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 98 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
1197.1.h.a	$1197$	$1$	1197.h	399.h	$2$	$4$	$4$	$0.597$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-19}) $	None		✓	✓	✓	1197.1.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q-q^{4}+(\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}+(\zeta_{8}+\cdots)q^{11}+\cdots$
1197.1.bt.a	$1197$	$1$	1197.bt	399.s	$6$	$8$	$4$	$0.597$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-19}) $	None		✓	✓	✓	1197.1.bt.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{8}q^{4}+(-\zeta_{24}^{9}+\zeta_{24}^{11})q^{5}+\cdots$
1197.1.ci.a	$1197$	$1$	1197.ci	133.m	$6$	$2$	$1$	$0.597$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			1197.1.ci.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q+\zeta_{6}q^{4}+\zeta_{6}q^{7}+(-1+\zeta_{6}^{2})q^{13}+\cdots$
1197.1.ci.b	$1197$	$1$	1197.ci	133.m	$6$	$2$	$1$	$0.597$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			1197.1.ci.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q+\zeta_{6}q^{4}-\zeta_{6}^{2}q^{7}+(1-\zeta_{6}^{2})q^{13}+\cdots$
1197.1.ci.c	$1197$	$1$	1197.ci	133.m	$6$	$4$	$2$	$0.597$	$\Q(\zeta_{12})$	$A_{4}$	None	None			✓		133.1.m.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{5}q^{5}-\zeta_{12}^{3}q^{7}+\cdots$
1197.1.cz.a	$1197$	$1$	1197.cz	133.r	$6$	$2$	$1$	$0.597$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-19}) $	None					133.1.r.a	$4$	$0$	$0$	$0$	$-1$	$-1$		$1$		$q+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{11}+\cdots$
1197.1.cz.b	$1197$	$1$	1197.cz	133.r	$6$	$4$	$2$	$0.597$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-19}) $	None		✓	✓		1197.1.cz.b	$8$	$0$	$0$	$0$	$0$	$2$		$3$		$q-\zeta_{12}^{2}q^{4}+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{5}+\cdots$
1197.1.ex.a	$1197$	$1$	1197.ex	133.x	$18$	$6$	$1$	$0.597$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1197.1.ex.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}q^{4}+\zeta_{18}^{7}q^{7}+(\zeta_{18}^{3}+\zeta_{18}^{8}+\cdots)q^{13}+\cdots$
1197.1.fp.a	$1197$	$1$	1197.fp	133.z	$18$	$6$	$1$	$0.597$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1197.1.ex.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{7}q^{4}-\zeta_{18}^{8}q^{7}+(-\zeta_{18}^{3}-\zeta_{18}^{8}+\cdots)q^{13}+\cdots$
1197.1.gi.a	$1197$	$1$	1197.gi	133.ad	$18$	$6$	$1$	$0.597$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1197.1.gi.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}q^{4}+\zeta_{18}^{7}q^{7}+(\zeta_{18}^{3}+\zeta_{18}^{8}+\cdots)q^{13}+\cdots$
1197.1.hb.a	$1197$	$1$	1197.hb	133.ae	$18$	$6$	$1$	$0.597$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1197.1.gi.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{7}q^{4}-\zeta_{18}^{8}q^{7}+(\zeta_{18}^{3}+\zeta_{18}^{8}+\cdots)q^{13}+\cdots$
1197.2.a.a	$1197$	$2$	1197.a	1.a	$1$	$1$	$1$	$9.558$	$\Q$	$_{}$	None	None	✓				399.2.a.c	$1$	$0$	$-1$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{7}+3q^{8}+2q^{11}-4q^{13}+\cdots$
1197.2.a.b	$1197$	$2$	1197.a	1.a	$1$	$1$	$1$	$9.558$	$\Q$	$_{}$	None	None	✓	✓			1197.2.a.b	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{7}+3q^{8}-2q^{11}-6q^{13}+\cdots$
1197.2.a.c	$1197$	$2$	1197.a	1.a	$1$	$1$	$1$	$9.558$	$\Q$	$_{}$	None	None	✓				399.2.a.b	$1$	$0$	$1$	$0$	$-4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-4q^{5}-q^{7}-3q^{8}-4q^{10}+\cdots$
1197.2.a.d	$1197$	$2$	1197.a	1.a	$1$	$1$	$1$	$9.558$	$\Q$	$_{}$	None	None	✓	✓			1197.2.a.b	$1$	$1$	$1$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{7}-3q^{8}+2q^{11}-6q^{13}+\cdots$
1197.2.a.e	$1197$	$2$	1197.a	1.a	$1$	$1$	$1$	$9.558$	$\Q$	$_{}$	None	None	✓				399.2.a.a	$1$	$0$	$1$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{7}-3q^{8}+2q^{11}+q^{14}+\cdots$
1197.2.a.f	$1197$	$2$	1197.a	1.a	$1$	$2$	$2$	$9.558$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1197.2.a.f	$1$	$0$	$-2$	$0$	$-4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-2q^{5}+\cdots$
1197.2.a.g	$1197$	$2$	1197.a	1.a	$1$	$2$	$2$	$9.558$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				133.2.a.c	$1$	$1$	$-1$	$0$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}+q^{7}+(-1+\cdots)q^{8}+\cdots$
1197.2.a.h	$1197$	$2$	1197.a	1.a	$1$	$2$	$2$	$9.558$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓				133.2.a.b	$1$	$0$	$1$	$0$	$6$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}+3q^{5}+q^{7}+3q^{8}+\cdots$
1197.2.a.i	$1197$	$2$	1197.a	1.a	$1$	$2$	$2$	$9.558$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1197.2.a.f	$1$	$0$	$2$	$0$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2q^{5}+q^{7}+\cdots$
1197.2.a.j	$1197$	$2$	1197.a	1.a	$1$	$2$	$2$	$9.558$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				133.2.a.a	$1$	$0$	$3$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}+(1-2\beta )q^{5}-q^{7}+\cdots$
1197.2.a.k	$1197$	$2$	1197.a	1.a	$1$	$3$	$3$	$9.558$	3.3.229.1	$_{}$	None	None	✓				133.2.a.d	$1$	$1$	$-2$	$0$	$2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(2+\beta _{1})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
1197.2.a.l	$1197$	$2$	1197.a	1.a	$1$	$3$	$3$	$9.558$	3.3.148.1	$_{}$	None	None	✓				399.2.a.d	$1$	$1$	$-1$	$0$	$-4$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$
1197.2.a.m	$1197$	$2$	1197.a	1.a	$1$	$3$	$3$	$9.558$	3.3.404.1	$_{}$	None	None	✓		✓		399.2.a.e	$1$	$0$	$-1$	$0$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$
1197.2.a.n	$1197$	$2$	1197.a	1.a	$1$	$4$	$4$	$9.558$	$\Q(\zeta_{24})^+$	$_{}$	None	None	✓	✓	✓	✓	1197.2.a.n	$2$	$1$	$0$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots$
1197.2.a.o	$1197$	$2$	1197.a	1.a	$1$	$5$	$5$	$9.558$	5.5.368464.1	$_{}$	None	None	✓		✓		399.2.a.g	$1$	$1$	$-3$	$0$	$-4$	$5$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
1197.2.a.p	$1197$	$2$	1197.a	1.a	$1$	$5$	$5$	$9.558$	5.5.1240016.1	$_{}$	None	None	✓		✓		399.2.a.f	$1$	$0$	$-1$	$0$	$2$	$5$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}+(1+\beta _{4})q^{4}-\beta _{2}q^{5}+q^{7}+\cdots$
1197.2.a.q	$1197$	$2$	1197.a	1.a	$1$	$6$	$6$	$9.558$	6.6.12730624.1	$_{}$	None	None	✓	✓	✓	✓	1197.2.a.q	$2$	$0$	$0$	$0$	$0$	$-6$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(1+\beta _{4})q^{4}+(\beta _{2}+\beta _{3})q^{5}+\cdots$
1197.2.c.a	$1197$	$2$	1197.c	133.c	$2$	$2$	$2$	$9.558$	$\Q(\sqrt{-3}) $	$_{}$	None	None					399.2.c.a	$2$	$0$	$0$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{2}-q^{4}-2\beta q^{5}+(-\beta-2)q^{7}+\cdots$
1197.2.c.b	$1197$	$2$	1197.c	133.c	$2$	$2$	$2$	$9.558$	$\Q(\sqrt{-3}) $	$_{}$	None	None					399.2.c.a	$2$	$0$	$0$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{2}-q^{4}+2\beta q^{5}+(\beta-2)q^{7}+\cdots$
1197.2.c.c	$1197$	$2$	1197.c	133.c	$2$	$2$	$2$	$9.558$	$\Q(\sqrt{-19}) $	$_{}$	$\Q(\sqrt{-19}) $	None					133.2.c.a	$4$	$0$	$0$	$0$	$0$	$-3$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{4}+(1-2\beta )q^{5}+(-1-\beta )q^{7}+\cdots$
1197.2.c.d	$1197$	$2$	1197.c	133.c	$2$	$4$	$4$	$9.558$	$\Q(i, \sqrt{13})$	$_{}$	None	None					133.2.c.b	$2$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}-\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots$
1197.2.c.e	$1197$	$2$	1197.c	133.c	$2$	$4$	$4$	$9.558$	$\Q(i, \sqrt{13})$	$_{}$	None	None					133.2.c.b	$2$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots$
1197.2.c.f	$1197$	$2$	1197.c	133.c	$2$	$4$	$4$	$9.558$	$\Q(i, \sqrt{19})$	$_{}$	$\Q(\sqrt{-19}) $	None		✓			1197.2.c.f	$8$	$0$	$0$	$0$	$0$	$6$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{4}-\beta _{2}q^{5}+(2+\beta _{3})q^{7}+(-2\beta _{1}+\cdots)q^{11}+\cdots$
1197.2.c.g	$1197$	$2$	1197.c	133.c	$2$	$8$	$8$	$9.558$	8.0.49787136.1	$_{}$	None	None		✓			1197.2.c.g	$8$	$0$	$0$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{4}+\beta _{2}q^{5}+\beta _{3}q^{7}+\beta _{1}q^{8}+\cdots$
1197.2.c.h	$1197$	$2$	1197.c	133.c	$2$	$12$	$12$	$9.558$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None					399.2.c.c	$2$	$0$	$0$	$0$	$0$	$5$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{6}q^{5}+(1+\cdots)q^{7}+\cdots$
1197.2.c.i	$1197$	$2$	1197.c	133.c	$2$	$12$	$12$	$9.558$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None					399.2.c.c	$2$	$0$	$0$	$0$	$0$	$5$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+\beta _{6}q^{5}+(1+\cdots)q^{7}+\cdots$
1197.2.c.j	$1197$	$2$	1197.c	133.c	$2$	$16$	$16$	$9.558$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	$\Q(\sqrt{-399}) $	None		✓	✓		1197.2.c.j	$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{8}q^{2}+(-2+\beta _{6})q^{4}+\beta _{3}q^{5}+\beta _{4}q^{7}+\cdots$
1197.2.d.a	$1197$	$2$	1197.d	21.c	$2$	$8$	$8$	$9.558$	$\Q(\zeta_{24})$	$_{}$	None	None		✓			1197.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{5}+\beta_{3})q^{2}-\beta_{4} q^{4}+2\beta_{6} q^{5}+\cdots$
1197.2.d.b	$1197$	$2$	1197.d	21.c	$2$	$40$	$40$	$9.558$		$_{}$	None	None		✓	✓		1197.2.d.b	$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{2}]$
1197.2.f.a	$1197$	$2$	1197.f	57.d	$2$	$4$	$4$	$9.558$	$\Q(\sqrt{-2}, \sqrt{5})$	$_{}$	None	None		✓			1197.2.f.a	$4$	$0$	$0$	$0$	$0$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+3q^{4}+2\beta _{1}q^{5}-q^{7}+\beta _{3}q^{8}+\cdots$
1197.2.f.b	$1197$	$2$	1197.f	57.d	$2$	$16$	$16$	$9.558$	16.0.$\cdots$.1	$_{}$	None	None		✓			1197.2.f.b	$4$	$0$	$0$	$0$	$0$	$-16$		$2^{6}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{2}+(\beta _{1}+\beta _{5})q^{4}+\beta _{9}q^{5}-q^{7}+\cdots$
1197.2.f.c	$1197$	$2$	1197.f	57.d	$2$	$20$	$20$	$9.558$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓	✓		1197.2.f.c	$4$	$0$	$0$	$0$	$0$	$20$		$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{11}q^{2}+(1-\beta _{1})q^{4}-\beta _{18}q^{5}+q^{7}+\cdots$
1197.2.j.a	$1197$	$2$	1197.j	7.c	$3$	$2$	$1$	$9.558$	$\Q(\sqrt{-3}) $	$_{}$	None	None					399.2.j.b	$2$	$0$	$0$	$0$	$2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{4}+2\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots$
1197.2.j.b	$1197$	$2$	1197.j	7.c	$3$	$2$	$1$	$9.558$	$\Q(\sqrt{-3}) $	$_{}$	None	None					399.2.j.a	$2$	$0$	$2$	$0$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots$
1197.2.j.c	$1197$	$2$	1197.j	7.c	$3$	$2$	$1$	$9.558$	$\Q(\sqrt{-3}) $	$_{}$	None	None					133.2.f.a	$2$	$0$	$2$	$0$	$3$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots$
1197.2.j.d	$1197$	$2$	1197.j	7.c	$3$	$4$	$2$	$9.558$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None					399.2.j.c	$2$	$0$	$-2$	$0$	$-2$	$-10$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+(-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1197.2.j.e	$1197$	$2$	1197.j	7.c	$3$	$4$	$2$	$9.558$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None					133.2.f.c	$2$	$0$	$-2$	$0$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+(-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1197.2.j.f	$1197$	$2$	1197.j	7.c	$3$	$4$	$2$	$9.558$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			1197.2.j.f	$4$	$0$	$0$	$0$	$0$	$10$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta_{2} q^{2}+(\beta_1-1)q^{4}-\beta_{2} q^{5}+\cdots$
1197.2.j.g	$1197$	$2$	1197.j	7.c	$3$	$4$	$2$	$9.558$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None					133.2.f.b	$2$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}-2\beta _{1}q^{5}+(2+3\beta _{2})q^{7}-2\beta _{3}q^{8}+\cdots$

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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.