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 162 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
567.1.d.a	$567$	$1$	567.d	7.b	$2$	$1$	$1$	$0.283$	$\Q$	$D_{3}$	$\Q(\sqrt{-7}) $	None	✓	✓			567.1.d.a	$2$	$0$	$-1$	$0$	$0$	$1$		$1$		$q-q^{2}+q^{7}+q^{8}-q^{11}-q^{14}-q^{16}+\cdots$
567.1.d.b	$567$	$1$	567.d	7.b	$2$	$1$	$1$	$0.283$	$\Q$	$D_{3}$	$\Q(\sqrt{-7}) $	None	✓	✓			567.1.d.a	$2$	$0$	$1$	$0$	$0$	$1$		$1$		$q+q^{2}+q^{7}-q^{8}+q^{11}+q^{14}-q^{16}+\cdots$
567.1.d.c	$567$	$1$	567.d	7.b	$2$	$2$	$2$	$0.283$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-7}) $	None	✓	✓	✓		567.1.d.c	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\beta q^{2}+2q^{4}-q^{7}-\beta q^{8}+\beta q^{11}+\cdots$
567.1.j.a	$567$	$1$	567.j	63.j	$6$	$2$	$1$	$0.283$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None			✓	✓	189.1.q.a	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q+q^{4}+\zeta_{6}^{2}q^{7}+\zeta_{6}q^{13}+q^{16}-\zeta_{6}q^{19}+\cdots$
567.1.k.a	$567$	$1$	567.k	63.k	$6$	$2$	$1$	$0.283$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None			✓	✓	189.1.m.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{7}+(-1+\zeta_{6}^{2})q^{13}+\cdots$
567.1.l.a	$567$	$1$	567.l	63.l	$6$	$2$	$1$	$0.283$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-7}) $	None		✓			567.1.d.a	$4$	$0$	$-1$	$0$	$0$	$-1$		$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{7}-q^{8}+\zeta_{6}^{2}q^{11}+\cdots$
567.1.l.b	$567$	$1$	567.l	63.l	$6$	$2$	$1$	$0.283$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{21}) $					63.1.d.a	$8$	$0$	$0$	$0$	$0$	$1$		$1$		$q+\zeta_{6}q^{4}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{16}+\zeta_{6}^{2}q^{25}+\cdots$
567.1.l.c	$567$	$1$	567.l	63.l	$6$	$2$	$1$	$0.283$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-7}) $	None		✓			567.1.d.a	$4$	$0$	$1$	$0$	$0$	$-1$		$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{7}+q^{8}-\zeta_{6}^{2}q^{11}+\cdots$
567.1.l.d	$567$	$1$	567.l	63.l	$6$	$4$	$2$	$0.283$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-7}) $	None		✓	✓		567.1.d.c	$8$	$0$	$0$	$0$	$0$	$2$		$3$		$q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}^{2}+\zeta_{12}^{4}+\cdots)q^{4}+\cdots$
567.1.n.a	$567$	$1$	567.n	63.n	$6$	$2$	$1$	$0.283$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None			✓	✓	189.1.q.a	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q-\zeta_{6}q^{4}-\zeta_{6}q^{7}-\zeta_{6}^{2}q^{13}+\zeta_{6}^{2}q^{16}+\cdots$
567.1.t.a	$567$	$1$	567.t	63.t	$6$	$2$	$1$	$0.283$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None			✓	✓	189.1.m.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-q^{4}+\zeta_{6}q^{7}+(1+\zeta_{6})q^{13}+q^{16}+\cdots$
567.2.a.a	$567$	$2$	567.a	1.a	$1$	$1$	$1$	$4.528$	$\Q$	$_{}$	None	None	✓	✓			567.2.a.a	$1$	$1$	$-1$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}-q^{7}+3q^{8}-q^{10}+\cdots$
567.2.a.b	$567$	$2$	567.a	1.a	$1$	$1$	$1$	$4.528$	$\Q$	$_{}$	None	None	✓	✓			567.2.a.a	$1$	$1$	$1$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}-q^{7}-3q^{8}-q^{10}+\cdots$
567.2.a.c	$567$	$2$	567.a	1.a	$1$	$3$	$3$	$4.528$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓		✓	✓	63.2.f.a	$1$	$1$	$-3$	$0$	$-3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots$
567.2.a.d	$567$	$2$	567.a	1.a	$1$	$3$	$3$	$4.528$	3.3.321.1	$_{}$	None	None	✓		✓		63.2.f.b	$1$	$1$	$-1$	$0$	$-5$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-2-\beta _{2})q^{5}+\cdots$
567.2.a.e	$567$	$2$	567.a	1.a	$1$	$3$	$3$	$4.528$	3.3.621.1	$_{}$	None	None	✓	✓			567.2.a.e	$1$	$0$	$0$	$0$	$-3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots$
567.2.a.f	$567$	$2$	567.a	1.a	$1$	$3$	$3$	$4.528$	3.3.621.1	$_{}$	None	None	✓	✓			567.2.a.e	$1$	$0$	$0$	$0$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots$
567.2.a.g	$567$	$2$	567.a	1.a	$1$	$3$	$3$	$4.528$	3.3.321.1	$_{}$	None	None	✓				63.2.f.b	$1$	$0$	$1$	$0$	$5$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(2+\beta _{2})q^{5}+\cdots$
567.2.a.h	$567$	$2$	567.a	1.a	$1$	$3$	$3$	$4.528$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓				63.2.f.a	$1$	$0$	$3$	$0$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
567.2.a.i	$567$	$2$	567.a	1.a	$1$	$4$	$4$	$4.528$	$\Q(\sqrt{3}, \sqrt{7})$	$_{}$	None	None	✓	✓	✓		567.2.a.i	$2$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}-\beta _{2}q^{4}-2\beta _{1}q^{5}-q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots$
567.2.c.a	$567$	$2$	567.c	21.c	$2$	$8$	$8$	$4.528$	8.0.$\cdots$.3	$_{}$	$\Q(\sqrt{-7}) $	None		✓			567.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$3^{5}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{4}q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots$
567.2.c.b	$567$	$2$	567.c	21.c	$2$	$8$	$8$	$4.528$	8.0.$\cdots$.6	$_{}$	None	None		✓			567.2.c.b	$4$	$0$	$0$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{3}-\beta _{5})q^{2}-\beta _{1}q^{4}+\beta _{2}q^{5}+\cdots$
567.2.c.c	$567$	$2$	567.c	21.c	$2$	$12$	$12$	$4.528$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None			✓		63.2.o.a	$4$	$0$	$0$	$0$	$0$	$4$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-\beta _{4}q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{6}+\cdots)q^{7}+\cdots$
567.2.e.a	$567$	$2$	567.e	7.c	$3$	$2$	$1$	$4.528$	$\Q(\sqrt{-3}) $	$_{}$	None	None					63.2.g.a	$2$	$1$	$-1$	$0$	$1$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots$
567.2.e.b	$567$	$2$	567.e	7.c	$3$	$2$	$1$	$4.528$	$\Q(\sqrt{-3}) $	$_{}$	None	None					63.2.g.a	$2$	$0$	$1$	$0$	$-1$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots$
567.2.e.c	$567$	$2$	567.e	7.c	$3$	$8$	$4$	$4.528$	8.0.1767277521.3	$_{}$	None	None		✓			567.2.e.c	$2$	$0$	$-1$	$0$	$-2$	$1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{2}-\beta _{6})q^{2}+(-\beta _{5}+\beta _{7})q^{4}+\cdots$
567.2.e.d	$567$	$2$	567.e	7.c	$3$	$8$	$4$	$4.528$	8.0.1767277521.3	$_{}$	None	None		✓			567.2.e.c	$2$	$0$	$1$	$0$	$2$	$1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{2}+\beta _{6})q^{2}+(-\beta _{5}+\beta _{7})q^{4}+(1+\cdots)q^{5}+\cdots$
567.2.e.e	$567$	$2$	567.e	7.c	$3$	$10$	$5$	$4.528$	10.0.$\cdots$.1	$_{}$	None	None					63.2.g.b	$2$	$0$	$-2$	$0$	$-4$	$5$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+(-1+\cdots)q^{5}+\cdots$
567.2.e.f	$567$	$2$	567.e	7.c	$3$	$10$	$5$	$4.528$	10.0.$\cdots$.1	$_{}$	None	None					63.2.g.b	$2$	$0$	$2$	$0$	$4$	$5$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+(1+\cdots)q^{5}+\cdots$
567.2.e.g	$567$	$2$	567.e	7.c	$3$	$16$	$8$	$4.528$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓		567.2.e.g	$4$	$0$	$0$	$0$	$0$	$6$		$3^{5}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-\beta _{5}-\beta _{7}-\beta _{8}-\beta _{12}+\cdots)q^{4}+\cdots$
567.2.f.a	$567$	$2$	567.f	9.c	$3$	$2$	$1$	$4.528$	$\Q(\sqrt{-3}) $	$_{}$	None	None					189.2.a.a	$2$	$1$	$-2$	$0$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$
567.2.f.b	$567$	$2$	567.f	9.c	$3$	$2$	$1$	$4.528$	$\Q(\sqrt{-3}) $	$_{}$	None	None					21.2.a.a	$2$	$0$	$-1$	$0$	$-2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots$
567.2.f.c	$567$	$2$	567.f	9.c	$3$	$2$	$1$	$4.528$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			567.2.a.a	$2$	$0$	$-1$	$0$	$1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots$
567.2.f.d	$567$	$2$	567.f	9.c	$3$	$2$	$1$	$4.528$	$\Q(\sqrt{-3}) $	$_{}$	None	None					189.2.a.b	$2$	$0$	$0$	$0$	$-3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{4}-3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots$
567.2.f.e	$567$	$2$	567.f	9.c	$3$	$2$	$1$	$4.528$	$\Q(\sqrt{-3}) $	$_{}$	None	None					189.2.a.b	$2$	$0$	$0$	$0$	$3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{4}+3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots$
567.2.f.f	$567$	$2$	567.f	9.c	$3$	$2$	$1$	$4.528$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			567.2.a.a	$2$	$0$	$1$	$0$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots$
567.2.f.g	$567$	$2$	567.f	9.c	$3$	$2$	$1$	$4.528$	$\Q(\sqrt{-3}) $	$_{}$	None	None					21.2.a.a	$2$	$0$	$1$	$0$	$2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots$
567.2.f.h	$567$	$2$	567.f	9.c	$3$	$2$	$1$	$4.528$	$\Q(\sqrt{-3}) $	$_{}$	None	None					189.2.a.a	$2$	$0$	$2$	$0$	$1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots$
567.2.f.i	$567$	$2$	567.f	9.c	$3$	$4$	$2$	$4.528$	$\Q(\sqrt{-3}, \sqrt{7})$	$_{}$	None	None					189.2.a.f	$4$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+5\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots$
567.2.f.j	$567$	$2$	567.f	9.c	$3$	$4$	$2$	$4.528$	$\Q(\zeta_{12})$	$_{}$	None	None					63.2.a.b	$4$	$0$	$0$	$0$	$0$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}+(-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
567.2.f.k	$567$	$2$	567.f	9.c	$3$	$4$	$2$	$4.528$	$\Q(\zeta_{12})$	$_{}$	None	None					189.2.a.e	$4$	$0$	$0$	$0$	$0$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}+(\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
567.2.f.l	$567$	$2$	567.f	9.c	$3$	$6$	$3$	$4.528$	6.0.1156923.1	$_{}$	None	None		✓			567.2.a.e	$2$	$0$	$0$	$0$	$-3$	$-3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{2}+(-\beta _{1}+\beta _{2}-2\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
567.2.f.m	$567$	$2$	567.f	9.c	$3$	$6$	$3$	$4.528$	6.0.1156923.1	$_{}$	None	None		✓			567.2.a.e	$2$	$0$	$0$	$0$	$3$	$-3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{2}+(-\beta _{1}+\beta _{2}-2\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
567.2.f.n	$567$	$2$	567.f	9.c	$3$	$8$	$4$	$4.528$	8.0.49787136.1	$_{}$	None	None		✓	✓		567.2.a.i	$4$	$0$	$0$	$0$	$0$	$4$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}+\beta _{4}q^{4}-2\beta _{7}q^{5}+(1-\beta _{5}+\cdots)q^{7}+\cdots$
567.2.g.a	$567$	$2$	567.g	63.g	$3$	$2$	$1$	$4.528$	$\Q(\sqrt{-3}) $	$_{}$	None	None					21.2.e.a	$2$	$1$	$-2$	$0$	$-4$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-2q^{5}+\cdots$
567.2.g.b	$567$	$2$	567.g	63.g	$3$	$2$	$1$	$4.528$	$\Q(\sqrt{-3}) $	$_{}$	None	None					189.2.e.a	$2$	$0$	$-1$	$0$	$-8$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-4q^{5}+(2+\cdots)q^{7}+\cdots$
567.2.g.c	$567$	$2$	567.g	63.g	$3$	$2$	$1$	$4.528$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None					189.2.e.b	$4$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+2\zeta_{6}q^{4}+(-3+2\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{13}+\cdots$
567.2.g.d	$567$	$2$	567.g	63.g	$3$	$2$	$1$	$4.528$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None					63.2.e.a	$4$	$0$	$0$	$0$	$0$	$5$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+2\zeta_{6}q^{4}+(3-\zeta_{6})q^{7}+(7-7\zeta_{6})q^{13}+\cdots$
567.2.g.e	$567$	$2$	567.g	63.g	$3$	$2$	$1$	$4.528$	$\Q(\sqrt{-3}) $	$_{}$	None	None					189.2.e.a	$2$	$0$	$1$	$0$	$8$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+4q^{5}+(2-3\zeta_{6})q^{7}+\cdots$
567.2.g.f	$567$	$2$	567.g	63.g	$3$	$2$	$1$	$4.528$	$\Q(\sqrt{-3}) $	$_{}$	None	None					21.2.e.a	$2$	$0$	$2$	$0$	$4$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+2q^{5}+(-1+\cdots)q^{7}+\cdots$

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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.