2.a.d	$1$	$1$	$0$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+\beta q^{7}+q^{9}+(-2-\beta )q^{13}+\cdots$
1860.2.a.e	$1860$	$2$	1860.a	1.a	$1$	$2$	$2$	$14.852$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓	✓	✓	1860.2.a.e	$1$	$1$	$0$	$2$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}-4q^{11}+\cdots$
1860.2.a.f	$1860$	$2$	1860.a	1.a	$1$	$3$	$3$	$14.852$	3.3.564.1	$_{}$	None	None	✓	✓	✓	✓	1860.2.a.f	$1$	$0$	$0$	$-3$	$-3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots$
1860.2.a.g	$1860$	$2$	1860.a	1.a	$1$	$3$	$3$	$14.852$	3.3.404.1	$_{}$	None	None	✓	✓	✓	✓	1860.2.a.g	$1$	$0$	$0$	$3$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+(-1+\beta _{2})q^{7}+q^{9}+2\beta _{2}q^{11}+\cdots$
1860.2.a.h	$1860$	$2$	1860.a	1.a	$1$	$3$	$3$	$14.852$	3.3.7636.1	$_{}$	None	None	✓	✓	✓		1860.2.a.h	$1$	$0$	$0$	$3$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-\beta _{1}q^{7}+q^{9}+2q^{11}+\cdots$
1860.2.a.i	$1860$	$2$	1860.a	1.a	$1$	$4$	$4$	$14.852$	4.4.224148.1	$_{}$	None	None	✓	✓	✓	✓	1860.2.a.i	$1$	$0$	$0$	$-4$	$4$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+(-1+\beta _{1})q^{7}+q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$
1860.2.g.a	$1860$	$2$	1860.g	5.b	$2$	$14$	$14$	$14.852$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		✓			1860.2.g.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{3}-\beta _{1}q^{5}+(-\beta _{7}-\beta _{8})q^{7}+\cdots$
1860.2.g.b	$1860$	$2$	1860.g	5.b	$2$	$14$	$14$	$14.852$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		✓			1860.2.g.b	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+\beta _{13}q^{5}+(-\beta _{2}+\beta _{6}-\beta _{9}+\cdots)q^{7}+\cdots$
1860.2.i.a	$1860$	$2$	1860.i	465.g	$2$	$16$	$16$	$14.852$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	$\Q(\sqrt{-155}) $	None		✓			1860.2.i.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{10}q^{3}+\beta _{5}q^{5}+\beta _{8}q^{9}-\beta _{12}q^{13}+\cdots$
1860.2.i.b	$1860$	$2$	1860.i	465.g	$2$	$48$	$48$	$14.852$		$_{}$	None	None		✓	✓		1860.2.i.b	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1860.2.o.a	$1860$	$2$	1860.o	93.c	$2$	$44$	$44$	$14.852$		$_{}$	None	None		✓	✓	✓	1860.2.o.a	$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{2}]$
1860.2.q.a	$1860$	$2$	1860.q	31.c	$3$	$2$	$1$	$14.852$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1860.2.q.a	$2$	$1$	$0$	$-1$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+\cdots$
1860.2.q.b	$1860$	$2$	1860.q	31.c	$3$	$2$	$1$	$14.852$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1860.2.q.b	$2$	$0$	$0$	$-1$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+4\zeta_{6}q^{11}+\cdots$
1860.2.q.c	$1860$	$2$	1860.q	31.c	$3$	$2$	$1$	$14.852$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1860.2.q.c	$2$	$1$	$0$	$-1$	$-1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots$
1860.2.q.d	$1860$	$2$	1860.q	31.c	$3$	$2$	$1$	$14.852$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1860.2.q.d	$2$	$0$	$0$	$1$	$-1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots$
1860.2.q.e	$1860$	$2$	1860.q	31.c	$3$	$4$	$2$	$14.852$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		✓			1860.2.q.e	$2$	$0$	$0$	$2$	$2$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{1})q^{3}+\beta _{1}q^{5}-\beta _{1}q^{9}+(3\beta _{1}+\cdots)q^{11}+\cdots$
1860.2.q.f	$1860$	$2$	1860.q	31.c	$3$	$6$	$3$	$14.852$	6.0.2958147.4	$_{}$	None	None		✓			1860.2.q.f	$2$	$0$	$0$	$-3$	$-3$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
1860.2.q.g	$1860$	$2$	1860.q	31.c	$3$	$6$	$3$	$14.852$	6.0.64616643.2	$_{}$	None	None		✓			1860.2.q.g	$2$	$0$	$0$	$3$	$3$	$-4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1})q^{3}-\beta _{1}q^{5}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
1860.2.q.h	$1860$	$2$	1860.q	31.c	$3$	$8$	$4$	$14.852$	8.0.$\cdots$.2	$_{}$	None	None		✓			1860.2.q.h	$2$	$0$	$0$	$4$	$-4$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{3}+(-1+\beta _{4})q^{5}+(-\beta _{1}+2\beta _{4}+\cdots)q^{7}+\cdots$
1860.2.q.i	$1860$	$2$	1860.q	31.c	$3$	$12$	$6$	$14.852$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓	✓		1860.2.q.i	$2$	$0$	$0$	$-6$	$6$	$-2$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{7}q^{3}+(1-\beta _{7})q^{5}+(-\beta _{4}-\beta _{9}+\cdots)q^{7}+\cdots$
1860.2.s.a	$1860$	$2$	1860.s	155.f	$4$	$64$	$32$	$14.852$		$_{}$	None	None		✓	✓	✓	1860.2.s.a	$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{4}]$
1860.2.z.a	$1860$	$2$	1860.z	31.d	$5$	$4$	$1$	$14.852$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			1860.2.z.a	$2$	$0$	$0$	$1$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}-q^{5}+\cdots$
1860.2.z.b	$1860$	$2$	1860.z	31.d	$5$	$16$	$4$	$14.852$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1860.2.z.b	$2$	$0$	$0$	$4$	$-16$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{10}q^{3}-q^{5}-\beta _{1}q^{7}-\beta _{9}q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$
1860.2.z.c	$1860$	$2$	1860.z	31.d	$5$	$20$	$5$	$14.852$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓			1860.2.z.c	$2$	$0$	$0$	$-5$	$-20$	$5$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{6}+\beta _{8}+\beta _{10})q^{3}-q^{5}+\cdots$
1860.2.z.d	$1860$	$2$	1860.z	31.d	$5$	$20$	$5$	$14.852$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓			1860.2.z.d	$2$	$0$	$0$	$-5$	$20$	$-5$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{8}q^{3}+q^{5}+(-\beta _{1}-\beta _{3}-\beta _{11}+\cdots)q^{7}+\cdots$
1860.2.z.e	$1860$	$2$	1860.z	31.d	$5$	$20$	$5$	$14.852$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓			1860.2.z.e	$2$	$0$	$0$	$5$	$20$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{5}q^{3}+q^{5}-\beta _{15}q^{7}+\beta _{2}q^{9}+(-\beta _{3}+\cdots)q^{11}+\cdots$
1860.2.bb.a	$1860$	$2$	1860.bb	93.g	$6$	$4$	$2$	$14.852$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			1860.2.bb.a	$4$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}+2\zeta_{12}^{3})q^{3}+(\zeta_{12}-\zeta_{12}^{3})q^{5}+\cdots$
1860.2.bb.b	$1860$	$2$	1860.bb	93.g	$6$	$80$	$40$	$14.852$		$_{}$	None	None		✓	✓		1860.2.bb.b	$4$	$0$	$0$	$0$	$0$	$12$			$\mathrm{SU}(2)[C_{6}]$
1860.2.bj.a	$1860$	$2$	1860.bj	155.j	$6$	$64$	$32$	$14.852$		$_{}$	None	None		✓	✓	✓	1860.2.bj.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
1860.3.e.a	$1860$	$3$	1860.e	155.c	$2$	$64$	$64$	$50.681$		$_{}$	None	None		✓	✓	✓	1860.3.e.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1860.3.k.a	$1860$	$3$	1860.k	31.b	$2$	$44$	$44$	$50.681$		$_{}$	None	None		✓	✓	✓	1860.3.k.a	$2$	$0$	$0$	$0$	$0$	$-16$			$\mathrm{SU}(2)[C_{2}]$

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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.