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 114 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
867.1.b.a	$867$	$1$	867.b	3.b	$2$	$1$	$1$	$0.433$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	✓			867.1.b.a	$2$	$0$	$0$	$-1$	$0$	$1$		$1$		$q-q^{3}+q^{4}+q^{7}+q^{9}-q^{12}-q^{13}+\cdots$
867.1.b.b	$867$	$1$	867.b	3.b	$2$	$1$	$1$	$0.433$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	✓			867.1.b.a	$2$	$0$	$0$	$1$	$0$	$-1$		$1$		$q+q^{3}+q^{4}-q^{7}+q^{9}+q^{12}-q^{13}+\cdots$
867.1.c.a	$867$	$1$	867.c	51.c	$2$	$2$	$2$	$0.433$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	867.1.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{3}+q^{4}-i q^{7}-q^{9}-i q^{12}+\cdots$
867.1.f.a	$867$	$1$	867.f	51.f	$4$	$4$	$2$	$0.433$	$\Q(\zeta_{8})$	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	867.1.b.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{3}-q^{4}+\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}+\cdots$
867.1.g.a	$867$	$1$	867.g	51.g	$8$	$8$	$2$	$0.433$	$\Q(\zeta_{16})$	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	867.1.b.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}^{7}q^{3}+\zeta_{16}^{4}q^{4}-\zeta_{16}^{5}q^{7}+\cdots$
867.2.a.a	$867$	$2$	867.a	1.a	$1$	$1$	$1$	$6.923$	$\Q$	$_{}$	None	None	✓				51.2.d.b	$1$	$1$	$-1$	$-1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{6}-4q^{7}+3q^{8}+\cdots$
867.2.a.b	$867$	$2$	867.a	1.a	$1$	$1$	$1$	$6.923$	$\Q$	$_{}$	None	None	✓				51.2.d.b	$1$	$0$	$-1$	$1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}+4q^{7}+3q^{8}+\cdots$
867.2.a.c	$867$	$2$	867.a	1.a	$1$	$1$	$1$	$6.923$	$\Q$	$_{}$	None	None	✓				51.2.a.a	$1$	$1$	$0$	$-1$	$-3$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-3q^{5}+4q^{7}+q^{9}+3q^{11}+\cdots$
867.2.a.d	$867$	$2$	867.a	1.a	$1$	$1$	$1$	$6.923$	$\Q$	$_{}$	None	None	✓				51.2.d.a	$1$	$1$	$2$	$-1$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-3q^{5}-2q^{6}+\cdots$
867.2.a.e	$867$	$2$	867.a	1.a	$1$	$1$	$1$	$6.923$	$\Q$	$_{}$	None	None	✓				51.2.d.a	$1$	$0$	$2$	$1$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+3q^{5}+2q^{6}+\cdots$
867.2.a.f	$867$	$2$	867.a	1.a	$1$	$2$	$2$	$6.923$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				51.2.a.b	$1$	$0$	$-1$	$2$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(2+\beta )q^{4}+(-1-\beta )q^{5}+\cdots$
867.2.a.g	$867$	$2$	867.a	1.a	$1$	$2$	$2$	$6.923$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			867.2.a.g	$1$	$0$	$2$	$-2$	$0$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}+2\beta q^{5}+\cdots$
867.2.a.h	$867$	$2$	867.a	1.a	$1$	$2$	$2$	$6.923$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			867.2.a.g	$1$	$0$	$2$	$2$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}-2\beta q^{5}+\cdots$
867.2.a.i	$867$	$2$	867.a	1.a	$1$	$3$	$3$	$6.923$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	✓			867.2.a.i	$1$	$1$	$-3$	$-3$	$3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-q^{3}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots$
867.2.a.j	$867$	$2$	867.a	1.a	$1$	$3$	$3$	$6.923$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	✓			867.2.a.i	$1$	$1$	$-3$	$3$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots$
867.2.a.k	$867$	$2$	867.a	1.a	$1$	$4$	$4$	$6.923$	4.4.7232.1	$_{}$	None	None	✓		✓		51.2.e.a	$1$	$1$	$-2$	$-4$	$-6$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+\beta _{3})q^{2}-q^{3}+(1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
867.2.a.l	$867$	$2$	867.a	1.a	$1$	$4$	$4$	$6.923$	4.4.7232.1	$_{}$	None	None	✓				51.2.e.a	$1$	$0$	$-2$	$4$	$6$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+\beta _{3})q^{2}+q^{3}+(1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
867.2.a.m	$867$	$2$	867.a	1.a	$1$	$4$	$4$	$6.923$	$\Q(\zeta_{16})^+$	$_{}$	None	None	✓				51.2.h.a	$1$	$0$	$0$	$-4$	$4$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(1+\beta _{1}+\beta _{3})q^{5}+\cdots$
867.2.a.n	$867$	$2$	867.a	1.a	$1$	$4$	$4$	$6.923$	$\Q(\zeta_{16})^+$	$_{}$	None	None	✓		✓		51.2.h.a	$1$	$1$	$0$	$4$	$-4$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$
867.2.a.o	$867$	$2$	867.a	1.a	$1$	$6$	$6$	$6.923$	6.6.3418281.1	$_{}$	None	None	✓	✓	✓		867.2.a.o	$1$	$0$	$3$	$-6$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots$
867.2.a.p	$867$	$2$	867.a	1.a	$1$	$6$	$6$	$6.923$	6.6.3418281.1	$_{}$	None	None	✓	✓	✓		867.2.a.o	$1$	$0$	$3$	$6$	$-3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots$
867.2.d.a	$867$	$2$	867.d	17.b	$2$	$2$	$2$	$6.923$	$\Q(\sqrt{-1}) $	$_{}$	None	None					51.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}-2 q^{4}-3 i q^{5}-4 i q^{7}+\cdots$
867.2.d.b	$867$	$2$	867.d	17.b	$2$	$4$	$4$	$6.923$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			867.2.a.g	$2$	$0$	$-4$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta_{3}-1)q^{2}+\beta_1 q^{3}+(2\beta_{3}+1)q^{4}+\cdots$
867.2.d.c	$867$	$2$	867.d	17.b	$2$	$4$	$4$	$6.923$	$\Q(i, \sqrt{17})$	$_{}$	None	None					51.2.a.b	$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{3})q^{2}+\beta _{2}q^{3}+(3-\beta _{3})q^{4}+\cdots$
867.2.d.d	$867$	$2$	867.d	17.b	$2$	$6$	$6$	$6.923$	6.0.419904.1	$_{}$	None	None		✓			867.2.a.i	$2$	$0$	$6$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{2}-\beta _{4})q^{2}+\beta _{3}q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
867.2.d.e	$867$	$2$	867.d	17.b	$2$	$8$	$8$	$6.923$	$\Q(\zeta_{16})$	$_{}$	None	None					51.2.h.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{7} q^{2}+\beta_1 q^{3}-\beta_{6} q^{4}+(\beta_{4}-\beta_{2}-\beta_1)q^{5}+\cdots$
867.2.d.f	$867$	$2$	867.d	17.b	$2$	$8$	$8$	$6.923$	8.0.836829184.2	$_{}$	None	None					51.2.e.a	$2$	$0$	$4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}+\beta _{3}q^{3}+(1+\beta _{6}-\beta _{7})q^{4}+\cdots$
867.2.d.g	$867$	$2$	867.d	17.b	$2$	$12$	$12$	$6.923$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	✓		867.2.a.o	$2$	$0$	$-6$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{2}+\beta _{6})q^{2}+\beta _{3}q^{3}+(2+\beta _{2}+\cdots)q^{4}+\cdots$
867.2.e.a	$867$	$2$	867.e	17.c	$4$	$4$	$2$	$6.923$	$\Q(\zeta_{8})$	$_{}$	None	None					51.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-2\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-2q^{4}+3\zeta_{8}q^{5}+\cdots$
867.2.e.b	$867$	$2$	867.e	17.c	$4$	$4$	$2$	$6.923$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			867.2.a.g	$2$	$0$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{2}+\zeta_{8}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots$
867.2.e.c	$867$	$2$	867.e	17.c	$4$	$4$	$2$	$6.923$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			867.2.a.g	$2$	$0$	$0$	$0$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{2}-\zeta_{8}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots$
867.2.e.d	$867$	$2$	867.e	17.c	$4$	$4$	$2$	$6.923$	$\Q(\zeta_{8})$	$_{}$	None	None					51.2.d.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{3}+q^{4}-\zeta_{8}q^{6}+\cdots$
867.2.e.e	$867$	$2$	867.e	17.c	$4$	$4$	$2$	$6.923$	$\Q(\zeta_{8})$	$_{}$	None	None					51.2.a.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}q^{3}+2q^{4}+3\zeta_{8}q^{5}+4\zeta_{8}^{3}q^{7}+\cdots$
867.2.e.f	$867$	$2$	867.e	17.c	$4$	$8$	$4$	$6.923$	8.0.5473632256.1	$_{}$	None	None					51.2.a.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{5}q^{2}+\beta _{7}q^{3}+(-2-\beta _{4})q^{4}+(\beta _{6}+\cdots)q^{5}+\cdots$
867.2.e.g	$867$	$2$	867.e	17.c	$4$	$8$	$4$	$6.923$	8.0.836829184.2	$_{}$	None	None					51.2.e.a	$2$	$0$	$0$	$0$	$4$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-1-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$
867.2.e.h	$867$	$2$	867.e	17.c	$4$	$8$	$4$	$6.923$	$\Q(\zeta_{16})$	$_{}$	None	None					51.2.h.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\beta_{7}+\beta_{4})q^{2}-\beta_1 q^{3}+(\beta_{5}-\beta_1)q^{4}+\cdots$
867.2.e.i	$867$	$2$	867.e	17.c	$4$	$8$	$4$	$6.923$	$\Q(\zeta_{16})$	$_{}$	None	None					51.2.h.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\beta_{7}+\beta_{4})q^{2}+\beta_1 q^{3}+(\beta_{5}-\beta_1)q^{4}+\cdots$
867.2.e.j	$867$	$2$	867.e	17.c	$4$	$12$	$6$	$6.923$	12.0.$\cdots$.1	$_{}$	None	None		✓			867.2.a.i	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\beta _{7}+\beta _{9})q^{2}+\beta _{3}q^{3}+(-1+2\beta _{2}+\cdots)q^{4}+\cdots$
867.2.e.k	$867$	$2$	867.e	17.c	$4$	$24$	$12$	$6.923$		$_{}$	None	None		✓	✓		867.2.a.o	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
867.2.h.a	$867$	$2$	867.h	17.d	$8$	$8$	$2$	$6.923$	$\Q(\zeta_{16})$	$_{}$	None	None		✓			867.2.a.g	$4$	$0$	$-8$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(-1+\zeta_{16}^{4}-\zeta_{16}^{6})q^{2}+\zeta_{16}q^{3}+\cdots$
867.2.h.b	$867$	$2$	867.h	17.d	$8$	$8$	$2$	$6.923$	$\Q(\zeta_{16})$	$_{}$	None	None					51.2.h.a	$2$	$0$	$0$	$0$	$-8$	$-8$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(\zeta_{16}+\zeta_{16}^{3})q^{2}-\zeta_{16}^{3}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots$
867.2.h.c	$867$	$2$	867.h	17.d	$8$	$8$	$2$	$6.923$	$\Q(\zeta_{16})$	$_{}$	None	None					51.2.a.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+\zeta_{16}^{5}q^{3}+2\zeta_{16}^{4}q^{4}-3\zeta_{16}q^{5}+\cdots$
867.2.h.d	$867$	$2$	867.h	17.d	$8$	$8$	$2$	$6.923$	$\Q(\zeta_{16})$	$_{}$	None	None					51.2.d.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+\zeta_{16}^{2}q^{2}-\zeta_{16}^{3}q^{3}-\zeta_{16}^{4}q^{4}+\cdots$
867.2.h.e	$867$	$2$	867.h	17.d	$8$	$8$	$2$	$6.923$	$\Q(\zeta_{16})$	$_{}$	None	None					51.2.d.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q-2\zeta_{16}^{6}q^{2}-\zeta_{16}q^{3}-2\zeta_{16}^{4}q^{4}+\cdots$
867.2.h.f	$867$	$2$	867.h	17.d	$8$	$8$	$2$	$6.923$	$\Q(\zeta_{16})$	$_{}$	None	None					51.2.h.a	$2$	$0$	$0$	$0$	$8$	$8$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(\zeta_{16}+\zeta_{16}^{3})q^{2}+\zeta_{16}^{3}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots$
867.2.h.g	$867$	$2$	867.h	17.d	$8$	$8$	$2$	$6.923$	$\Q(\zeta_{16})$	$_{}$	None	None					51.2.h.a	$2$	$0$	$0$	$0$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(\zeta_{16}+\zeta_{16}^{3})q^{2}-\zeta_{16}^{7}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots$
867.2.h.h	$867$	$2$	867.h	17.d	$8$	$8$	$2$	$6.923$	$\Q(\zeta_{16})$	$_{}$	None	None		✓			867.2.a.g	$4$	$0$	$8$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(1-\zeta_{16}^{4}-\zeta_{16}^{6})q^{2}-\zeta_{16}q^{3}+\cdots$
867.2.h.i	$867$	$2$	867.h	17.d	$8$	$16$	$4$	$6.923$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					51.2.e.a	$4$	$0$	$-8$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(\beta _{2}+\beta _{6})q^{2}+\beta _{15}q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
867.2.h.j	$867$	$2$	867.h	17.d	$8$	$16$	$4$	$6.923$	16.0.$\cdots$.1	$_{}$	None	None					51.2.a.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(\beta _{3}+\beta _{5})q^{2}+\beta _{7}q^{3}+(3\beta _{8}+\beta _{9}+\cdots)q^{4}+\cdots$
867.2.h.k	$867$	$2$	867.h	17.d	$8$	$16$	$4$	$6.923$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					51.2.e.a	$4$	$0$	$8$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(-\beta _{2}-\beta _{6})q^{2}+\beta _{13}q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$

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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.